Speed Control of a Simplified Direct Torque Neuro Fuzzy Controlled Induction Machine Drive Using a Variable Gain PI Controller

Abstract

This paper presents an original variable gain PI (VGPI) controller for speed control of a simplified direct torque neuro fuzzy controlled (DTNFC) induction motor drive. First, a simplified direct torque neuro fuzzy control (DTNFC) for a voltage source PWM inverter fed induction motor drive is presented. This control scheme uses the stator flux amplitude and the electromagnetic torque errors through an adaptive NF inference system (ANFIS) to generate a voltage space vector (reference voltage) which is used by a space vector modulator to generate the inverter switching states. In this paper a four rules ANFIS structure is proposed. This structure generates the desired reference voltage by acting on both the amplitude and the angle of its components. Then a VGPI controller is designed in order to be used as the speed controller in the simplified DTNFC induction motor drive. Simulation of the simplified DTNFC induction motor drive using VGPI for speed control shows promising results. The motor reaches the reference speed rapidly and without overshoot, load disturbances are rapidly rejected and the detuning problem caused by the stator resistance variation is fairly well dealt with.

Full text

Page 1

Speed Control of a Simplified Direct Torque Neuro Fuzzy Controlled
Induction Machine Drive Using a Variable Gain PI Controller

A. Miloudi 1, E. A. Alradadi 2, A. Draou 2, Y. Miloud 1
1 University Centre of Saïda, BP 138, En – Nasr, Saïda 20000, ALGERIA
Email : amiloudidz@yahoo.frT
2 Department of Electronics Technology, Madina College of Technology, Madinah, Council of Technical Teaching and
Vocational Training, SAUDI ARABIA Email : adraou@yahoo.com



Abstract – This paper presents an original variable gain PI
(VGPI) controller for speed control of a simplified direct
torque neuro fuzzy controlled (DTNFC) induction motor
drive.
First, a simplified direct torque neuro fuzzy control
(DTNFC) for a voltage source PWM inverter fed induction
motor drive is presented. This control scheme uses the
stator flux amplitude and the electromagnetic torque
errors through an adaptive NF inference system (ANFIS)
to generate a voltage space vector (reference voltage)
which is used by a space vector modulator to generate the
inverter switching states. In this paper a four rules ANFIS
structure is proposed. This structure generates the desired
reference voltage by acting on both the amplitude and the
angle of its components.
Then a VGPI controller is designed in order to be used
as the speed controller in the simplified DTNFC induction
motor drive.
Simulation of the simplified DTNFC induction motor
drive using VGPI for speed control shows promising
results. The motor reaches the reference speed rapidly and
without overshoot, load disturbances are rapidly rejected
and the detuning problem caused by the stator resistance
variation is fairly well dealt with.

1. INTRODUCTION

HE apparition of the field oriented control (FOC)
made induction machine drives a major candidate in
high performance motion control applications.
However, the complexity of field oriented algorithms
led to the development in recent years of many studies
to find out different solutions for the induction motor
control having the features of precise and quick torque
response. The direct torque control technique (DTC)
proposed by I. Takahashi [1] and M. Depenbrock [2] in
the mid eighties has been recognised to be a viable
solution to achieve these requirements [1]–[3], [7]–[9],
[11]–[17].
In the DTC scheme [1] (Figure 1), the
electromagnetic torque and flux signals are delivered to
two hysteresis comparators. The corresponding output
variables and the stator flux position sector are used to
select the appropriate voltage vector from a switching
table which generates pulses to control the power
switches in the inverter. This scheme presents many
disadvantages (variable switching frequency - violence
of polarity consistency rules - current and torque
distortion caused by sector changes - start and low-

