Intelligent Control and Automation, 2011, 2, 320-329
doi:10.4236/ica.2011.24037 Published Online November 2011 (http://www.SciRP.org/journal/ica)
Reduce To rque Ripple of IM by Approach Method DTC
Lotfi El M’Barki1,2,3, Moez Ayadi1,2,3, Rafik Neji1,2,3
1University of Sfax, Sfax, Tunisia
2Laboratory of Electronic and Information Technology (LETI), Enis, Tunisia
3Electric Vehicle and Power Electronics Group (VEEP), Enis, Tunisia
Received May 27, 2011; revised July 6, 2011; accepted July 23, 2011
Abstract
This paper presents a new methodology for direct torque control (DTC) with improvement method control
for induction motor (IM) systems. The application of approached method DTC (AMDTC), allows by using
two hysteresis controllers to regulate torque and flux with the information of the angular location to address
the switching table. The principal advantage of this AMDTC (optimization method of DTC) enables the
minimization of the electromagnetic torque ripple and the reduction of the output current total harmonic dis-
tortion (THDI). Furthermore, it improved consumption quality of IM and it improved the lifespan of the mo-
tor. The switching characteristics of an inverter feeding an IM controlled with the AMDTC system are as-
sessed in steady state.The proposed method of AMDTC is illustrated by computer simulations.
Keywords: AMDTC, Minimum RMS, THD, Evolution of Temperature
1. Introduction
The DTC is widely applied in industry of manufacturing
and electromechanical energy utilization [1-25]. The
principal advantage of AMDTC, improve the difficulty
of large torque ripple and inconstant inverter switching
frequency in the conventional DTC, however, many re-
searchers have given attentions to these difficulty. The
AMDTC of the three-phase asynchronous machine is
subjected to values of the successive voltages, which
realizes the protecting of its insulators of motor and ame-
lioration the lifespan of IM [1,3,6-10]. Takahashi (1989)
and Depenbrock (1988) have developed the DTC spe-
cifically for IM [7,8]. Because the DTC was applied in
1980s for IM drives, the technique has also been used to
the commands asynchronous motors. The work applica-
tion of different approach DTC of asynchronous motor,
allows by using two hysteresis controllers to regulate
flux and torque with temperature evolution of insulated
gate bipolar transistor (IGBT). The voltages of the in-
verter, by using two hysteresis controllers (torque and
flux), are determined by comparing between; the refer-
ence flux and the estimated flux, at the same time with
the reference torque and the estimated torque. The re-
mainder of this article is organized as follows; principles
of the proposed method in Section 2, performance en-
hancement of AMDTC is discussed in Section 3, thermal
modeling of the power hybrid module is presented in Sec-
tion 4, the simulations results and discussion are dealt with
in Section 5 and conclusion is presented in Section 6.
2. Principles of the Proposed Method
Generally, in the AMDTC system of IM; the equations of
the three phases IM are modified in the equivalents
two-phase components [1,3,4,6-9]. The equations for the
IM are given by the following equations.
d
d
ds
ds ds
VRsI t

 (1)
d
d
qs
qs qs
VRsI t

 (2)
d
d
dr
drdrr qr
VRrI W
t


 (3)
d
d
qr
qrqrr dr
VRrIW
t


 (4)
For squirrel-cage IM; Vdr = Vqr = 0


d
dsds ds
VRsI  
t (5)


d
qsqs qs
VRsI  
t (6)

L. EL M’BARKI ET AL.
321
t

t

d
drdrdrr qr
VRrIW  
 (7)

d
qrqrqrr dr
VRrIW  
 (8)
The components, stator flux and rotor flux, are bound
to the currents (stator and rotor).These fluxes are given
by the following equations.
M
s
ss r
LI I

 (9)
M
rrr
LI I
s

 (10)
The absolute value and phase angle of stator flux are
given by the following equation.
22
and arc tg qs
sds qs
ds
s




 



(11)
The electromagnetic torque is given by the following
equation.
3sin
2
ess
TPI

  (12)
where from P = 2 is the number of pole-pairs, θ is the
angle between the stator flux and stator current.
3sin
ess
TI

  (13)
The electromagnetic torque is given by the following
equation.

3
eds qsqs ds
TI  

I (14)
From Figure 1, the voltage Vdc is the DC bus voltage,
the commands (S1, S2 and S3) are the outputs signals of
model switching table (inputs signals of IGBTs) and they
are appropriate to the AMDTC strategy.
1
2
3
2 1 1
1 2 1
31 1 2
A
dc
B
C
VS
V
VS
VS

 

  
 
  
  


 
(15)
The commands (S1, S2, and S3) can be either 1 or 0, the
voltage vectors d-q-0 axes are given by the following
equations.
Figure 1. Three-phase voltage inverter.

