FPGA-Based Implementation Direct Torque Control of Induction Motor

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 5, No. 3, February 2015, pp. 293~304
ISSN: 2088-8694  293
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
FPGA-Based Implementation Direct Torque Control of
Induction Motor
Saber KRIM1
, Soufien GDAIM2
, Abdellatif MTIBAA3
, Mohamed Faouzi MIMOUNI4
1,2,3
Laboratory of Electronics and Microelectronics (EuE), Faculty of Sciences of Monastir
University of Monastir, Tunisia
4
Research Unit of industrial systems Study and renewable energy (ESIER),
University of Monastir, Tunisia.
3,4
Department of Electrical Engineering, National Engineering School of Monastir, University of Monastir, Tunisia
Article Info ABSTRACT
Article history:
Received Aug, 2014
Revised Jan 13, 2015
Accepted Jan 28, 2015
This paper proposes a digital implementation of the direct torque control
(DTC) of an Induction Motor (IM) with an observation strategy on the Field
Programmable Gate Array (FPGA). The hardware solution based on the
FPGA is caracterised by fast processing speed due to the parallel processing.
In this study the FPGA is used to overcome the limitation of the software
solutions (Digital Signal Processor (DSP), Microcontroller...). Also, the DTC
of IM has many drawbacks such as for example; The open loop pure
integration has from the problems of integration especially at the low speed
and the variation of the stator resistance due to the temperature. To tackle
these problems we use the Sliding Mode Observer (SMO). This observer is
used estimate the stator flux, the stator current and the stator resistance. The
hardware implementation method is based on Xilinx System Generator
(XSG) which a modeling tool developed by Xilinx for the design of
implemented systems on FPGA; from the design of the DTC with SMO from
XSG we can automatically generate the VHDL code. The model of the DTC
with SMO has been designed and simulated using XSG blocks, synthesized
with Xilinx ISE 12.4 tool and implemented on Xilinx Virtex-V FPGA.
Keyword:
Direct Torque Control
Induction Motor
Field Programmable Gate Array
Real Time
Sliding mode observer
VHDL
Xilinx System Generator
Copyright © 2015 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Saber KRIM,
Laboratory of Electronics and Microelectronics (EuE), Faculty of Sciences of Monastir,
National Engineering School of Monastir, University of Monastir, Tunisia
E-mial: krimsaber@hotmail.fr
1. INTRODUCTION
With technological advancement in the field of microelectronics new digital solutions such as
FPGAs (Field Programmable Gate Array) or ASIC (Application Specific Integrated Circuit) are available and
can be used as numerical targets for the implementation of algorithms command. The inherent parallelism of
these digital solutions and their high calculation capacity make the calculation time is negligible in spite of
the complexity of the algorithms to be implanted. These hardware solutions can meet the new demands of
modern controls, such as reduction of the calculation time, the processing parallelism of these hardware
solutions allows integrating on a single target several algorithms that provide various features and which can
work independently of each other. For the control of the variable speed electrical machines, various control
algorithms can be used. These algorithms often have several nested control loops. In our case we use the
DTC that contains a speed control loop, stator flux regulator, electromagnetic torque regulator and the sliding
mode observer; this is why we are interested in the implementation on FPGA of Direct Torque Control based
on the sliding mode observer for controlling an induction motor. During the past few years several
researchers use the FPGA for controlling electrical system [1]-[7]. Most of them develop the algorithm on a
VHDL hardware description language. For the hardware implementation of the Directe Torque Control with