speed operation problems - high sampling frequency
needed for digital implementation of hysteresis
comparators) [8], [11], [13]–[15], [17].
To eliminate the above difficulties, a Direct Torque
Neuro Fuzzy Control scheme (DTNFC) has been
proposed [17]. This scheme uses a controller based on
an adaptive NF inference system (ANFIS) [5], [6], [10]
together with a space voltage modulator to replace both
the hysteresis comparators and the switching table.
The ANFIS controller combines fuzzy logic and
artificial neural networks to evaluate the reference
voltage required to drive the flux and torque to the
demanded values within a fixed time period. This
evaluation is performed using the electromagnetic
torque and stator flux magnitude errors together with the
stator flux angle. This calculated voltage is then
synthesised using Space Vector Modulation (SVM).
To generate the desired reference voltage using this
scheme, the ANFIS controller acts only on the
amplitude of the reference voltage components whereas
the angle is chosen from a table. A proposed
modification of this scheme is to design an ANFIS
controller in order to act on both the amplitude and the
angle of the reference voltage components.
All the schemes cited above use a PI controller for
speed control. The use of PI controllers to command a
high performance direct torque controlled induction
motor drive is often characterised by an overshoot
during start up. This is mainly caused by the fact that
the high value of the PI gains needed for rapid load
disturbance rejection generates a positive high torque
error. This will let the DTC scheme take control of the
motor speed driving it to a value corresponding to the
reference stator flux.
At start up, the PI controller acts only on the error
torque value by driving it to the zero border. When this
border is crossed, the PI controller takes control of the
motor speed and drives it to the reference value.
To overcome this problem, we propose the use of a
variable gains PI controller (VGPI) [18]. A VGPI
controller is a generalisation of a classical PI controller
where the proportional and integrator gains vary along a
tuning curve.
In this paper, a variable gain PI controller is used to
replace the classical PI controller in the speed control of
a modified direct torque neuro fuzzy controlled
induction machine drive where the ANFIS of the
DTNFC acts on both the amplitude and the angle of
space vector components.
T

Page 2

2. MACHINE EQUATIONS
The dynamic behaviour of an induction machine is
described by the following equations written in terms of
space vectors in a stator reference frame :
d
i rv
sss
+=
r
r
−+=
rr
r
+=ϕ
(3)
i Mi L
+=ϕ
(4)

Where
and
sr
resistances,
,
s L
inductances,
m
ω the rotor angular speed expressed
radians,
s
ϕ and
r
ϕ the stator and rotor flux vectors and
input voltage vector.
s v
The electromagnetic torque is expressed in terms of
stator and rotor fluxes as :

(
s
rs
LL
σ
dt
ϕ
s
ϕr
r
r
(1)
rm
r
rr
j
dt
d
i r0
ϕω
r
(2)
r
r
s
r
ss
i Mi L
srrr
r
rr represent the stator and rotor
r L and M the self and mutual
r
j
M
pT
ϕϕ
rr
⋅=
) (5)
where p is the pole pair number and
rs
2
LL
M
1−=
σ
.
In (5) the symbol “ . “ represents the scalar product.
The elimination of
si
and
leads to the state – variable form of the induction
machine equations with stator and rotor fluxes as state
variables :