123
12
3
ds DC
VVSSS

(16)

23
1
3
qs DC
VVSS

 (17)
3. Performance Enhancement of AMDTC
The AMDTC of Figure 2, represents three cases ((a), (b)
and (c)) of the switching frequency of IGBT to command
an IM.
The switching state of the inverter is resulted from the
calculated stator voltage. An AMDTC is investigated in
this technique, which features in very low flux undulate
and improving torque ripple with almost fixed switching
frequency. This work uses an improvement torque ripple,
the reduction of the THDI and optimization of consump-
tion quality of IM [20,22,25]. The input reference control
of the torque and input reference control of the flux are
the entries of the AMDTC. One can indicate that the
voltage space vector can be used via Figure 3 and by the
switches S1, S2 and S3 as follows.
07
2
with e,
3
π
(1) with 1,2,6
3
for 0
i
j
iD
i
VV VV
ii
VV






C
(18)
The electromagnetic torque (Te) and stator current by
the IM; are given by following equations.
For , with
srr
s
s
ss r
r
m
IH
M
HLm L






(19)
3 sin, with
2
r
esr
s
pm
T
H
 sr

 


 (20)
The position θβ of Figure 4, is represented the angle
difference between the rotor flux and stator flux; use a
critical role in scheming output torque. Mathematically
the couple is given by the following equations.
3 , with 90
2
3 , with 270
2
0, For 0or 180
r
esr
s
r
esr
s
e
pm
T
H
pm
T
H
T



 
 




 




(21)
The flux control (


) on Figure 5, is placed in one of
he four regions fixed by the following constraints. t

L. EL M’BARKI ET AL. 322
φ
→
Figure 2. AMDTC principle.
max
s

min
s

ref

s

Figure 5. Hysteresis control of flux.
Conforming to the approach of DTC, the information
of a voltage vector is used to regulate the stator flux and
torque within the limits of two hysteresis controllers
(torque and flux). Allows by the output of tow hysteresis
bands with the address of the angular flux location is
used to data of the switching Table 1.
Figure 3. The stationary plane of inverter voltage vectors.
The proposed technique; improvements RMS of
torque ripple, THD of IM and the reduction strategy con-
sisted by approach method for trimming minimum of
torque ripple [5] The torque and flux errors (εe, εφ), are
realized by comparing between; the reference flux and
the estimated flux, at the same time with the reference
torque and the estimated torque [1]. The AMDTC strat-
egy is to choose the technical of better voltage vector
that propels the flux magnitude (Φs) to arrive a value of
reference flux (Φref) and by the same time in turns over
flux to an adjustment corresponding to a reference torque
Tref.
Figure 4. The principle of stator flux compared to the rotor
flux.
The torque control (e

) on Figure 6, is placed in one
of the four regions fixed by the following constraints.
max max max , sref 

  (22)
minmin min
,
sref 

  (23) maxmax max ,
erefeee
TT



 (24)

L. EL M’BARKI ET AL.
323
Table 1. Selectable seven-state voltage-vector switching table
for IM control system.
Sector
Flux Torque
1 2 3 4 5 6
1T V2 V3 V4 V5 V6V1
0T V7 V0 V7 V0 V7V0
1


1T V6 V1 V2 V3 V4V5
1T V3 V4 V5 V6 V1V2
0T V0 V7 V0 V7 V0V7
0


1T V5 V6 V1 V2 V3V4
min.e
T
max.e
T
ref
T
e
T
Figure 6. Hysteresis control of torque.
minmin min
,
erefeee
TT

  (25)
The AMDTC, allows to make the instantaneous torque
equal with the reference torque at the end of the cycle and
the technique is given by the following equation.

1
e
Tk T
ref
(26)
The Table 2 of AMDTC represented the commuta-
tions number of switches between 0 s to 1 s. The switches
commutations are recapitulated in the following Table 2.
The fluxes of the induction motor are determined by the
following equation.
d 1
d
0 d
d
SS
s
SSs
s
rr rr
Sr
RmrR
HH
tV
mr RR
jWr
tH L








 

  


 






(27)
The fluxes of (27) are expressed in the discrete form
as.

