Induction Motor Speed Control using Fuzzy Neural
Network Speed Estimation
Tien-Chi Chen and Wei-Chung Wang
Department of Electrical Engineering, Kun Shan University, Tainan, Taiwan
Keywords: Induction Motor, Encoder, Speed Sensorless Control, RFNN, Fuzzy Neural Network Speed Estimation,
Steepest Descent Algorithm, Back-propagation Algorithm.
Abstract: The field-oriented control (FOC) of induction motor has high static and dynamic performance. In order to
achieve the speed loop feedback control, precise rotor speed information is important for induction motor
control. In the past, encoder was widely used to obtain the speed information of induction motor. However,
speed sensor would increase the cost of entire system and reduce the system reliability. In addition, for some
special applications such as very high speed motor drives, some difficulties are encountered in mounting
these speed sensors. The speed sensorless control would overcome these problems. This paper proposes a
fuzzy neural network speed estimation for induction motor speed sensorless control. The speed estimation is
based on the deduction of rotor flux and estimated rotor flux, which is calculated by fuzzy neural network.
The fuzzy neural network includes a four-layer network. The steepest descent algorithm and back-
propagation algorithm are used to adjust the parameters of fuzzy neural network in order to minimize the
error between the rotor flux and the estimated rotor flux, which is implied to enable precise estimation of the
rotor speed.
1 INTRODUCTION
The motor is one of the most important mechanical
power sources in electrical machinery industry. The
induction motor have applied in many industry
(Angelo et al., 2006), which are very economical,
rugged and reliable. Furthermore, because of the
advances in power electronics and microprocessors,
the induction motor applications in speed control
have become more and more attractive.
The control scheme is important in order to
precisely control the induction motor. The V/f
control method was used in induction motor speed
control (Perera et al., 2003). However, due to the
influence of the stator resistance and the necessary
rotor slip to produce torque, its application at low
speed is still challenging.
The invention of field-oriented control (FOC) in
1970s can solve the foregoing problems. The FOC
which has high static and dynamic performance
becomes very popular in recently (Singh et al.,
2005); (Consoli et al., 2004). The FOC applied to
induction motor drives allow us to perform fast and
fully decoupled control of torque and flux.
In modern control techniques of the induction
motor drives, the closed loop speed control system
uses shaft encoder to measure motor speed.
However, speed sensor has several disadvantages
from the viewpoint of drive cost, noise immunity
and reliability. From the point of view, as well as for
general purpose and low cost drives, speed
sensorless control have been published (Kwon et al.,
2005). These methods are further classified into the
following methodologies such as Kalman filter
techniques, model reference adaptive systems and
sliding mode method (Zhen and Xu, 1998); (Lascu
et al., 2004). The Kalman filtering algorithm dose
not contain the feedback signal to train the
parameter that would increase the system
uncertainty. The model reference adaptive systems
speed sensorless methods are mainly affected by
motor’s parameters which affect the accuracy of the
speed estimation then it could spoil the system’s
stability.
In order to obtain good performance on speed
estimation, this paper proposes a speed estimation
algorithm based on fuzzy neural network. Up to
now, the fuzzy neural network has been applied for
many cases, mainly in the controller of converters
and drives, but its application in speed estimation is
620
Chen T. and Wang W..
Induction Motor Speed Control using Fuzzy Neural Network Speed Estimation.
DOI: 10.5220/0004153106200625
In Proceedings of the 4th International Joint Conference on Computational Intelligence (NCTA-2012), pages 620-625
ISBN: 978-989-8565-33-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
practically new (Kim et al., 2001). The proposed
fuzzy neural network which has feedback signal
incorporates a four-layer network including input
layer, membership layer, rule layer and output layer.
The rotor flux is derived from the motor’s dynamic
model. The estimated rotor flux is the fuzzy neural
network output. The error between the rotor flux and
the estimated rotor flux is used as the feedback
signal to adjust the parameters of fuzzy neural
network through back-propagated method (Chen et
al., 2011). This method is to minimize the difference
between the rotor flux and the estimated rotor flux,
the back-propagation mechanism is easy to derive so
that a precise estimation of the rotor speed can track
the actual motor speed soon.
The proposed control scheme is implemented in
TMS320F2808 DSP. Simulation and experimental
results are shown to confirm that the proposed fuzzy
neural network speed estimation can provide good
performance for induction motor speed control.