Mr
L
dt
r
⎢
⎣
⎦⎣
ο

3. VGPI CONTROLLER STRUCTURE
ri
from equations (1) – (4)

s
r
s
r
r
m
sr
r
L
sr
s
L
s
s
r
s
v
0
1
L
r
j
L
Mr
L
r
dt
d
d
r
r
r
r
⎥
⎦
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎡
+
⎥
⎦
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎡
⎥
⎦
⎥
⎥
⎥
⎤
⎢
⎢
⎢
⎡
−
−
=
⎥
⎥
⎥
⎥
⎤
⎢
⎢
⎢
⎢
⎡
ϕ
ϕ
σ
ω
οσ
ϕ
ϕ
(6)
The use of PI controllers to command a high
performance direct torque controlled induction motor
drive is often characterized by an overshoot during start
up. This is mainly caused by the fact that the high value
of the PI gains needed for rapid load disturbance
rejection generates a positive high torque error which
will cause the speed to go beyond its reference value.
When the torque error value crosses the zero border due
to the action of the PI controller, the speed of the motor
begins to decrease towards its reference value.
To overcome this problem, we propose the use of
variable gains PI controllers. A variable gain PI (VGPI)
controller is a generalization of a classical PI controller
where the proportional and integrator gains vary along a
tuning curve [18]. Each gain of the proposed controller
has four tuning parameters:
• Gain initial value for overshoot elimination.
• Gain final value for rapid load disturbance
rejection.
• Gain transient mode function which is a
polynomial curve that joins the gain initial value to
the gain final value.
• Saturation time which is the time at which the gain
reaches its final value.
The degree n of the gain transient mode polynomial
function is defined as the degree of the variable gain PI
controller.
If e(t) is the signal input to the VPGI controller then the
output is given by :

(7)
τ
∫
0
+=
t
ip
d ) ( eK) t ( eK) t ( y
τ
with

()
⎪
⎩
⎪
⎨
⎧
≥
<+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
spf
spi
n
s
pipf
p
T
(8)
t if K
Tt if K
T
t
KK
K


⎪
⎩
⎪
⎨
⎧
≥
<
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
sif
s
n
s
if
i
Tt if K
Tt if
T
t
K
K
(9)
Where Kpi and Kpf are the initial and final values of the
proportional gain Kp, and Kif is the final value of the
integrator gain Ki. The initial value of Ki is taken to be
zero. It is noted that a classical PI controller is a VGPI
controller with degree zero.

4. SIMPLIFIED DIRECT TORQUE NEURO FUZZY
CONTROLLER

Fuzzy logic and artificial neural networks can be
combined to design a direct torque neuro fuzzy
controller. Human expert knowledge can be used to
build an initial artificial neural network structure whose
parameters could be obtained using online or offline
learning processes.
The adaptive NF inference system (ANFIS) [5], [6],
[10] is one of the proposed methods to combine fuzzy
logic and artificial neural networks. Figure 1 shows the
adaptive NF inference system structure proposed in [5],
[6], [10]. It is composed of five functional blocks (rule
base, database, a decision making unit, a fuzzyfication
interface and a defuzzyfication interface) which are
generated using five network layers :
Layer 1: This layer is composed of a number of
computing nodes whose activation functions
are fuzzy logic membership functions
(usually, triangular or bell-shaped functions).

Page 3

Layer 2: This layer chooses the minimum value of the
inputs.
Layer 3: This layer normalises each input with respect
to the others (The ith node output is the ith
input divided the sum of all the other inputs).
Layer 4: This layer’s ith node output is a linear function
of the third layer’s ith node output and the
ANFIS input signals.
Layer 5: This layer sums all the incoming signals.
The ANFIS structure can be tuned automatically by a
least-square estimation (for
functions) and a back propagation algorithm (for output
and input membership functions).
output membership

The block scheme of the proposed self-tuned direct
torque neuro-fuzzy controller (DTNFC) for a voltage
source PWM inverter fed induction motor is presented
in Figure 2. The internal structure of the Neuro Fuzzy
Controller is shown in Figure 3.
In the first layer of the NF structure, sampled flux
error εψ and torque error εT , multiplied by respective
weights wψ and wT, are each mapped through two fuzzy
logic membership functions. These functions are chosen
to be triangular shaped as shown in Figure 4.
The second layer calculates the minimum of the input
signals. The output values are normalised in the third
layer, to satisfy the following relation:
w
σ
(10)

∑
k
=
k
i
w
i
where
and
i w
i
σ ( i=1..4 ) are the output signal of
the second and third layer respectively.
th
i
i
σ is
considered to be the
amplitude of the desired reference voltage (component
2
normalized component
amplitude divided by
th
i
dc
U
3
(11)
i
) so that :

SNCi
V
σ=

isVSNCi
γ∆+γ=ϕ
(12)
where :

desired reference voltage.
ϕ
:
i
: normalized component amplitude of the
SNCi
V
th
i