1
SS
s
ksk rksk
sk
SS
RmrR
Vt
HH
 

 
 

cp


(28)

1
rr
rkskrk cp
rk
Sr
mr RR
jWr t
HL
 





 








(29)
where tcp is controlled period of a small value and k + 1,
the sampling instants. In our work, the root-mean-square
(RMS) value of the torque ripple can be expressed as
follows.
Table 2. Commutations number of switches.
AMDTC a b c
N. Commutations1370 3600 26000
 
22
00
11
dd
tt
cp cp
ond e
cp cp
TtTe Treft
tt
 

(30)
With Tond is the RMS value of the torque ripple. The
total harmonic distortion (THD) is defined as the RMS
value of the current (IKRMS), divided by the RMS value of
its fundamental current (I1RMS). The quality of the current
is measured with the THDI.
2
2
1
kRMS
k
I
RMS
I
THDI



(31)
4. Thermal Modeling of the Power Hybrid
Module
The equivalent electrical circuit shown in [23-25] can
represent the finite element method (FEM), the finite
difference method (FDM) and the thermal model of the
material for IGBT. The electric model used for the Se-
mikron module SKM 75 GB 123 D of IGBT is used in
AMDTC with a temperature without cooling; the power
dissipated (Pdis), with voltage drop at the boundaries
(VCEsat(t) ) and internal resistance (RCE(Tj) ). The technique
investigation that was performed with the Semikron
module SKM 75 GB 123 D (75 A/1200 V) is presented
by the following equations
  

2
dis Ct tCETjctCETj
PVIRI

T
(32)


1.5 0.00225
j
CE Tj
V (33)


0.000100.0275
0.000080.018
j CE Tj
j
CE Tj
RT
RT


 (34)
5. Simulation Results and Discussion
The output voltage space vector with reduce torque rip-
ple of IM by AMDTC; can be realized via switching
Table 2 and determined by the two basic variables T

and


.
Because of the AMDTC, has large number of select-
able voltage vectors, it benefit reduce torque and current
ripples of induction motor. With Table 2, represent the
commutations number of switches between 0 s to 1s. The
switches commutations are recapitulated in the response

L. EL M’BARKI ET AL. 324
of voltages (Vd and Vq), for AMDTC of cases ((a), (b)
and (c)).
According to results of Figure 7 for the three cases ((a),
(a)
(b)
(c)
Figure 7. The response of voltages (Vd and Vq), for AMDTC
of cases ((a), (b) and (c)).
(b) and (c)) one finds the same forms. With these ap-
proaches one finds; the selection seven-state voltage-
vector switching Table 1 is prepared via the Equation
(18) of inverter. One can indicate that the voltage space
vector can be used via Figure 7 (Vq in function of Vd)
and by the switches (IGBTs). The voltage maximal Vq
equal 265.581 V and the voltage maximal Vd equal
306.666 V. One notices the passages enter the vectors Vj
with j = 0, 1, 2, ···, 7. Finally one notes the passages enter
the vectors, one finds with each vector contains seven of
possible combinations.
The output voltage of inverter via commutation switch,
provoke reduce torque ripple of IM by AMDTC. Figure
8 of reference torque (60 Nm) illustrates; the electro-
magnetic torque during startup produced at 0.008 s of
(a)
(b)
(c)
Figure 8. Electromagnetic torques (Te) and reference torque
(Tref) of AMDTC during startup.