2 THE DYNAMIC MODEL
OF INDUCTION MOTOR
The dynamic model of the induction motor in the
synchronous rotating d-q frame can be expressed as
follows (Bose, 1986):
2
2
(1 )
(1 )
()
e
eeeee
s
mr rm ds
r
ds ds e qs dr qr
s
r srsrs
e
qs
ee e e e
srmmr
r
qs e ds qs dr qr
s
r srsrs
eee e
mr
r
dr ds dr e r qr
rr
e
mr
qr
r
RLRLv
R
iii
L L LL LL L
v
RLLR
R
ii i
L L LL LL L
LR
R
i
LL
LR
i
L
()
eee
r
qs e r dr qr
r
R
L
(1)
The torque equation is given as follows:
3
2
()
4
ee ee
m
r
e drqs qrds r L
r
PL
d
TiiJBT
LPdt
(2)
where
,,
s
rm
L
LL
: stator inductance, rotor inductance
and mutual inductance,
,
s
r
RR
: stator resistance and
rotor resistance,
2
1( / )
msr
L
LL
,
,
ee
qs ds
vv
: q-axis and
d-axis stator voltage in the synchronous rotating
frame,
,
ee
qs ds
ii
: q-axis and d-axis stator current in the
synchronous rotating frame,
,
ee
qr dr
: q-axis and d-
axis rotor flux in the synchronous rotating frame, P:
pole number of the induction motor,
,
eL
TT
:
electromagnetic torque and load torque,
,
J
B
:
moment of inertial and viscous coefficient of the
induction motor,
r
: rotor angular velocity,
e
:
electrical angular velocity.
3 FUZZY NEURAL NETWORK
SPEED ESTIMATION
A fuzzy neural network is employed for induction
motor speed estimation. Fig. 1 illustrates the block
diagram of proposed speed sensorless estimation
using fuzzy neural network. There are two
independent fluxes in the proposed method. One is
the rotor flux (
e
r
) of the induction motor’s dynamic
model. The other is the estimated rotor flux (
e
r
)
obtain from the fuzzy neural network. The error (
e
)
between the two independent fluxes is used to adjust
the parameters (
,,
j
jj
ii
yx
) of fuzzy neural network
by using the back-propagation algorithm such that
the estimated rotor flux coincide with the rotor flux,
and the estimated speed (
r
) can tracks the actual
motor speed (
r
) precisely.
,
ee
qs ds
ii
Induction Motor
,
ee
qs ds
vv
Dynamic Model of
Induction Motor
Self-Tuning Fuzzy Identifier
& Speed Estimation
Back-Propagation
Algorithm for
,,
j
jj
ii
yx
e
r
e
r
e
r
r
,
ee
qs ds
vv
Figure 1: A fuzzy neural network for induction motor
speed estimation.
3.1 The Principle of Speed Estimation
Taking some manipulations of the first and third row
of (1) yields:
()
ee
ee e e
dr ds r s e
r
ds s ds s qs e qr
mm
ddiLL
L
vRi L i
dt L dt L
(3)
Taking some algebraic operation of the second
and forth rows of equation (1) yields:
=( )
ee
qr qs
ee e e
sr e
r
qs s qs s ds e dr
mm
ddi
LL
L
vRi L i
dt L dt L
(4)
InductionMotorSpeedControlusingFuzzyNeuralNetworkSpeedEstimation
621
Equations (3) and (4) can be rewritten as the
following matrix form of the rotor flux equation:
()
e
e
ee e e
srse
rr
s
ss s s e r
mm
dI L L
dL
IV RI L JI J
dt L dt L
(5)
where
,, ,, ,,
TTT
eee eee eee
r dr qr s ds qs s ds qs
Vvv Iii
10 0 1
,.
01 1 0
IJ
The estimated rotor flux equation is derived form
the third and the forth row of equation (1). Taking
some algebraic operation of the third and the forth
rows of equation (1) yields:
e
eeee
dr m r
r
ds dr e qr r qr
rr
dLR
R
i
dt L L
(6)
e
qr
eee e
mr
r
qs e dr r dr qr
rr
d
LR
R
i
dt L L
(7)
Combining equations (6) and (7), the estimated
rotor flux equation can be expressed as the following
matrix form:
1
()
e
ee
m
r
re r s
rr
L
d
I
JII
dt
(8)
where
,
T
eee
rdrqr
,
/
rrr
LR
is the rotor time
constant,
r
is the estimated rotor speed.
The discrete-time form of equation (8) can be
expressed as:
( 1) (1 ) () () ()
ˆ
( ) ( ) ( )
eee
rrer
r
ee
m
rr s
r
T
kIkkTJk
LT
kTJ k II k
(9)
Since the estimated rotor speed
r
is unknown
and may vary with time, the estimation process
becomes time varying due to the unknown term
(
() ()
e
rr
kTJ k
) in equation (9). For resolving the
estimated problem, the proposed fuzzy neural
network consisting of four-layer structure can get
over the problem.