SNCi
V
normalized component angle of the
desired reference voltage.;

s
γ : actual angle of the stator flux vector;

∆
: increment angle (from Table 1).
The normalized components of the desired reference
voltage vector are added to each other and the
result, is delivered to the space vector modulator which
calculates the switching states Sa ,
according to the following algorithm :

a) Calculate the normalized components
θ (
θ
0
≤
r
.
b) Calculate the reference voltage position sector using
the following equation :
⎛
=
π
c) Get the two switching vectors
1t
th
i γ
and Sc
Sb
Figure 1: Two - input NF controller structure
, and
the angle
α
n
V
β
n
V
s
π
2
s<
) of the reference
voltage sV

1
3/
FloorSector
s
+
⎟
⎠
⎞
⎜
⎝
θ
(13)
and and
their duty cycles
calculate the zero switching vector duty cycle
1
ttt
−−=
.
d) Calculate the relative clock position (RCP) within
the sampling time using the following equation :
Rem(t/Ts)/RCP =
and using table 2, then
1
SV
2
SV
2t
210

Ts
(14)
The value of RCP will give the components
and
of the switching vectors
the following routine :
,

according to
Sa Sb
ScSV
• If
• Else if
• Else if
SV =
• Else if
SV
• Else if
SV =
• Else if
SV =
• Else the switching vector is
The proposed NF structure is a simplification of the
structure used in [17] and [19] where the first layer is
composed of three membership functions (NEGATIVE,
ZERO and POSITIVE) and was then governed by nine
/4tRCP
0
<
RCP
RCP
SV
RCP
V
RCP
SV
RCP
SV
then
)0 0 0
SV =
2
then
(V
then
t
SV
t
+
t (
+
0==
2
/
+
/4
/4
t
t
10
<
<
1
SV

2 / )
10
2

23

3
2/ ) tt (/4
1) 1
t
0
t
10
++<
(
<
then
1
7==

2
2
t/t/4
1
++
then
2

2
3
tt/4 t
10
++<
then
1


0
V

Page 4

fuzzy rules. To decrease the number of rules used by the
NF structure, we had the idea of merging the zero
membership function into both the positive and negative
membership functions. This will result in only two
membership functions as shown in Figure 4.
The proposed NF structure is then governed by only
four fuzzy rules. This will result in an important
decrease in the calculation time.

5. VGPI CONTROLLER IN SPEED CONTROL OF THE
SIMPLIFIED DTNFC MOTOR DRIVE
In this section a simulation study of the performances
of the modified direct torque neuro fuzzy controlled
induction motor drive is performed by using a VGPI
controller. The parameters of the motor used in the
simulation are given in table 3. The reference speed
used is
.
rpm
ref
1000
=Ω
TABLE 1 : REFERENCE VOLTAGE INCREMENT ANGLE

ε εψ ψ
ε εT
∆γ∆γi
P N
P
π
+
N
π
−
P
2π
N
2π
3

3

3
+

3
−


TABLE 2 : SVM DUTY SWITCHING VECTORS AND
DUTY CYCLES

Sector 1
⎤
⎢
⎣
⎦
⎣
n
2
3/20
t
)0 0 1(VSV
==
11

)0 1 1(VSV
==
22

⎥
⎦
⎡
⎥
⎤
⎢
⎡
−
=
⎥⎦
⎤
⎢⎣
⎡
β
α
n
V
1
V
3/ 11
t

Sector 2
⎡−
/ 1 1
(V
=
3
(V
=
2
⎥
⎦
⎤
⎢
⎣
)
)
⎡
⎥
⎦
⎤
⎢
⎣
=
⎥⎦
⎤
⎢⎣
SV
SV
⎡
β
n
α
n
2
1
V


V
3

3/ 11
t
t

0
0
1
1
0
1
=
=
1
2
Sector 3
0
⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
)
)1 1 0
⎤
⎢
⎣
⎡
−
(
(
−
V
V
=
⎥⎦
⎤
⎢⎣