 ISSN: 2088-8694
IJPEDS Vol. 5, No. 3, February 2015 : 293 – 304
294
Sliding Mode Observer of an induction motor on the FPGA we use Xilinx System Generator (XSG) toolbox
developed by Xilinx and added to matlab/simulink. The XSG advantages are the rapid time to market, real
time and portability. Once the design and simulation of the proposed algorithme is completed we can
automatically generate the VHDL code in Xilinx ISE.
The DTC of IM is based on the orientation of the stator flux by a direct action on the states of the
switches of the inverter [8]-[11]. The DTC control based on an open loop estimator of stator flux having
well-known problems of integration especially at a low speed [12]-[14]; also, it is sensitive to the variation of
the machine parameters such as stator resistance [15]. To solve these problems many observation methods
are used, such as the Extended Kalman Filter [16] but the drawback of this observer that the knowledge of
load dynamics is not usually possible, Model Reference Adaptive System (MRAS) [17], [18]; the drawback
of this algorithm that it is sensitive to uncertainties of the induction motor parameters, the luenberger
Observer is used for state estimation of IM [19]. In this work, we propose to use the adaptive sliding mode
observer for the estimation of the stator flux, stator current and the adaptation of the variation of the stator
resistance. That is a powerful observer that can estimate simultaneously the stator flux, stator current, rotor
speed and motor parameters. It is introduced to replace the open-loop estimator of stator flux. Furthermore it
has been provided with an adaptation mechanism of the stator resistance. Thus, the aim of this paper is first,
to give a fair comparison between a DTC with an open loop estimator and DTC with sliding mode observer
at the stage of adjustment of the stator resistance. Secondly, the proposed model is developed using Xilinx
System Generator for implementation on FPGA, to enjoy the performances of FPGAs in the field of digital
control of electrical machines in real time. The performance of the proposed model is proved by simulation
results, Resources used and execution time.
2. DIRECT TORQUE CONTROL OF AN INDUCTION MOTOR
2.1. Induction Machine Model
The state model of an induction machine can be expressed as follows:
   
.
d X
A X B U
d t
  (1)
Where A, B, X and U are the evolution matrix, the control matrix, state vector X and the stator voltage
respectively.
[ ]
0 0 0
0 0 0
S r
S r r
r S S
S r
S r r
S r S
S
S
R R
L L R
L L L
R R
A
L L R
L L L
R
R


  


  
 
 
  
 
 
 
 
  
 
 
 
  ,
 



















1
0
1
0
0
1
0
1
S
S
L
L
B 

,





















s
s
s
s
i
i
X
,











s
s
V
V
U
The state vector X is composed by stator current and flux components. The vector command U is
constituted by the stator voltage components.
2.2. Direct Torque Control Principle
Direct torque control of an induction machine is based on the direct determination of the control
sequence applied to the switches of a voltage inverter. The choice of sequences is based on the two hysteresis
comparators of the stator flux and electromagnetic torque [20]. The voltage vector Vs is the output of a three-
phase voltage inverter whose the state of the inverter switches are controlled by three Boolean variables Sj (j
= a, b, c). The voltage vector can be written as:
2 4
3 3
s s s
2
( . . )
3
v = v v
j j
S a bV U S S e S e
j
 
 

  

 
(3)

IJPEDS ISSN: 2088-8694 
FPGA-Based Implementation Direct Torque Control of Induction Motor (Saber KRIM)
295
The components of the stator voltage vector   SSS VVV , and the stator flux vector
 ,S S S    in Concordia reference are given by Equation (4) and (5). The calculation of the position and
module of the stator flux are based on the use of components ,S S   . The module of the stator flux and
its position are given by Equation (6).
0
0
(v )
(v )
s
s
t
s s s
t
s s s
R i dt
R i dt


 
 



 


  




(4)









)(
3
2
))(
2
1
(
3
2
ScSbUV
ScSbSaUV
S
S

 (5)
2 2
arg
s s s
s
S s
s
arctg
 


  

 

  


 

(6)
The electromagnetic torque is expressed in terms of the components of stator flux vector and the
components of stator current vector as:
3
( )
2
e s s s sC p i i      (7)
The estimated values of the stator flux and electromagnetic torque are compared with their reference
values Φsref, Teref respectively. Switching states are selected by the switching table, where CE is the error
of electromagnetic torque after hysteresis block and E is the error of the stator flux after hysteresis block,
( 1...6)iS i  means the sector (Table 1) [21]:
Table 1. Switching table for direct torque control
E Ec S1 S2 S3 S4 S5 S6
1 V2 V3 V4 V5 V6 V1
1 0 V7 V0 V7 V0 V7 V0
-1 V6 V1 V2 V3 V4 V5
1 V3 V4 V5 V6 V1 V2
0 0 V0 V7 V0 V7 V0 V7
-1 V5 V6 V1 V2 V3 V4
The structure of DTC of an induction motor is given, as shown by the Figure 1:

 ISSN: 2088-8694
296
Inverter
E
Switching Table
 cba SSS
ref
Tref
+
-
+
sabci
 cba SSSOpen loop Estimator
PI
r
S
Tem
abc

Si
N
ref
SV
abc

-
   dtiRv SSSS ),(),(),( 
  sss 
   sss arctg
   3 2e s s s sT p i i     
Hysteresis
comparator
E
CE
S
ref S      
Figure 1. Schematic of conventional DTC
3. DIRECT TORQUE CONTROL OF AN INDUCTION MOTOR WITH SLIDING MODE
OBSERVER
The sliding mode observer (SMO) is wedely used for non linear systems due to its robustness to the
parameter variations. The SMO is used to contstruct the state variables and the stator resistance. The diagram
of the SMO is shown in Figure 2.
Nonlinear system
Sign(.)
h ( x

)
K
f ( x

, u)
x

x


u y




Figure 2. Principle of the sliding mode observer
The mathematical model of the observed stator current is presented as:
11 1
1 1
0
11 0
S r r
S rS S S Sr S S S
r SS r
SS SS r SS r
S
R R R
L L L L L L
RR R
LL L LL L
i i v A
v
i
i
   





   


 




 
                                                                                   
 
12
21 22 2
S
S
IA
A A I
  
   
  
(8)
The matimatical model of the observed stator flux is given by the following system:
13 1 3 2
4 1 4 2 2
1
0
0
0 1
0
S S SS SS
S S S
S S
S
LR
R
L
i v IA A
A Av I
i
  







 
    
                                                
 
 
(9)
Where:
1 1 1 2
2 1 2 2
A A
A A
 
 
 
, 3 1 3 2
4 1 4 2
A A
A A
 
 
 
and 1 1
22
( )
( )
S
S
sig n e S
sig n e S
I
I
   
       
: are the matrixes of gains of the observed
stator current, matrix of gains of the observed stator flux, and the sign vector of the sliding mode surface
respectively.

297
3.1. Determining of the SMO Characteristics
The sliding surface is based on the error between the real stator current si  and si  , and the observed
stator current si 

and si 

as follows:
1
22
2
1
1
1 1( )
S Sr
S S S
r r
S T
S
S L
T T
i i
i i
 
 

  


 
                    
 
(10)
Where:
T
s s si i i     and
T
s s si i i 
  
 
   
are the real and observed stators currents vectors
respectively.
r
r
r
R
L
T  : Rotor time constant.
The matrix of gains related to the current observer is as follows:













2
1
43
21
0
0


ii
ii
i
AA
AA
A (11)
Where 21  and are two positive constants, which are determined by applying the stability conditions
defined by the Lyapunov approach.
The gain matrix of the stator flux is as follows:




















22
1
43
21
1









q
L
L
q
AA
AA
A
S
S (12)
Where 21 qandq are two positive constants.
The stability of the SMO depends on its convergence towards its sliding surface. To study the
stability of this observer the following Lyapunov function is used:
1
2
T
V S S (13)
When the sliding surface S=0, the error between the real and observed stator current must bee zero,
0S Si i 

  and the derivate of the lyapunov fuction is strictly negative ( 0V

 ).
0T
V S S
 
  (14)
The major drawback of the SMO observer is the chattering phenomenon. To weaken this
phenomenon a saturation function is used to replace the Bang-Bang function. The saturation function is given
by the system (15).
2,1;1
1
)( 










 i
Ssi
S
Ssi
Ssi
Ssign
i
i
i
i
i




(15)
Where  is a positive constant with a low value.

