This paper presents a novel design of a control scheme for induction motor as a fuzzy logic application, incorporating fuzzy control technique with direct torque control method for induction motor drives. The direct torque control method has been optimized by using fuzzy logic controller instead of a conventional PI controller in the speed regulation loop of induction motor drive system. The presented fuzzy based control scheme combines the benefits of fuzzy logic control technique along with direct torque control technique. Compared to the conventional PI regulator, the high quality speed regulation of induction motor can be achieved by implementing a fuzzy logic controller as a PI-type fuzzy speed regulator which is designed based on the knowledge of experts without using the mathematical model. The stability of the induction motor drive during transient and steady operations is assured through the application of fuzzy speed regulator along with the direct torque control. The proposed fuzzy speed regulated direct torque control of induction motor drive system has been validated by using MATLAB simulink.

1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
Fuzzy Speed Regulator for Induction Motor Direct
Torque Control Scheme
Jagadish H. Pujar 1, S. F. Kodad 2
1
Research Scholar JNTU, Anantapur & Faculty Department of EEE, B V B College of Engg. & Tech., Hubli, India
Email: jhpujar@bvb.edu
2
Professor, Department of EEE, Aurora’s Engineering College, Hyderabad, India
Email: kodadsf@rediffmail.com
Abstract—This paper presents a novel design of a control the performance of conventional DTC a fuzzy logic
scheme for induction motor as a fuzzy logic application, controller is used along with conventional DTC [7].
incorporating fuzzy control technique with direct torque The main objective of this paper is to simulate the fuzzy
control method for induction motor drives. The direct torque speed regulator for induction motor direct torque control
control method has been optimized by using fuzzy logic
controller instead of a conventional PI controller in the speed
scheme to improve the speed regulation performance
regulation loop of induction motor drive system. The under transient and steady state uncertainties caused by
presented fuzzy based control scheme combines the benefits of variation in load torque which in term replacing PI
fuzzy logic control technique along with direct torque control regulator of DTC by FLC.
technique. Compared to the conventional PI regulator, the
high quality speed regulation of induction motor can be II. INDUCTON MOTOR STATE MODEL
achieved by implementing a fuzzy logic controller as a PI-type
fuzzy speed regulator which is designed based on the The dynamic input and out put equations of induction
knowledge of experts without using the mathematical model. motor are formulated as a state model in the stator
The stability of the induction motor drive during transient reference frame under the assumptions of linear magnetic
and steady operations is assured through the application of circuits, equal mutual inductances and neglecting iron
fuzzy speed regulator along with the direct torque control. losses as follows;
The proposed fuzzy speed regulated direct torque control of & (1)
X (t ) = A X (t ) + B U (t )
induction motor drive system has been validated by using
MATLAB simulink. Y (t ) = C X (t ) (2)
Where A is the system, B is the control and C is the
Index Terms—Fuzzy Logic Control (FLC), Direct Torque
Control (DTC), Induction Motor (IM), Space Vector
observation matrices. And X(t) is the state, U(t) is input
Modulation (SVM), switching table. and Y(t) is out put vectors with elements as follows;
X (t ) T = [i sd i sq φ sd φ sq ] (3)
I. INTRODUCTION
⎡ V sd ⎤ & ⎡ i sd ⎤ (4)
Fuzzy logic is recently getting increasing emphasis in U (t ) = ⎢ ⎥ Y (t ) = ⎢ ⎥
drive control applications. Recent years, fuzzy logic control ⎣ V sq ⎦ ⎣ i sq ⎦
has found many applications in the past two decades. This ⎡ 1−σ ω (1 − σ )⎤
⎢− δ 0
σM τ σM ⎥
is so largely increasing because fuzzy logic control has the ⎢ r
⎥
capability to control nonlinear uncertain systems even in ⎢ ω (1 − σ ) ω (1 − σ ) ⎥
⎢ 0 −δ −
the case where no mathematical model is available for the σM σM τ ⎥