⎡
β
n
α
n
2
1
V
V
3
0
/1
0
1
3/2
t
SV
SV
t

1
=
=
=
=
31
42
Sector 4
−
1
(V
=
5
V
=
4
⎥
⎦
⎤
⎢
⎣
)
)1 1 0
⎡
⎥
⎦
1
⎤
⎢
⎣
⎡
−
=
⎥⎦
⎤
⎢⎣


⎡
β
n
α
n
2
1
V
V
3

/

1
0
(
3/20
t
SV
SV
t

0
=
=
1
2
Sector 5
−−
1
0(V
=
5
(V
=
6
⎥
⎦
⎤
⎢
⎣

⎡
⎥
⎦
)
⎤
⎢
⎣
⎡
−
=
⎥⎦
⎤
⎢⎣
SV
SV
⎡
β
n
α
n
2
1
V
V
3
1
1
/1
3/11
t
t

0
0

=
=
1
) 1
2

Sector 6
11
⎥
⎦
⎤
⎢
⎣

)
⎡
⎥
⎦
)
⎤
⎢
⎣
V
V
⎡
−
(
=
⎥⎦
⎤
⎢⎣
SV
SV
⎡
β
n
α
n
2
1
V
V
3/
0

2
1
1(
0
3/
t
t

0
0
==1
=
1
1
=
62


TABLE 3 : INDUCTION MACHINE PARAMETERS

2 pairs of poles, 50Hz
Ω

=
85. 4Rs

mH

274
s
L
=

220/380 V, 6.4/3.7 A
2 hp , 1420 rpm
Ω

=
805. 3 Rr
Lm=
f =

mH274 Lr=
mH 258

2
kgm 031. 0J =

Nms 00114. 0










Figure 2: Direct Torque Neuro Fuzzy Controller
scheme












Figure 3: Proposed Neuro Fuzzy Controller Structure













Tuning the modified DTNFC system comes to tuning
the weights ωψ and ωT so as to minimise the flux and
torque errors. These weights are the scaling factors of
the flux and torque errors and their tuning corresponds
to the three ANFIS structure membership functions
width.
Since the proposed DTNFC is a high order non linear
system, a simple way of tuning it is the successive trials
method. It has been shown in [17] that for nonzero
synchronous angular speed, the changes of the flux
influence the output torque, while the changes in the
torque does not influence the flux. That is why the
proposed method searches first the flux error minimum,
before searching the torque error minimum. The tuning
method proposed searches by successive trials method
in a grid of values of ωψ the value that gives the
minimum stator flux error, then by using this value,
searches in a grid of values of ωT the value that gives
the minimum torque error. Using this method the tuning
values of the DTNFC are given by
ω
.
20
=
ψ
ω
and
2 . 0
T=
Figure 4: Triangular membership function sets
T
ε
NEGATIVE
POSITIVE
-1
0
1
)(T
εµ

ψ
ε
NEGATIVE
POSITIVE
)(ψ
εµ

-1
0
1

Page 5

Figure 5: Settling performance of the proposed DTNFC motor drive using a VGPI speed controller
Time (sec)
Time (sec)
Rotor speed (rpm)
Stator Current (A)
Electromagnetic
torque (Nm)
Zoomed Stator
Current (A)
Stator voltage (V)
Command torque
(Nm)
line to line voltage
(V)
Stator flux
(Wb)
Sc
Sa
Switching States
Sb
Stator flux
imaginary part
Stator flux
real part
Stator Current (A)
Rotor speed (rpm)
Time (sec) Time (sec)
Figure 6: Speed tracking performance of the proposed DTNFC motor drive using a VGPI speed controller.