The third term of equation (9) is expressed as:
() () ()
e
frr
yk kTJ k
(10)
where
__
() () ()
T
ffdfq
yk y k y k
. By multiplying
T
e
r
on
the both sides of equation (10), it can be expressed
as:
ˆ
() () ()
TT
eee
rf rr r
yk kTJ k
(11)
Any mismatch between the rotor flux
()
e
r
k
and
the estimated flux
()
e
r
k
estimated by the fuzzy
neural network system would automatically produce
an error. This error is further used to adjust the
parameters of the fuzzy neural network. If
()
e
r
k
is
equal to
()
e
r
k
, the estimated rotor speed
r
can be
obtained as:
2
()
()
()
T
e
rf
r
e
r
yk
k
Tk
(12)
In this way, the motor speed can be predicted
accurately by the fuzzy neural network speed
sensorless estimation.
3.2 Structure of Fuzzy Neural Network
A four-layer fuzzy neural network, as shown in Fig.
2, which includes an input layer, a membership
layer, a rule layer and an output layer, is used to
implement the fuzzy neural network. The input of
the fuzzy neural network is
1234
,,,
eeee
ds qs ds qs
x
vx vx ix i
. For every node in
the input layer, its output is equal to input. In the
membership layer, each node performs a
membership function. The Gaussian function is
selected as the membership function, it can be
described as:
2
() exp
j
j
ii
ii
j
i
xx
x
(13)
where j=1, …, M, and M is the number of
membership function of each input node. In this
paper, the value of M is set to 4,
j
i
x
and
j
i
are,
respectively, the mean and the standard deviation of
the Gaussian function.
Each node in the rule layer is denoted by
,
which multiplies the all input signals. The output of
rule layer for the j node is expressed as follows:
2
4
1
exp
j
j
ii
j
i
i
xx
z
(14)
Furthermore, the signal node in the output layer
is labelled as
, which computes the summation of
all input signal and the output of output layer is
expressed as follows:
1
M
jj
id
j
yyz
(15)
where
e
id r
y
.
IJCCI2012-InternationalJointConferenceonComputationalIntelligence
622
1
y
id
y
2
y
M
y
1
11
()
x
11
()
M
x
1
z
2
z
M
z
1
x
1
22
()
x
22
()
M
x
2
x
1
44
()
x
44
()
M
x
4
x
Figure 2: The structure of four-layer fuzzy neural network.
3.3 Training Algorithm for Fuzzy
Neural Network
The section describes the online training algorithm
of the fuzzy neural network using the back-
propagation training algorithm. First, the error
function is defined as
2
1
() () ()
2
Iid
E
kykyk
(16)
where
() ()
e
r
y
kk
The objective is to train the fuzzy neural network
such that
()
I
Ek
is minimized. Hence, the
identification problem now becomes to train the
parameters
j
y
,
j
i
x
and
j
i
of fuzzy neural network.
The training method is based on the steepest
descent algorithm. The derivation of the training
algorithm is described as follows.
(a) Training Algorithm for
j
y
:
In order to train
j
y
, the steepest descent algorithm is
expressed as follows:
(1) ()
jj
I
I
j
k
E
yk yk
y
(17)
where
I
is the learning rate of fuzzy identifier.
Using the chain rule for equation (16), it can be
expressed as:
id
I
id
jj
y
E
yy
yy
(18)
Substituting (17) into (18), then combining
equation (17) and readjusting it, the training
algorithm for
j
y
can be expressed as:
(1) () () ()()
jj j
Iid
yk yk yk ykzk
(19)
(b) Training Algorithm for
j
i
x
:
For training
j
i
x
, the steepest descent algorithm
for
j
i
x
can be expressed as follows:
(1) ()
jj
I
iiI
j
i
k
E
xk xk
x
(20)
Applying the chain rule for equation (2.28) to
obtain
2
1
2
j
id
id
I
id
j
ljj
ii i
yy
y
Ez
yy
x
xzx
(21)
Taking partial differential of
id
y
with respect
to
j
z
and partial differential of
j
z
respect to
j
i
x
by
using equation (15) and (14) respectively, then (21)
can be expressed as:
2
2
j
jj
id i i
I
j
j
i
i
y
yzy x x
E
x
(22)
Substituting (22) into (20), the training algorithm
for
j
i
x
can be expressed as:
2
2()()()() ()()
(1) ()
()
jjj
id i i
jj
iiI
j
i
yk ykykxk xkzk
xk xk
k
(23)
(c) Training Algorithm for
j
i
:
Using the same method as given above, the training
algorithm for
j
i
can be expressed as follows:
2
3
2()()()() () ()
(1) ()
()
jjj
id i i
jj
iiI
j
i
yk ykykxk xk zk
kk
k
(24)
The training algorithms given in (19), (23) and
(24) perform a back-propagation algorithm for the
fuzzy neural network.