A=⎢ ⎥ (5)
r
control system [1]. So, the development of high- ⎢M 1 ⎥
performance control strategies for AC servo system drives ⎢τ 0 − −ω ⎥
τ
resulted in a rapid evolution. To overcome the ⎢ r r
⎥
⎢ M 1 ⎥
disadvantages of vector control technique, in the middle of ⎢ 0 ω − ⎥
⎣ τ τ ⎦
1980’s, a new quick response technique for the torque r r
control of induction motors was proposed by Takahashi as ⎡ 1 ⎤
⎢σL 0 0 0⎥
direct torque control (DTC) [2]. DTC provides very quick B =⎢
T s
⎥ (6)
response with simple control structure and hence, this ⎢ 1 ⎥
technique is gaining popularity in industries [2]. Though, ⎢ 0 σL
0 0⎥
⎣ s ⎦
DTC has high dynamic performance, it has few drawbacks ⎡1 0 0 0 ⎤ (7)
such as high ripple in torque, flux, current and variation in C = ⎢
⎣0 1 0 0 ⎥
⎦
switching frequency of the inverter. The effects of flux and
torque hysteresis band amplitudes in the induction motor Lr ; L ⎛ 1 1−σ ⎞ ;
τs = s ; σ = 1− M ; δ =⎜
2
drive performance have been analyzed in [3]. To improve
τr =
Rr Rs ⎜ στ + στ ⎟⎟
Lr Ls ⎝ s r ⎠
1
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2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
Where ω represents rotor speed. Rs and Rr are the stator ⎛ 2π ⎞
and rotor resistances respectively. Ls, Lr are the stator and V BN = V m cos ⎜ ω t − ⎟ (11)
⎝ 3 ⎠
rotor self-inductances and M is the mutual inductance
respectively. ⎛ 2π ⎞
The electromagnetic torque developed by the induction V CN = V m cos ⎜ ω t + ⎟ (12)
⎝ 3 ⎠
motor is expressed as,
T em =
3
P (i sq φ sd − i sd φ sq ) (8) Vi =
2
3
(
V AN + aV BN + a 2VCN ) (13)
4
Where φ sd, and φ sq, are respectively, the stator fluxes where i = 0 to 7
projections on the (d, q) axis reference frame. These three phase voltages are applied to the three phase
The induction motor electromagnetic torque and load induction motor employing the equation (13). The three
torque balancing under equilibrium can be expressed as, phase bridge inverter of Fig.1 has eight permissible
dω switching states. The switching states and the
T em = J + Bω + TL (9)
dt
corresponding phase to neutral voltage of isolated neutral
Where J is the moment of inertia of the rotor, B damping induction motor are summarized in Table.I in which “0” is
coefficient and TL is the load torque. off state and “1” is on state indication for the switches S1 to
From the above mathematical representation, we can see S3.
Table 1
that the dynamic model of an induction motor is a strongly SVM Iverter Switching States
coupled nonlinear multivariable system. The control
problem is to choose (Vsd , Vsq) in such a way as to force the V S1 S2 S3 VAN VBN VCN
motor electrical angular speed ω and the rotor flux
V0 0 0 0 0 0 0
magnitude φ s=[ φ 2sd + φ 2sq]1/2 to track given reference
V1 1 0 0 2VDC /3 -VDC /3 -VDC /3
values by denoted ωref and φ ref respectively. Note that the
choice of a reference frame rotating at the same angle and V2 1 1 0 VDC /3 VDC /3 -2VDC /3
is more suitable for the control problems since in this frame V3 0 1 0 -VDC /3 2VDC /3 -VDC /3
the steady state signals are seems to be constant.
V4 0 1 1 -2VDC /3 VDC /3 VDC /3
III. DTC SCHEME FOR INDUCTON MOTOR DRIVE V5 0 0 1 -VDC /3 -VDC /3 2VDC /3
V6 1 0 1 VDC /3 -2VDC /3 VDC /3
A. Working Strategy of Conventional DTC
V7 1 1 1 0 0 0
The SVM technique is used to approximate the voltage
reference vector by employing the combination of two out
of eight possible vectors generated by the three phase Consider, for example state V5 space vector voltage is,
voltage source inverter for IM drive is as shown in Fig.1. 2 ⎛ − V DC − V DC 2V ⎞
V5 = ⎜ +a + a 2 DC ⎟ (14)
3⎝ 3 3 3 ⎠
S1 S2 S3 As there are three independent limbs, there will be eight
different logic states, provides eight different voltages
obtained applying the vector transformation described as:
A
2π 4π
2 ⎡ j j ⎤
B
Vi = VDC ⎢ S1 + S 2e 3 + S3e 3 ⎥ (15)
VDC 3
N ⎢
⎣ ⎥
⎦
C Eight switching combinations can be taken according to
Inducton the above expression (15). So, the partitions of d-q plane in
S1 S2 S3 Motor to two zero voltage vectors and six non-zero voltage
vectors are as shown in Fig.2.
Figure 1. SVM Inverter for Induction Motor Drive
The three phase sinusoidal instantaneous voltage
equations of three phase inverter of Fig.1 are as follows.