 ISSN: 2088-8694
298
3.2. Mechanism of Adaptation of the Stator Resistance
During operation the stator résistance vary, due to the temperature and the low speed operation. To
online estimate of the stator resistance another term added to the lyapunov fuction.
2
1
2 2
T
S SV S S R R
 
 
   
 
(16)
0T
S SSV S S R R R

   
 
   
 
 (17)
To satisfy the condition of the Equation (17), the estimated stator resistance can be expressed as
follow:
*( ) *( )S S S S SS SR k i i i i i i    

    
 
     
 
(18)
With k is a positive constant.
4. USE OF XILINX SYSTEM GENERATOR (XSG) IN THE CONTROLLER DESIGN
4.1. Description of Xilinx System Generator
Xilinx System Generator (XSG) is a modeling tool developed by Xilinx for the design of
implemented systems on FPGA. It has a library of varied blocks, which can be automatically compiled into
an FPGA [22]. In this work, Xilinx System Generator (XSG) is used to implement the architecture of the
Direct Torque Control of induction Motor with sliding mode observer on FPGA. In the first step, we begin by
implementing of the proposed architectures using the XSG blocks available on the Simulink library. Once
the Design of the system is completed and gives the desired simulation results, the VHDL code can be
generated by the XSG tool [23]. The design flow of the Xilinx System Generator is given by figure 3. After
generation of VHDL code and the synthesis, we can generate the bitstream file. Then we can move this
configuration file to program the FPGA [24].
Xilinx System Generator Design Gereration of VHDL Code
Synthesis (Bitsteam)
1111110000011111000111
1111111100011111111000
0011010111000011100000
1111111111111100011111
Download into FPGA
Figure 3. Configuring an FPGA
4.2. Design of the Sliding Mode Observer using XSG
4.2.1. Design of the Currents Observed
The Design of the direct component of the observed stator current vector introduced into the
equation system (8) given by Figure 4.

299
Figure 4. Design of the Component Si

from the XSG
4.2.2. Design of Sliding Surface, gain Matrix and Sign Function
The sliding surface, the saturation function and the gain matrix are given in equations (10), (11),
(12) and (15), are illustrated using XSG as shown in Figure 5.
(a) (b)
Figure 5. Design of sliding surface, gain matrix and sign function from the XSG
4.3. Simulation Results using Xilinx System Generator and Discussions
The structure of the direct torque control with the adaptative sliding mode observer of an induction
motor is shown in Figure 6.
Inverter
E
Switching Table
 cba SSS
ref
Tref
+
-
+
sabci
Sliding Mode
Observer
PI
r
S
Te
abc

Si
N
ref
SV
abc

-
SR

E
Figure 6. Schematic of a conventional DTC with an adaptative sliding mode observer

 ISSN: 2088-8694
300
4.3.1. The Stator Resistance is Constant (Rs=5.717Ω)
The simulation of the conventional DTC with sliding mode observer is achieved using the XSG. The
speed and flux references used in the simulation results are 150rad/s and 0.91wb respectively. The
electromagnetic torque reference presents the output of PI controller of speed. At time t = 0.5sec a load
torque of 10 Nm is applied.
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
140
160
t(s
RotorSpeed(rd/s)
Real speed
Reference speed
Estimated Speed
(a)
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
t(s)
StatorFlux(wb)
(b)
0 0.2 0.4 0.6 0.8 1
-5
0
5
10
15
20
25
t(s)
Electromagnetictorque(Nm)
Real Tem
Estimated Tem
(c)
Figure 7(a). Evolution of real and
estimated speed
Figure 7(b). Evolution of the real
and observed stator flux
Figure 7(c). Evolution of the real
and estimated electromagnetic
torque
0 0.2 0.4 0.6 0.8 1
-20
-10
0
10
20
t(s)
Statorcurrent(A)
Real Stator Current
Observed Stator Current
0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54
-5
0
5
0 0.2 0.4 0.6 0.8 1
-20
-10
0
10
20
t(s)
Statorcurrent(A)
Real Stator current
Observed Stator current
0.45 0.5 0.55 0.6
-5
0
5
10
Figure 8(a). Variation of the real and observed stator
current Si 