Page 6

2
×
s R

Rotor speed (rpm)
Command torque
(Nm)
2
×
s R

Time (sec)
Time (sec)
Figure 7: Variation of the stator's resistance
Figure 5 shows the settling performance and the
disturbance rejection capability of the proposed DTNFC
motor drive with a VGPI speed controller. Using the
tuning method given in [18] with
, the tuned
VGPI controller is given by :
⎪⎨
=
10
⎧
=
100
100
=
if
K

(15)
⎪⎩
⎪⎨
⎧
≥
<+
1t if
1t if t 5 . 95 . 0
K
3
p

(16)
⎪⎩
≥
<
1 t if
1 tif t 100
K
3
i
Initially the machine is started up with a load of
10Nm. At 1s, a 2Nm load disturbance is applied during
a period of 1s. The sampling time has been set to 100µs
what gave flux and torque errors in the range of 0.5%
and 44.8%, respectively.
The speed of the motor reaches the 1000 rpm
reference speed in less than a second without overshoot.
The VGPI controller compensates the 2N.m load
disturbance by increasing the mean value of the
command torque by 2.06N.m. It rejects the load
disturbance in less than 0.6s with a maximum speed dip
of 1.8 rpm (0.18%). One can note that the current
waveform is not distorted by the sector changes as in the
conventional DTC and the stator flux trajectory is
circular. The motor magnetization process takes about
12 ms. We can also note that the steady state inverter
switches duty ratio is in the interval [0.1 , 0.9].
Figure 6 shows the speed tracking performance of the
system under no load. The slope of the trapezoidal
command speed is 2000 rpm/s. The motor speed tracks
the trapezoidal commands with zero steady state error
and no overshoot
Figure 7 shows the reaction of the proposed VGPI
controller to stator resistance variation. The motor is
started up with a load of 10 Nm. The rotor resistance is
supposed to double at 1sec.
Stator resistance variation is shown to affect the
estimated electromagnetic torque which increases by
about 18%.
The VGPI controller compensates the torque
estimator detuning problem by increasing the mean
value of the torque command to about 19 % of its rated
value.
The VGPI controller rejects the stator resistance
disturbance in less than 0.5 s with a maximum speed dip
of 2.2 rpm (0.22 %).

6. CONCLUSION

In this paper a simplified direct torque neuro fuzzy
controlled induction motor drive is presented. This
control scheme uses the stator flux amplitude and the
electromagnetic torque errors through a four rules
adaptive NF inference system (ANFIS) to calculate the
desired reference voltage. This vector is used by a space
vector modulator to generate the inverter switching
states.
A VGPI controller has been designed and used as a
speed controller in the DTNFC control scheme.
Simulation of the simplified DTNFC induction motor
drive using VGPI for speed control shows promising
results. The motor reaches the reference speed rapidly
and without overshoot, trapezoidal commands under no
load are tracked with zero steady state error and no
overshoot, load disturbances are rapidly rejected and the
detuning problem caused by the stator resistance
variation is fairly well dealt with.

7. REFERENCES

[1] Takahashi and T. Noguchi, “A new quick response
and high efficiency control strategy of an induction
motor,” IEEE Trans. Ind. Applicat., vol. IA-22, pp.
820–827, Sept./Oct. 1986.
[2] M. Depenbrok, “Direct self-control (DSC) of
inverter fed induction machine,” IEEE Trans.
Power Electron., vol. PE-3, pp. 420–429, Oct.
1988.
[3] I. Boldea and S. A. Nasar, “Torque vector control
(TVC)—A class of fast and robust torque speed
and position digital controller for electric drives,”
in Proc. EMPS, vol. 15, 1988, pp. 135–148.
[4] T. G. Hableter, F. Profumo, M. Pastorelli, and L.
M. Tolbert, “Direct torque control of induction
machines using space vector modulation,” IEEE
Trans. Ind. Applicat., vol. 28, pp. 1045–1053,
Sept./Oct. 1992.

Page 7

[5] J.-S. R. Jang, “Self-learning fuzzy controllers
based on temporal back propaga-tion,” IEEE
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Serra, and A. Tani,