V AN = V m cos ω t (10)
2
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3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
we can write, the expression for change in stator flux over
the sampling time period TS as,
φ S (k + 1) ≈ φ S (k ) + V S TS (24)
Δφ S ≈ φ S (k + 1) − φ S (k ) ≈ V STS (25)
Equation (25) implies that by applying a vector of
tension which is co-linear in its direction, we can increase
the stator flux.
Therefore, by selecting adequate voltage vector one can
increase or decrease the stator flux amplitude and phase to
obtain the required performances [3] [5].
C. Switching Table Formation
Figure 2. Partition of the d-q planes in to six angular sectors
The vectors Vi+1 or Vi-1 are selected to increase the
B. Stator Flux and Torque Estimation amplitude of flux, and Vi+2 or Vi-2 to decrease it when flux
is in sector I. If V0 or V7 is selected, then the rotation of
The components of the current (Isd, Isq) and stator voltage flux is stopped and the torque decreases whereas the
(Vsd, Vsq) are obtained by the application of the module of flux remains unchanged. Which shows that the
transformation [5] given by (1) and (2). The components of choice of the vector tension depends on the sign of the
the stator flux (ϕsd, ϕsq) are given by (18). The stator flux error of flux is independent of its amplitude [5].
linkage per phase and the electromagnetic torque estimated
are given by (19) and (21) respectively. Table II
Switching table for DTC basis
1
I sd =
2
I A & I sq = (I B − I C ) (16)
3 2 Sector
I II III IV V VI
1 Flux Torque
2 ⎛ 1 ⎞
Vsd = VDC ⎜ S1 − (S 2 + S3 )⎟ & Vsq = VDC(S2 − S3 ) (17)
3 ⎝ 2 ⎠ 2 T=1 V2 V3 V4 V5 V6 V1
F=1 T=0 V7 V0 V7 V0 V7 V0
∫ (V ) ∫ (V )
t t
φ sd = sd − R S I sd dt & φ sq = sq − R S I sq dt (18) T=-1 V6 V1 V2 V3 V4 V5
0 0
T=1 V3 V4 V5 V6 V1 V2
φs = φ sd + φ sq
2 2
(19) F=0 T=0 V0 V7 V0 V7 V0 V7
T=-1 V5 V6 V1 V2 V3 V4
The angle between referential and stator flux is given by
⎛φ ⎞ (20) Obviously, the exit of the corrector of flux must be a
θ = tan − 1 ⎜ sd ⎟
⎜φ ⎟ Boolean variable. One adds a band of hysteresis around
⎝ sq ⎠ zero to avoid unwanted commutations when the error of
Tem = P (φsd I sq − φsq I sd ) (21) flux is very small [2] [5]. Indeed, with this type of corrector
in spite of its simplicity, one can easily control and
The stator resistance RS can be assumed constant during
maintain the end of the vector flux in a circular ring form.
a large number of converter switching periods TS. The
The switching table proposed by Takahashi [2] is as given
voltage vector applied to the induction motor also remains
in Table.II. The voltage vector switching table receives the
constant over the time period TS. Therefore, resolving first
input signals from change in flux hysteresis controller,
equation of system leads to;
change in torque hysteresis controller and another signal
( ) φS (t) =φS (0) +VSTS
t
from space vector modulation block, hence develops the
φ S = ∫ V S − RS I S dt → (22)
appropriate control voltage vector switching states for
0
PWM inverter according to the Table II.
In equation (22), φS(0) stands for the initial stator flux
condition. This equation shows that when the term RSIS D. Hysteresis controllers
can be neglected in high speed operating condition of the The change in flux and change in torque are
extremity of stator flux vector VS. Also, the instantaneous compensated by using two hysteresis controllers as
flux speed is only governed by voltage vector amplitude [3] represented in below Fig.3 respectively.
given in (23).