Figure 8(b): Variation of the observed and real stator
current Si 

4.3.2. The Stator Resistance Varies from 100% (Rs=2*5.717=11.434Ω)
The simulation of the conventional DTC with an open loop estimator and the conventional DTC
with a sliding mode observer is achieved using the XSG at a low speed. The rotor speed and stator flux
references used in the simulation results are 31.4 rad/s and 0.91 wb, respectively. At time t = 0.2sec a load
torque of 10 Nm is applied. At t = 0.4sec the stator resistance increases by 100%.
(a) An open loop estimator (b) A sliding mode observer
Figure 9. Variation of Rs for DTC with
0 0.5 1 1.5 2 2.5
5
6
7
8
9
10
11
12
t(s)
Statorresistance(Ohm)
DTC resistance
Machine Resistance
0 0.5 1 1.5 2 2.5
0
2
4
6
8
10
12
t(s)
Statorresistance(Ohm)
Real resistance
Observed resistance

301
(a) An open loop estimator (b) With a sliding mode observer
Figure 10. Evolution of the stator flux for DTC with
(a) without adjustment of the stator resistance
variation
(b) with adjustment of the stator resistance variation
Figure 11. Evolution of the stator flux trajectories
(a) An open loop estimator (b) With a Sliding Mode Observer
Figure 12. Variation of electromagnetic torque for DTC with
The simulation results of the direct torque control with sliding Mode Observer given by Figure 7 and
8 show that the real and the estimated variables are similar. In Figure 7(b) and 7(c) it can be seen that the
stator flux and the electromagnetic torque are characterized by high ripples due to the use of the hysteresis
comparator.
Figure 9 show the sensitivity of the Direct Torque Control of an Induction Motor. In Figure 9(a) we
can see at t=0.4sec that the stator resistance increases 2 times the nominal stator resistance due to
temperature, it can be seen that in the case of the DTC with an open loop estimator, the stator resistance used
in the DTC kept constant. By contrast, in Figure 9(b) the observed stator resistance converges rapidly to the
nominal value, this is due to the on line adaptation of the stator resistance by the sliding mode observer. The
simulation results demonstrates the robustness of the Sliding Mode Observer against the abruptly variation of
the machine parametres.
In Figure 10(a), at t = 0.4sec the real stator flux is affected by de variation of the stator resistance, it
decreases abruptly to 0.72 wb, the error between the real and the reference stator flux kept constant. Yet, in
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
t(s)
Statorflux(wb)
Real stator flux
estimated stator flux
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
t(s)
StatorFlux(wb)
Real stator flux
observed stator flux
0 0.5 1 1.5 2 2.5
-5
0
5
10
15
20
25
30
t(s)
Real Tem
Estimated Tem
0 0.5 1 1.5 2 2.5
-10
0
10
20
30
t(s)
Estimated Tem
Real Tem

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302
the Figure 10(b), the static error gradually vanishes due to the presence of the adaptive online mechanism of
the stator resistance using the Sliding Mode Observer.
In Figure 11(a), we can notice that the stator flux trajectories increase due to the variation of the
stator resistance at t=0.4sec. By contrast, in Figure 11(b) the stator flux trajectory is kept constant due to the
presence of the adaptive online mechanism of the stator resistance using the Sliding Mode Observer.
In Figure 12(a), at t = 0.4sec the electromagnetic torque increases, and the error between the
electromagnetic torque and the load torque remains constant. However, in Figure 12(b), for the sliding mode
observer; the electromagnetic torque is kept constant.
4.4. FPGA Implementation Results of the Proposed Approach and Discussions
Once the simulation is completed and gives the desired results, we can generate the VHDL code and
synthesized the hardware block. The implementation results are given by Figure 13 and Table 2.
T(k) T (k+1)
T(k)
T (k+2)
T (k+2)
T (k+2)
T(k)
T (k+1)
T (k+1)
ADCT
ADCT
ADCT
exT
exT
exT
(a)
(b)
(c)
50µs
(b)
Figure 13(a). RTL schematic of the conventional
DTC with a sliding mode observer from Xilinx ISE
Figure 13(b). Timing Diagram for the Imlementation
on (a): Microcontroller, (b): Digital Signal Processor
(DSP), (c): Field Programmable Gate Array (FPGA)
Table 2. Resources Utilisation for the DTC with SMO
Resourses Used resources Available resources
Number of bonded I/O 68 640
Number of Slice LUTs 2087 44800
Number of Slices Registers 478 44800
Number of DSP48Es 8 128
Execution time: exT = 0.94 µs
The Table 2 shows the implementation results in term of the used resources and the execution time
of the Direct Torque Control with SMO using the FPGA Virtex-5 Device. The RTL schematic of the CDTC
with SMO is given by Figure 13(a). The Figure 13(b), shows the performance of computing time for the
hardware implementation on FPGA compared to software solutions (Microcontroller, Digital Signal
Processor). TADC and Tex are the analogue to digital conversion time and the execution time respectively.
In this work the execution time equal to 0.94 µs. But in papers [25] and [26], the sampling time
equal to 100 µs using the dSPACE 1104 (digital signal processing and control engineering). In paper [27],
the sampling time equal to 500 µs. It can be seen that the execution time is too important relative to the
FPGA due to the sequential processing of the dSPACE.
5. CONCLUSION
In this paper, the digital implementation of the Direct Torque Control with Sliding Mode Observer
using the FPGA has been presented. The Sliding mode Observer has been proposed to improve the