4 EXPERIMENTS
In order to demonstrate the feasibility of the control
scheme, the experiments are necessary. The
parameters of induction motor are:
1.1 Ω
s
R
,
1.3 Ω
r
R
,
0.1452H
s
L
,
0.1456H
r
L
,
0.1363H
m
L
,
42
6.8 10 kg mJ
,
4
5.15 10 N m s/radB
, P=2.
The block diagram of the indirect FOC method
for induction motor speed control is shown in Fig. 3.
The block diagram of overall experiment
configuration is showed in Fig. 4. The experiment
equipment includes the induction motor driver:
converter and inverter, isolated circuit, Hall current
InductionMotorSpeedControlusingFuzzyNeuralNetworkSpeedEstimation
623
1/
m
L
*
bs
i
*
as
i
*
cs
i
*e
ds
i
*e
qs
i
*
r
ˆ
r
*
e
*
r
as
i
bs
i
s
l
*
sin
e
t
*
cos
e
t
as
v
bs
v
5
S
4
S
6
S
2
S
1
S
3
S
ˆ
r
,
ee
qs ds
vv
,
ee
qs ds
ii
*
*
e
mr
qs
rr
LR
i
L
Figure 3: The block diagram of the indirect field-oriented
control (FOC) method for induction motor speed control.
sensor circuit and DSP TMS320F2808 experiment
board. The indirect field-oriented control method is
used for induction motor speed control. The
proposed control scheme and indirect field-oriented
control method are implemented in DSP
TMS320F2808 experiment board.
The software control program of experiment
includes the adaptive current PWM control, fuzzy
neural network speed sensorless estimation, speed
controller and sin/cos generator. All of the detailed
actions will be described as the flowchart in Fig. 5.
The experimental results of the proposed
algorithm are showed in Fig. 6. The actual motor
speed response and estimated motor speed response
for a speed command of 500 rpm are shown in
Figures 6(a) and 6(b) respectively. The speed error
between the actual motor speed and the estimated
motor speed is shown in Fig. 6(c). The actual d-axis
rotor flux and estimated d-axis rotor flux are shown
in Figures 6(d) and 6(e) respectively. The d-axis
rotor flux error between the actual d-axis rotor flux
and estimated d-axis rotor flux is shown in Fig. 6(f).
According to Figs. 6(a) and 6(b), the actual
motor speed has a good transient response and the
estimated motor speed can track the actual motor
speed quickly. Figure 6(c) shows that the speed error
decays very soon and the speed error is very slight in
steady state. According to Figs. 6(d) to 6(f), the
estimated d-axis rotor flux can track the actual d-
axis rotor flux quickly. The d-axis rotor flux error is
very slight in steady state. This experimental results
show that the proposed algorithm has fairly good
performance, which is similar to the simulation
results.
TMS320F2808
DSP
Software
Configuration
Hardware
Configuration
XDS510 PP
Emulator
JTAG
GPIO
QEP
DAC
ADC
Photo Coupler
Isolated Circuit
Converter Inverter
AC 110V
60Hz
IM
Shift and Scale
Circuits
Computer
135
, , SS S
246
, , SSS
as
i
bs
i
Hall Sensor
iMac
Figure 4: Block diagram of overall experiment
configuration.
,
s
s
as bs
ii
c
, ,
s
ss
as bs s
iii
***
c
, ,
s
ss
as bs s
iii
,
as bs
VV
*
r
e* e*
,
qs ds
ii
e* e* * * *
qd c
, , ,
s
ss
s
sasbss
ii i ii
ˆ
e
r
ˆ
r
Figure 5: The software procedures of the control algorithm
for the proposed scheme.
5 CONCLUSIONS
The main purpose of this paper is to develop a fuzzy
neural network speed estimation for the induction
motor speed control. The experiment results proved
that the proposed fuzzy neural network speed
estimation is practical and the performance is great.
By using TMS320F2808 experiment board and
motor drivers to control induction motor, the
performance of fuzzy neural network speed
estimation for the induction motor speed control has
great effect.
IJCCI2012-InternationalJointConferenceonComputationalIntelligence
624
(a) Actual motor speed response
(b) Estimated motor speed response
(c) Speed error
(d) Actual d-axis rotor flux
(e) Estimated d-axis rotor flux
(f) The d-axis rotor flux error
Figure 6: Experimental results for speed command of 500
rpm.
ACKNOWLEDGEMENTS
The authors would like to express their appreciation
to NSC for supporting under contact NSC 100-2218-
E-168 -004.
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