dφ S (23)
1 1
≈V S
dt 0 ∆φ S 0 ∆Tem
The vector tension applied to the induction motor -1
remains constant during the sampling time period TS. Thus
Figure 3. Flux and Torque Hystereses controllers respectively
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4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
The change in flux is compensated using one level C. PI-type Fuzzy Logic Controller as a Fuzzy Speed
hysteresis band as shown Fig.3. But, as the dynamic torque Regulator
is generally faster than the flux, the use of a compensator
with two level hysteresis band is used in order to adjust the e(k)
K1 FLC
change in torque and minimize the frequency switching du(k)
u(k)
average as shown in Fig.3 [7]. K3
z-1 K2 z-1
IV. STRATEGY OF PROPOSED FUZZY SPEED REGULATOR
ce(k)
FOR IM DTC SCHEME
The proposed DTC employs an induction motor model Figure 5. Basic Structure PI-type Fuzzy Logic Controller
to predict the voltage required to achieve a desired output In the DTC scheme of SVM voltage source inverter-fed
torque [5]. By using only current and voltage induction motor drive system, simultaneous control of the
measurements, it is possible to estimate the instantaneous torque and the flux linkage was required. So, the reference
stator flux and output torque. An induction motor model is torque to DTC is fed from speed loop of the IM drive as
then used to predict the voltage required to drive the flux shown in Fig.5 which is regulated using PI-type FLC
and torque to the demanded values within a fixed time shown inFig.6. In which K1, K2 and K3 are normalization
period. This calculated voltage is then synthesized using factors. The input linguistic variables speed error e(k),
SVM. change in speed error ce(k) and output linguistic variable
A. The structure of Fuzzy Speed Regulator for Induction du(k) membership functions will be divided into seven
Motor DTC Scheme fuzzy sets with the linguistic values NL (negative large),
NM (negative medium), NS (negative small), ZE (zero), PS
The DTC scheme of Induction Motor drive system
(positive small), PM (positive medium), PL (positive large)
includes flux and torque estimators, flux and torque
respectively.
hysteresis controllers, fuzzy logic controller as a fuzzy
speed regulator and a switching table and a three phase
The fuzzy logic controller is basically an input output
PWM inverter as shown in Fig.4. In addition, we need a
static non-linear mapping technique. The PI-type FLC
DC bus voltage sensor and two output current sensors for
control action can be expressed as [6],
flux and torque estimation [7].
VDC
du(t ) = K e(t ) + K ce(t ) I
(26)
P
Ф ref
Hysteresis
Controlle r
Where KP and KI are proportional and integral gains. On
Фr Switching PWM integrating above equation, we get
ωre f Te m Hysteresis Table Inverter
FLC Controlle r u (t ) = K e(t ) + K ∫ e(t )dt
P
(27)
I
ω VDC S
TL The discrete form of equation (21) can be expressed as,
Flu x and V
Torque M id du(k ) = K e(k ) + K ce(k ) I
(28)
P
Estimator
iq Equation (28) is a PI-type FLC with non-linear gain
Encoder factors. The fuzzy associative memory (FAM) of Mamdani
Z -1 IM
rule base model to develop the PI-type FLC as a fuzzy
speed regulator which in term replace the PI speed
regulator of conventional DTC [8] is given in
Figure 4. The Structure of Fuzzy speed regulator for IM Direct Torque Table. III.
Control scheme
Table III
B. Fuzzy Logic Controller Concepts FAM of FLC as a Fuzzy Speed Regulator of IM
In the research work considered in this paper, fuzzy CHANGE IN ERRO R (ce)
du
logic controller is used to coordinate between the various NB NM NS ZE PS PM PB
parameters induction motor drive system as shown in the NB NVB NVB NVB NB NM NS ZE
block diagram of the Fig.5. These fuzzy controllers have
NM NVB NVB NB NM NS ZE PS
got a lot of advantages compared to the the conventional PI
ERRO R (e)
controllers, such as the simplicity of control, low cost, high NS NVB NB NM NS ZE PS PM
reliability, compactness of the hardware as fuzzy logic ZE NB NM NS ZE PS PM PB
controller just makes use of fuzzy rules and the possibility PS NM NS ZE PS PM PB PVB
to design without knowing the exact mathematical model
PM NS ZE PS PM PB PVB PVB
of the process [1].
PB ZE PS PM PB PVB PVB PVB
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5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
V. SIMULATION AND RESULTS Vector locations are shown in order to validate the
control strategies as discussed above. The digital
To verify the proposed scheme, a numerical simulation
simulation studies were made by using MATLAB
has been carried out by using MATLAB SIMULINK. In
environment for the system described in Fig.4. The speed
the performed simulation, certain stator flux and torque
regulation loop of the induction motor drive is designed
references are compared to the values calculated in the
and simulated with fuzzy logic controller. The feedback
driver and errors are sending to the hysteresis comparators.
control algorithms were iterated until best simulation
The outputs of the flux and torque comparators are used in
results were obtained. The system dynamic responses
order to determine the appropriate voltage vector and stator
obtained by simulation were shown in Fig.5 and Fig.6 for
flux space vector.
stator current, torque and speed to conclude the
comparative results of conventional DTC with PI speed
regulator and proposed DTC with FLC as a fuzzy speed
regulator. The DTC with FLC as a fuzzy speed regulator of
IM presents the high quality performances compare to the
conventional DTC with PI speed regulator shown in Fig.6
and Fig.7.