303
performences of the Direct Torque Control of an Induction Motor. Using the Sliding Mode Observer consists
to remplacing the open loop pure integration. The simulations results using Xilinx System Generator have
shown that the proposed observation strategy has better performances than the open loop pure integration
especially in term of variation of the stator resistance. The obtained design of the Direct Torque Control with
Sliding Mode Observer from XSG can be translated automatically into a VHDL (VHSIC Hardware
Description Language) from Xilinx Integrated Software Environment tool (ISE) and can be embedded into
the Xilinx Virtex-V FPGA.
Induction Machine Parameters
Number of pairs of poles: 2
Rated frequency: 50 Hz
Rated voltage :220/380 V
Stator resistance :5,717 Ω
Rotor resistance: 4,282 Ω
Stator inductance :464mH
Rotor inductance :464mH
Mutual inductance :441,7mH
Moment of inertia :0.0049 kg.m²
Viscous friction coefficient:
0.0029kg.mˆ2/s
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BIOGRAPHIES OF AUTHORS
Saber KRIM received the degree in Electrical Engineering from National School of
Engineering of Monastir, Tunisia in 2011. In 2013 he received his M.S degree in electrical
Engineering from Monastir University, Tunisia. He is currently pursuing the Ph.D. degree with
University of Monastir, Tunisia. His current research interests include rapid prototyping and
reconfigurable architecture for real-time control applications of electrical system.
Soufien GDAIM received the degree in Electrical Engineering from National School of
Engineering of Sfax, Tunisia in 1998. In 2007 he received his M.S degree in electronic and real-
time informatic from Sousse University and received his PhD degree in Electrical Engineering in
2013 from ENIM, Tunisia. His current research interests include rapid prototyping and
reconfigurable architecture for real-time control applications of electrical system.
Abdellatif MTIBAA is currently Professor in Micro-Electronics and Hardware Design with
Electrical Department at the National School of Engineering of Monastir and Head of Circuits
Systems Reconfigurable ENIM-Group at Electronic and microelectronic Laboratory. He holds a
Diploma in Electrical Engineering in 1985 and received his PhD degree in Electrical
Engineering in 2000. His current research interests include System on Programmable Chip, high
level synthesis, rapid prototyping and reconfigurable architecture for real-time multimedia
applications. Dr. Abdellatif Mtibaa has authored/coauthored over 100 papers in international
journals and conferences. He served on the technical program committees for several
international conferences. He also served as a co-organizer of several international conferences.
Mohamed Faouzi Mimouni received his Mastery of Science and DEA from ENSET, Tunisia in
1984 and 1986, respectively. In 1997, he obtained his Doctorate Degree in Electrical
Engineering from ENSET, Tunisia. He is currently Full Professor of Electrical Engineering with
Electrical Department at the National School of Engineering of Monastir. His specific research
interests are in the area Power Electronics, Motor Drives, Solar and Wind Power generation. Dr.
Med Faouzi MIMOUNI has authored/coauthored over 100 papers in international journals and
conferences. He served on the technical program committees for several international
conferences.

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