L. EL M’BARKI ET AL.
325
case (a), which is reduced at 0.0064 s of case (b) and
case (c) the electromagnetic torque during startup at
0.0062 s. According the Figure 8, one finds the electro-
magnetic torque to follow the reference torque.
The commutations numbers of switches are realized;
by 1370 of case (a), case (b) equal 3600 and case (c)
equal 26000. As suggested in Figure 9, the ripples are
caused by the unbalanced output voltage, because of the
AMDTC has large number of selectable voltage vectors,
it benefit reduce torque ripples and current ripples of
induction motor. Efficacy optimization of the IM used
three proposing approaches in Figure 9 for a load of 60
Nm. For the reason of AMDTC, the voltages switching
by improve torque ripple; provoke ameliorating quality
of consumption IM. In Figures 9 and 10, it is noticed
that there are improved torque ripples and reduced THD.
The AMDTC strategy reduces the THD in the IM. In-
deed, the cases improve output current, reduces THD and
current stress on semiconductors switches. By improving
DTC of Figure 10(c) equal 71.88 A and the THDI is
reduced to 2.5%. The THDI is showed in Figure 10(c),
which is better THDI comparing to the current form
shown in Figures 10(a) and 10(b) .
Figure 11, affirm of improving respectively the torque
ripple by the proposed AMDTC under the same IM con-
dition; realized torque ripple at ±9.55 Nm of case (a),
torque ripple at ±3 Nm of case (b), and torque ripple at ±
0.4 Nm of case (b), The torque ripple minimization
method for AMDTC of induction motor. If compared
with the cases (a) and (b), the proposed case (c) has the
advantage of global minimum RMS torque ripple.
For Figure 12 (a2), the maximum junction tempera-
ture of IGBT1 at 0.15 s via approaches DTC; provoke
case (a) equal 324.588 K with case (b) equal 332.296 K
and case (c) equal 404.533 K. Thus the Figure 12 (a3),
represent the maximum case temperature of IGBT1 at
0.15s for Figure 12 (a3); with case (a) equal 323.654 K,
case (b) equal 332.089 K and case (c) equal 385.395 K.
To consider the results of the approaches, they are nec-
essary a system of temperature cooling of IGBTs.
Figures 7-12, illustrates ameliorations respectively the
torque ripples, the currents of IM and temperatures evo-
lutions of three approaches scenario (a, b and c). The
idea is improved the DTC by the operation of commuta-
tions number and modification voltage space vector. The
following Table 3 determines the results AMDTC of the
IM.
6. Conclusions
In this paper, the comparison of AMDTC strategy for
approaches method (a, b and c) via advantages of Table
3 are realized; by the minimizing THD, improve torque
(a)
(b)
(c)
Figure 9. Electromagnetic torques responses of AM DTC.

L. EL M’BARKI ET AL. 326
(a)
(b)
(c)
Figure 10. Phase currents responses and THDI of AMDTC
for a load of 60 Nm.
(a)
(b)
(c)
Figure 11. Reduce torques ripples of AMDTC.

L. EL M’BARKI ET AL.
327
(a1)
(a2)
(a3)
Figure 12. Improvements for commutations and tempera-
tures of AMDTC ; (a1). Commutation switches of inverter,
(a2). Evolution of the junction temperature (in the IGBT1
of S1) and (a3). Evolution of the case temperature (in the
IGBT1).
Table 3. The results AMDTC of the IM for a load of 60 Nm.
AMDTC a b c
Startup time (s) 0.008 0.0064 0.0062
Phase current IA (A) 73.55 72.01 71.88
THD of IA (%) 6.11 2.6 2.5
Torque ripple (Nm) 9.55 3 0.4
Reduction in torque ripple (%)Nothing 68.58 95.81
N. Commutation 1370 3600 26000
Case temperature (K) in the
IGBT1 at 0.15 s 323.654 332.089385.395
Junction temperature (K) in the
IGBT1 at 0.15 s 324.588 332.296404.533
ripples and thereafter improve quality of consumption
IM. The proposed scenario using AMDTC enables to
reduce torque ripple and obtain improvements inputs
currents of IM, while guarding torque dynamic response
to follow one reference torque and switching frequency
to follow Figure 7. The effective of in Figures 7-12 has
been realized with different approaches ((a), (b) and (c)).
We have according to the Figure 11 an approximately
95.81% reduction in torque ripple in AMDTC. The phase
current with THDI of approach (c) operation contains
lowest THD to that of approaches ((a) and (b)) opera-
tions. The Table 3, recapitulate advantages of the
AMDTC for the IM.
7. Acknowledgements
The authors would thank my colleagues in ENIS-Tunisia,
in FSGF-Tunisia, and in ESSTT-Tunisia for the helpful
support in the works.
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L. EL M’BARKI ET AL.
329
Appendix: List of Symbols
Rs: Stator resistance (1.4534 Ω),
Rr: Rotor resistance (1.4160 Ω),
Lr: Rotor inductance (0.0143 H),
Ls: Stator inductance (0.0144 H),
M: Mutual inductance (0.0132 H),
Vds, Vqs: d-axis and q-axis stator voltages,
Ids, Iqs: d-axis and q-axis stator currents,
2
1: Blondel coefficient,
M
LrLs
  
Φr: Rotor Flux,
Φs: Stator flux,
Tr: Load of torque (60 Nm),
Te: Electromagnetic torque,
Tref: Reference torque,
F: Friction coefficient (0.015 kg·m2/s),
J: Moment of inertia (0.30 kg·m2),
p: Number of pole pairs in the motor (2),
f: Fundamental frequency (50 Hz),
Vdc: Continuous tension (460 V),
tsp: Small control period,
ωr: Rotor pulsation,
(k + 1): Sample instant.