CONCLUSIONS
The paper presents a new approach for speed control of
three phase induction motor using fuzzy logic technique.
The paper develops a DTC with FLC methodology for AC
drive systems is intended for an efficient control of the
torque and flux without changing the motor parameters.
Also the flux and torque can be directly controlled with the
inverter voltage vector using SVM technique. Two
independent hysteresis controllers are used in order to
satisfy the limits of the flux and torque. The proposed
system was analyzed, designed and performances were
studied extensively by simulation to validate the theoretical
concept. The simulation results shows that the proposed
DTC with FLC as a fuzzy speed regulator is superior to
Figure 6. Conventional DTC simulated responses with PI speed conventional DTC with PI speed regulator in robustness, in
regulator tracking precision and in presence of load disturbances
because FLC is inherently adaptive in nature.
REFERENCES
[1] Jagadish H. Pujar, S. F. Kodad “Simulation of Fuzzy Logic
Based Direct Torque Controlled Permanent Magnet
Synchronous Motor Drive”, Proceedings of the International
Conference on Artificial Intelligence- ICAI'09, Vol. I, pp.
254-257, July 13-16, 2009, Las Vegas Nevada, USA.
[2] Takahashi I, Naguchi T. “A new quick-response and high-
efficiency control strategy of an induction motor”. IEEE
Transactions on Industry Application [ISSN 0093-9994],
1986, IA-22(5): 820-827.
[3] D. Casadei, G. Grandi, G. Serra, A. Tani ”Effectes of flux
and torque hysteresis band amplitude in direct torque control
of induction machines”, IEEE-IECON-94, 1994, 299–304.
[4] Jia-Qiang Yang, Jin Huang, ″Direct Torque Control System
for Induction Motors With Fuzzy Speed Pi Regulator″
Proceedings of the Fourth International Conference on
Machine Learning and Cybernetics, Guangzhou, 18-21
August 2005.
[5] R.Toufouti S .Meziane ,H. Benalla, “Direct Torque Control
for Induction Motor Using Fuzzy Logic” CGST Trans. on
ACSE, Vol.6, Issue 2, pp. 17-24, June, 2006.
[6] Lee, C. C. “Fuzzy Logic in Control System: Fuzzy Logic
Controller”, Part I/II, IEEE Trans. Systems Man. Cybernet
20 (1990), 404-435.
[7] Hui-Hui Xia0, Shan Li, Pei-Lin Wan, Ming-Fu Zhao, ″Study
Figure 7. Proposed DTC simulated responses with Fuzzy speed regulator on Fuzzy Direct Torque Control System″, Proceedings of the
Fourth International Conference on Machine Learning and
Cybernetics, Beijing, 4-5 August 2002.
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6. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
[8] Jagadish H. Pujar, S. F. Kodad “Digital Simulation of Direct Dr. S. F. Kodad received the M.Tech. degree in Energy
Torque Fuzzy Control of PMSM Servo System”, Systems Engg. from JNTU, Hyderabad,
International Journal of Recent Trends in Engineering-
IJRTE, Vol. 2, Nov. 2009 Issue, pp. 89-93, Academy India in the year 1992. He received his
Publishers, Finland. Ph.D. degree in Electrical Engg. from
JNTU, Hyderabad, India in the year
Mr. Jagadish. H. Pujar received the M. 2004. Currently, he is working as
Tech in Power and Energy Systems from Professor and Head in Aurora College of
NITK Surthkal, Mangalore University in Engg., Hyderabad, Andhra Pradesh,
the year 1999. Currently, he is working as India in the Dept. of Electrical & Electronics Engg. He has
an Asst. Professor in B V B College of published a number of papers in various national &
Engineering & Technology, Hubli, international journals & conferences & done a number of
Karnataka, India in the Dept. of Electrical in-house & industry projects. He is also guiding a number
& Electronics Engg. & simultaneously pursuing his Ph.D. of PhD. His area of interests is neuro-fuzzy systems,
in Electrical & Electronics Engg. from the prestigious Renewable energy systems, etc.
Jawaharlal Nehru Technological University, Anatapur,
Andhra Pradesh, India. His area of interests is Soft
Computing techniques based systems.
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© 2010 ACEEE
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