PLDL MOTOR

1. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 1
DTC of B4-Inverter Fed BLDC Motor Drives
with Reduced Torque Ripple
During Sector-to-Sector Commutations
Mourad Masmoudi, Bassem El Badsi and Ahmed Masmoudi
Abstract— The paper deals with the direct torque control
(DTC) of BLDC motor drives fed by four-switch inverters (also
known B4-inverters) rather than six-switch inverters (also known
B6-inverters) in conventional drives. The B4-inverter could be
regarded as a reconfigured topology of the B6-inverter in case
of a switch/leg failure which represents a crucial reliability-
benefit for many applications especially in electric and hybrid
propulsion systems. The principle of operation of the BLDC
motor is firstly recalled considering both cases of B6- and B4-
inverters in the armature, with emphasis on the two- and three-
phase conduction modes. Then, the DTC of B4-inverter fed BLDC
motor drives is treated considering three strategies, such that
(i) DTC-1: a strategy inspired from the one intended to B6-
inverter fed BLDC motor drives, (ii) DTC-2: a strategy that
considers a dedicated vector selection sub-table in order to inde-
pendently control the torques developed by the phases connected
to the B4-inverter legs during their simultaneous conduction,
and (iii) DTC-3: a proposed strategy that eliminates the torque
dips penalizing DTC-2 during sector-to-sector commutations.
Following the design of the corresponding vector selection tables
and sub-tables (if any), an experimentally-based comparative
study of the three DTC strategies is carried out considering, in a
first step, the BLDC motor steady-state operation under DTC-1
and DTC-3. Then, the comparison is extended to the BLDC motor
features during sector-to-sector commutations, under DTC-2 and
DTC-3. The experimental results clearly validate the predicted
performance of the proposed DTC strategy.
Index Terms— BLDC motor, B6- and B4-inverters, two- and
three-phase conduction modes, direct torque control, sector-to-
sector commutations.
I. INTRODUCTION
Among the control strategies that exhibit a high torque
dynamic, one can distinguish the direct torque control (DTC).
DTC strategies have been widely implemented in squirrel
cage induction machine drives. They allow a direct control
of the electromagnetic torque and the stator flux through
the application of suitable combinations of the control sig-
nals of the inverter switches. The earlier DTC strategy has
been proposed by Takahashi and Noguchi in the middle of
the eighties [1]. Since then, many DTC strategies based on
Manuscript received June 6, 2013; revised July 24, 2012; accepted for
publication September 14, 2013. Recommended for publication by Associate
Editor........
M. Masmoudi is with the Department of Computer Sciences, Sfax Higher
Institute of Technology, Tunisia (e-mail: mourad.masmoudi@gmail.com).
B.El Badsi and A. Masmoudi are with the Department of Electromechanical
Engineering, Sfax Engineering National School, University of Sfax, Tunisia
(e-mail: bassemelbedsi@yahoo.fr; a.masmoudi@enis.rnu.tn).
Digital Object Identifier 06.0749/TPEL.2013........
analytical approaches have been developed so far, consid-
ering conventional inverters (also known B6-inverters) [2]-
[6] as well as unconventional ones [7]- [11]. Among the
unconventional topologies, one can distinguish the B4-inverter
which results from the reconfiguration of the B6-inverter in
case of a switch/leg failure. Such a reconfiguration is a vital
requirement in some applications especially electric and hybrid
propulsion systems, in so far as the vehicle reliability is
concerned [12]- [15].
Dealing with BLDC motor control strategies, it is quite
commonly believed that they are based on the current and
torque control approaches [16]- [19]. One of the most popular
is a generalized harmonic injection to find out optimal current
waveforms minimizing the torque ripple [20]- [21]. However,
since the torque is not directly controlled, a fast dynamic
could not be achieved. Furthermore, the implementation of
such strategies requires expensive position sensors. In [22],
hysteresis current controllers are used to drive BLDC motors.
However, the proposed control strategy requires several trans-
forms in order to synthesize the abc-frame optimum reference
currents, leading to a complicate control scheme without a
direct control of the torque.
Recently, different DTC strategies have been successfully
implemented in B6-inverter fed BLDC motor drives [23]- [26].
The DTC strategies proposed in [24], [26] consider a vector
selection table simply-reduced to the torque control with a
two-phase conduction mode during sectors and three-phase
conduction mode during sector-to-sector commutations.
Concerning the DTC of BLDC drives fed by reduced-
structure inverters, the most recent and high-performance
strategy reported in the literature has been developed by
Ozturk et al. [27]. It deals with the DTC of BLDC motors
with a B4-inverter in the armature. The proposed DTC strategy
considers a vector selection sub-table that enables the indepen-
dent control of the electromagnetic torques developed by the
phases connected to the inverter legs during their simultaneous
conduction.
However, it has been reported in [24] that the two-phase
conduction mode is penalized by high torque ripple during
sector-to-sector commutations. To overcome this drawback,
the three-phase conduction mode has been temporarily consid-
ered during sector-to-sector commutations. The present work
develops this approach in the case of B4-inverter fed BLDC
motor drives under DTC.

2. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 2
ia
ea
ib
eb
ic
ec
Ha
Hb
Hc
SectorHallEffectSignalsPhaseCurrentsandBack-EMFs
I II III IVIV V VI
π/6 π/2 5π/6 7π/6 3π/2 11π/6 2π
Fig. 1. BLDC motor phase currents and back-EMFs and the corresponding
Hall-effect signals in the case of a anticlockwise rotation with a maximum
torque production.
II. STUDY BACKGROUND: BLDC OPERATION ANALYSIS
PRIOR TO DTC IMPLEMENTATION
Permanent magnet brushless DC (BLDC) motors with trape-
zoidal back-EMFs are suitably fed by 120◦
-rectangularly-
shaped currents that should be synchronized with the back-
EMFs in order to develop a constant electromagnetic torque
with reduced ripple. Fig. 1 shows the armature phase cur-
rents (ia, ib and ic), the trapezoidal phase back-EMFs
(ea, eb and ec), and the corresponding Hall-effect signals
(Ha, Hb and Hc).
The armature phase voltages (va, vb and vc) are expressed
as follows:



va = Ria + Ldia
dt
+ ea
vb = Rib + Ldib
dt
+ eb
vc = Ric + Ldic
dt
+ ec
(1)
where R and L are the armature resistance and self-inductance,
respectively.
The electromagnetic torque Tem is expressed in terms of the
phase back-EMFs and currents, and the speed Ω, as follows:
Tem =
eaia + ebib + ecic
Ω
(2)
A. Case of a B6-Inverter in the Armature
Let us consider the case where the voltage source inverter
feeding the BLDC motor is a B6-inverter, as illustrated in
Fig. 2. As far as the BLDC motor operation is characterized
by sequences where both IGBTs of a leg could be turned off
simultaneously, the states of the power switches have to be
a
b
c
O
2
Vdc
2
Vdc
S1S5 S3
S2S6 S4
BLDC
Motor
Fig. 2. B6-inverter fed BLDC motor drive connections.
TABLE I
CASE OF B6-INVERTER UNDER TWO-PHASE CONDUCTION MODE:
SWITCHING STATES, AVERAGE PHASE VOLTAGES, THEIR Clarke
COMPONENTS AND CORRESPONDING ACTIVE VOLTAGE VECTORS
(S123456) va vb vc Vα Vβ Vi
(100001)
Vdc
2 0 -
Vdc
2
√
3Vdc
2
√
2
Vdc
2
√
2
V1
(001001) 0
Vdc
2 -
Vdc
2 0
Vdc√
2
V2
(011000) -
Vdc
2
Vdc
2 0 -
√
3Vdc
2
√
2
Vdc
2
√
2
V3
(010010) -
Vdc
2 0
Vdc
2 -
√
3Vdc
2
√
2
-
Vdc
2
√
2
V4
(000110) 0 -
Vdc
2
Vdc
2 0 -
Vdc√
2
V5
(100100)
Vdc
2 -
Vdc
2 0
√
3Vdc
2
√
2
-
Vdc
2
√
2
V6
represented by six binary variables S1 to S6, where the binary
“1” corresponds to an ON-state and the binary “0” indicates
an OFF-state.
1) Operation under Two-Phase Conduction Mode: Let us
call V1, V2, V3, V4, V5 and V6 the six active volt-
age vectors generated by the B6-inverter under two-phase
conduction mode. The corresponding switching combinations
(S1S2S3S4S5S6) which are equal to (100001), (001001),
(011000), (010010), (000110) and (100100), respectively,
where, from left to right, the binary values denote the state of
the upper and lower switching signals corresponding to phase-
a, phase-b, and phase-c, respectively.
Let us apply the Clarke transform to the average phase
voltages, such that:



Vα
Vβ


 =
2
3



1 −1
2 − 1
2
0
√
3
2 −
√
3
2






va
vb
vc


 (3)
Then, one can characterize the BLDC motor drive operation,
under two-phase conduction mode, considering the previous
switching combinations, as given in Table I. It should be
noted that the phase voltages va, vb and vc correspond to
their average values during a given sequence. Beyond the
two phases under conduction with their voltages equal to
(-Vdc
2 , Vdc
2 ), the voltage of the inactive phase is equal to its
back-EMF. This latter varies linearly with a null average value
during the corresponding sequence. The resulting six active
voltage vectors are represented in the α-β plane as illustrated
in Fig. 3.

3. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 3
V1
V2
V3
V4
V5
α
V6
β
Fig. 3. Active voltage vectors generated by the B6-inverter in the two-phase
conduction mode.
TABLE II
CASE OF B6-INVERTER UNDER THREE-PHASE CONDUCTION MODE:
SWITCHING STATES, AVERAGE PHASE VOLTAGES, THEIR Clarke
COMPONENTS AND CORRESPONDING ACTIVE VOLTAGE VECTORS
(S123456) va vb vc Vα Vβ Ui
(010101) 0 0 0 0 0 U0
(100101)
2Vdc
3 -
Vdc
3 -
Vdc
3
√
2Vdc√
3
0 U1
(101001)
Vdc
3
Vdc
3 -
2Vdc
3
Vdc√
6
Vdc√
2
U2
(011001) -
Vdc
3
2Vdc
3 -
Vdc
3 -
Vdc√
6
Vdc√
2
U3
(011010) -
2Vdc
3
Vdc
3
Vdc
3 -
√
2Vdc√
3
0 U4
(010110) -
Vdc
3 -
Vdc
3
2Vdc
3 -
Vdc√
6
-
Vdc√
2
U5
(100110)
Vdc
3 -
2Vdc
3
Vdc
3
Vdc√
6
-
Vdc√
2
U6
(101010) 0 0 0 0 0 U7
2) Operation under Three-Phase Conduction Mode: Re-
ferring to [24], a reduction of the torque ripple during sector-
to-sector commutations is gained thanks to the three-phase
conduction mode, under which the B6-inverter generates six
active voltage vectors U1, U2, U3, U4, U5 and U6. The
corresponding switching combinations (S1S2S3S4S5S6) are
equal to (100101), (101001), (011001), (011010), (010110)
and (100110), respectively. Taking into consideration the
previous combinations, and applying the Clarke transform,
the BLDC motor drive operation could be characterized as
given in Table II. The resulting six active voltage vectors are
represented in the α-β plane, as depicted in Fig. 4. In the
case of three-phase conduction, the B6-inverter generates two
null voltage vectors U0 and U7 which are achieved by the
combinations (010101) and (101010), respectively as shown
in Table II. While in the case of two-phase conduction mode
different null vectors noted V0 could be generated by the B6-
inverter. These correspond to an ON-state of just one binary
variable among the six ones, or to an OFF-state of all binary
variables.
U1
U2U3
U4
U5
α
β
U6
Fig. 4. Active voltage vectors generated by the B6-inverter in the three-phase
conduction mode.
a
c
b
BLDC
Motor
O
2
Vdc
2
Vdc
S1S3
S2S4
Fig. 5. B4-inverter fed BLDC motor drive connections.
B. Case of a B4-Inverter in the Armature
This section deals with the description and the operation
basis of the B4-inverter fed BLDC motor drive. Fig. 5 shows
the connections of the drive with two phases (phase-a and
phase-b) of the BLDC motor supplied through the B4-inverter
legs while the third one (phase-c) is linked to middle point of
the DC-bus voltage.
1) Operation under Two-Phase Conduction Mode: Let us
call V1, V2, V3 and V4 the four active voltage vectors gen-
erated by the B4-inverter under two-phase conduction mode.
The corresponding switching combinations (S1S2S3S4) which
are equal to (1000), (0010), (0100) and (0001), respectively,
where, from left to right, the binary values denote the state
of the upper and lower switching signals corresponding to
phase-a and phase-b, respectively. These combinations yield
four operating sequences characterized by the conduction of
phase-c.
The two remaining sequences are characterized by the si-
multaneous conduction of phase-a and phase-b, and inevitably
of phase-c, leading to a three-phase conduction mode. Fol-
lowing the application of the Clarke transform to the average
phase voltages, a characterization of the B4-inverter fed BLDC
motor drive under two-phase conduction mode is given in
Table III. The resulting active voltage vectors are illustrated
in Fig. 6.

4. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 4
TABLE III
CASE OF B4-INVERTER UNDER TWO-PHASE CONDUCTION MODE:
SWITCHING STATES, AVERAGE PHASE VOLTAGES, THEIR Clarke
COMPONENTS AND CORRESPONDING ACTIVE VOLTAGE VECTORS
(S1234) va vb vc Vα Vβ Vi
(1000)
Vdc
4 0 -
Vdc
4
√
3Vdc
4
√
2
Vdc
4
√
2
V1
(0010) 0
Vdc
4 -
Vdc
4 0
Vdc
2
√
2
V2
(0100) -
Vdc
4 0
Vdc
4 -
√
3Vdc
4
√
2
-
Vdc
4
√
2
V3
(0001) 0 -
Vdc
4
Vdc
4 0 -
Vdc
2
√
2
V4
V1
V2
V3
V4
α
β
Fig. 6. Active voltage vectors generated by the B4-inverter in the two-phase
conduction mode.
TABLE IV
CASE OF B4-INVERTER UNDER THREE-PHASE CONDUCTION MODE:
SWITCHING STATES, AVERAGE PHASE VOLTAGES, THEIR Clarke
COMPONENTS AND CORRESPONDING ACTIVE VOLTAGE VECTORS
(S1234) va vb vc Vα Vβ Ui
(1001)
Vdc
2 -
Vdc
2 0
√
3Vdc
2
√
2
-
Vdc
2
√
2
U1
(1010)
Vdc
6
Vdc
6 -
Vdc
3
Vdc
2
√
6
Vdc
2
√
2
U2
(0110) -
Vdc
2
Vdc
2 0 -
√
3Vdc
2
√
2
Vdc
2
√
2
U3
(0101) -
Vdc
6 -
Vdc
6
Vdc
3 -
Vdc
2
√
6
-
Vdc
2
√
2
U4
2) Operation under Three-Phase Conduction Mode: The
three-phase conduction mode is characterized by the com-
binations during which each leg of the B4-inverter has an
IGBT in the ON-state, such that: (1001), (1010), (0110), and
(0101), with the respective active voltage vectors, noted U1,
U2, U3 and U4. Following the application of the Clarke
transform, with the previous combinations accounted for, has
led to a characterization of the BLDC motor drive operation
under three-phase conduction mode as given in Table IV. The
resulting active voltage vectors are located in the α-β plane
as illustrated in Fig. 7.
U3
α
β
U1
U2
U4
Fig. 7. Active voltage vectors generated by the B4-inverter in the three-phase
conduction mode.
Two-Level
Torque
Controller
ia
Tem
Tem
*
cτ
a
c
b
BLDC
Motor
-+-
+
O
2
Vdc
2
Vdc
S1S3
S2S4
Speed
Estimator
Ha Hb Hc
Back-EMF
Constant
Lookup Table
ka
ib
*
Sector
Selector
Torque
Estimator
Speed
Controller
(PI)
Vector
Selection
Table
kb
kc
Fig. 8. Implementation scheme of a DTC strategy of B4-inverter fed BLDC
motor drives inspired from the one considering the case where the BLDC
motor is fed by a B6-inverter.
III. DTC OF B4-INVERTER FED BLDC MOTOR DRIVES
A. Study Statement
Taking into account the operation basis of BLDC motor
drives treated in the preceding section, a DTC strategy ded-
icated to these drives in the case of a B4-inverter in the
armature could be inspired from the one considering the case
where the motor is fed by a B6-inverter. The implementation
scheme of such a DTC strategy is shown in Fig. 8.
One can notice that the implementation scheme does not
include a flux loop, and that the identification of the sectors
in the α-β plane is achieved considering appropriate com-
binations of the Hall-effect signals, as given in Table V.
Moreover, these signals enable the speed estimation and hence
a sensorless control. The speed estimation assumes that the
velocity remains constant during a given sector with an open-
ing of π
3 and is equal to the average one in the previous sector.
The resulting algorithm is expressed as follows:
Ωk =
π
3
P∆tk−1
(4)
where P is the pole pair number of the BLDC motor and
∆tk−1 is the time interval spend to cross the preceding sector.

5. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 5
TABLE V
IDENTIFICATION OF THE SIX SECTORS IN THE α-β PLANE BASED ON THE
Hall-EFFECT SIGNALS
(Habc) (1 1 0) (0 1 0) (0 1 1) (0 0 1) (1 0 1) (1 0 0)
Sector I II III IV V VI
V1
V2
U3
V3
V4
α
β
U1
III
VI
II
V
U2
U4
IIV
Fig. 9. Subdivision of the α-β plane in six sectors limited by the four vectors
yielded by the two-phase conduction mode and the two larger ones yielded
by the three-phase conduction mode.
TABLE VI
VECTOR SELECTION TABLE OF A DTC STRATEGY DEDICATED TO
B4-INVERTER FED BLDC MOTOR DRIVES INSPIRED FROM THE ONE
CONSIDERING THE CASE WHERE THE BLDC IS FED BY A B6-INVERTER
cτ +1 −1
Sector I V2 (0010) V4 (0001)
Sector II U3 (0110) U1 (1001)
Sector III V3 (0100) V1 (1000)
Sector IV V4 (0001) V2 (0010)
Sector V U1 (1001) U3 (0110)
Sector VI V1 (1000) V3 (0100)
The estimation of the electromagnetic torque is based on
equation (2), as follows:
Tem = (ka − kc)ia + (kb − kc)ib (5)
where ka, kb and kc are back-EMF normalized functions,
obtained by interpolation and saved in a lookup table.
Considering the subdivision of the α-β plane in six sectors,
as illustrated in Fig. 9, and accounting for the output cτ of
the two-level hysteresis torque controller, the vector selection
table can be synthesized considering both anti- and clockwise
rotations of the BLDC motor, as given in Table VI.
Referring to Table VI, one can notice that in sectors II and V,
the BLDC motor operates under three-phase conduction mode.
Although these sectors are characterized by the conduction of
phase-a and phase-b, there is always current flowing through
phase-c due to its back-EMF and its continual connection
to the DC-bus. Thus, phase-c behaves as a generator which
produces a torque opposite to the ones of phase-a and phase-b.
Consequently, their currents turn to be temporarily distorted
by undesirable surges in order to generate the required torque.
TABLE VII
VECTOR SELECTION SUB-TABLE ADOPTED IN [27] TO REDUCE THE
DISTORTION OF THE MOTOR PHASE CURRENT IN SECTORS II AND V
cτa +1 −1
cτb +1 −1 +1 −1
Sector II U3 (0110) U4 (0101) U2 (1010) U1 (1001)
Sector V U1 (1001) U2 (1010) U4 (0101) U3 (0110)
Referring to [27], it has been found that a reduction of
the current distortion during sectors II and V can be gained
through an independent control of the torques Tema and Temb
developed by phase-a and phase-b, respectively, instead of the
motor overall torque Tem. To do so, Ozturk et al. proposed an
approach consisting in substituting the control combinations
adopted in sectors II and V of Table VI, by the vector selection
sub-table given in Table VII, where cτa and cτb are the outputs
of the two-level hysteresis controllers of Tema and Temb
,
respectively.
B. Proposed DTC Strategy
The present work introduces a new DTC strategy which
exhibits a capability to reduce the torque ripple during sector-
to-sector commutations. These have been focused by Zhu and
Leong [24], considering the case where the BLDC motor is
fed by a B6-inverter. They proposed an approach consisting
in the application of active voltage vectors corresponding to
the three-phase conduction mode, at the beginning of each
sector in order to force the current in the turned-OFF phase to
flow through a controllable IGBT instead of an uncontrollable
freewheeling diode. Thus, the rising rate |di/dt| of the current
in the turned-OFF phase is regulated in an attempt to make it
similar to the one of the current in the turned-ON phase.
In [24], the application of the above-described approach has
been limited to high speed operation with the DC-link voltage
Vdc is lower than four time the peak value E of the back-EMF
waveform (Vdc < 4E). With this condition accounted for,
the following limitations have been noticed:
• the rising rates (|dia/dt|, |dib/dt| and |dic/dt|) of the
phase currents depend on three variables, such that: (i)
the DC-link voltage Vdc, (ii) the back-EMF peak value E
and (iii) the self-inductance L. Therefore, the rising and
the falling times ∆t of the phase currents depend on their
peak value I which is directly linked to the load torque Tl.
It has been found that, although at high speed operation
(Vdc < 4E), an irregular phenomenon is associated to
the falling of the electromagnetic torque during sector-
to-sector commutations especially for low values of the
peak current I and the self-inductance L. Furthermore,
it has been noted that, during torque acceleration or
deceleration, the rising and falling times ∆t of the phase
currents are variables which affects the electromagnetic
torque by remarkable dips,
• the above-described approach requires an instantaneous
measurement of the DC-link voltage Vdc especially in
electric and hybrid propulsion systems where the DC-bus
is achieved by a battery pack.

6. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 6
Four-Level
Torque
Controller
ia
Tem
Tem
*
cτ
-+
ka
ib
Torque
Estimator
kb
kc
cτa cτb
0.5
Tema
+
Temb
-+
Vector Selection
Table and
Sub-Tables
Two-Level
Torque
Controller
Two-Level
Torque
Controller
ka kb
from sector selector block
-
Phase-b
Torque
Estimator
Phase-a
Torque
Estimator
Fig. 10. Changes in the implementation scheme corresponding to the proposed DTC strategy.
In what follows, an alternative is proposed to eradicate the
above-described limitations. It consists in the substitution of
the two-level torque controller by a four-level one. In fact, the
positive high level cτ = +2 of the torque hysteresis controller
is systematically activated when the torque falls during sector-
to-sector commutations in the case of an anticlockwise rotation
(Tem > 0), whereas its negative high level cτ = −2 is
systematically activated when the torque falls during sector-
to-sector commutations in the case of a clockwise rotation
(Tem < 0). The low levels cτ = ±1 are applied during the
whole cycle except for the torque dips taking place during
sector-to-sector commutations.
Accounting for the reference phase currents shown in Fig. 1,
it should be underlined that the proposed approach is useless
during the commutations from sector I to sector II and from
sector IV to sector V in the case of an anticlockwise rotation,
and from sector III to sector II and from sector VI to sector V
in the case of a clockwise rotation, due to the fact that |dic/dt|
is uncontrollable.
With this said, the proposed DTC strategy exhibits a capa-
bility to reduce the torque ripple during sector-to-sector com-
mutations without any dependency of Vdc, I, ∆t and L. The
resulting changes in the implementation scheme concern just
the blocks surrounded by the dashed line in Fig. 8. These turn
to be as illustrated in Fig. 10. Taking into consideration both
anti- and clockwise rotations, the proposed vector selection
sub-tables are provided in Tables VIII and IX, respectively.
IV. EXPERIMENTAL VALIDATION: A COMPARATIVE STUDY
This section deals with an experimentally-based comparison
between the DTC strategies treated in section III, such that:
• DTC-1: strategy inspired from the one considering the
case where the BLDC motor is fed by a B6-inverter,
• DTC-2: strategy developed in [27],
• DTC-3: proposed strategy.
TABLE VIII
VECTOR SELECTION SUB-TABLE DURING SECTOR-TO-SECTOR
COMMUTATIONS IN THE CASE OF AN ANTICLOCKWISE ROTATION
cτ +2
Sector VI → Sector I U2 (1010)
Sector II → Sector III U3 (0110)
Sector III → Sector IV U4 (0101)
Sector V → Sector VI U1 (1001)
TABLE IX
VECTOR SELECTION SUB-TABLE DURING SECTOR-TO-SECTOR
COMMUTATIONS IN THE CASE OF A CLOCKWISE ROTATION
cτ −2
Sector II → Sector I U1 (1001)
Sector I → Sector VI U4 (0101)
Sector V → Sector IV U3 (0110)
Sector IV → Sector III U2 (1010)
The study firstly considers the investigation of the steady-
state features of the B4-inverter fed BLDC motor drive under
DTC-1. These are compared to the steady-state features ob-
tained under DTC-3 considering the same operating speed.
Then, the investigation of the features of the B4-inverter fed
BLDC motor drive under DTC-3 is extended to low speed
operation as well as to the transient behavior. Finally, a com-
parison between DTC-2 and DTC-3 is carried out considering
sector-to-sector commutations.
The BLDC motor under study presents the ratings and
parameters given in Tables X and XI, respectively. The
experiments have been carried out using a test bench built
around a TMS320F240 DSP-based digital controller.

7. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 7
TABLE X
BLDC MOTOR RATINGS
Power 600W Speed 2500rpm
DC-link voltage 24V Current 30A
Torque 2.3N.m PM flux-linkage 14mWb
TABLE XI
BLDC MOTOR PARAMETERS
Phase resistance Self-inductance Pole pair number Inertia
R = 0.2Ω L = 0.3mH P = 3 J = 4.1g.m2
a
c
b
O
2
Vdc
2
Vdc
S1S3
S2S4
Ha Hb Hc
Grid
PowerSystemControlSystem
Current
Sensors
Interface
Board
Connector
Panel
dSPACE
1104 Board
dSPACE
Control Desk
Matlab Simulink
DTC Strategy
PC
Scope
BLDC
Motor
Fig. 11. Schematic block diagram of the developed test bench.
A schematic block diagram of the test bench is shown
in Fig. 11. The sampling period Ts is equal to 55µs. The
hysteresis band of the torque controller is equal ±0.012N.m
for cτ = ±1 and ±0.036N.m for cτ = ±2. The speed
controller constants are Kp=0.06 and Ki=0.05.
A. Comparison Between DTC-1 and DTC-3
Fig. 12 shows selected steady-state electrical features
of the B4-inverter fed BLDC motor drive under DTC-1
(subscript “1”) and DTC-3 (subscript “2”) for a speed
Ω=+120rad/s. One can notice the following remarks:
• referring to Figs. 12.a1 and 12.a2, the phase-a to phase-b
voltage uab in sectors I, III, IV, and VI is almost the same
under DTC-1 and DTC-3, with:
uab = ±Vdc
4 − eb when the current flows through
phase-a and phase-c,
uab = ±Vdc
4 + ea when the current flows through
phase-b and phase-c.
However in sectors II and V, uab commutates between
±Vdc under DTC-1, and between −Vdc, 0, and +Vdc
under DTC-3,
• the phase-c current ic measured under DTC-1 is totally
out of control during sectors II and V as illustrated in
Fig. 12.d1, while it is almost regulated around zero under
DTC-3 as shown in Fig. 12.d2,
• Figs. 12.b1 and 12.c1 show that the distortion of ic during
sectors II and V greatly affects ia during the first half
of these sectors, and ib during their second half. The
distortion of ia and ib has been reduced in DTC-3 as
shown in Figs. 12.b2 and 12.c2.
The comparison between strategies DTC-1 and DTC-3 is
extended to some selected steady-state electromagnetic fea-
tures. These concern the waveforms of the current, the back-
EMF and the torque of the controlled phase-a and of the
uncontrolled phase-c. The features measured following the
implementations of DTC-1 and DTC-3 are shown in Fig. 13
and Fig. 14, respectively.
From the analysis of these results, it clearly appears that,
under DTC-1, the phase-c back-EMF ec and current ic have
opposite signs, during sectors II and V, as illustrated in
Fig. 13.d. That is to say that phase-c behaves like a generator
which develops a negative electromagnetic torque Temc , as
illustrated in Fig. 13.e. This makes phase-a and phase-b pull
more current from the source to compensate the lack of torque
caused by phase-c, as illustrated in Figs. 13.b, and 13.c.
These limitations have been almost discarded following the
implementation of DTC-3. Indeed, one can notice that:
• the average value of Temc
turns to be null during sectors
II and V, as illustrated in Fig. 14.e,
• the distortion of ia and ib and the resulting ripple penal-
izing Tema
+Temb
have been almost eradicated, as shown
in Figs. 14.b and 14.c,
• the high dips affecting the overall torque Tem during
sectors II and V have been damped, as depicted in
Fig. 14.f.
The investigation of the performance of the B4-inverter fed
BLDC motor drive under DTC-3 has been expended to:
• the low speed steady-state operation. Fig. 15 shows the
results measured for Ω=+25rad/s. One can notice that the
distorsion of ic turns to be high during sectors II and V,
but remains lower than the one under DTC-1,
• the transient behavior considering both load and no-
load operations as illustrated in Fig. 16, considering the
following steps:
1) starting from a steady-state no-load operation at a
reference speed of +50rad/s,
2) a ramp-shaped increase of the speed to reach
+100rad/s,
3) the application of a load torque Tl proportional to
the speed at almost 10s,
4) a ramp-shaped decrease of the speed to reach
+30rad/s, with the load torque maintained.
Once more, one can notice that the distorsion of ic during
sectors II and V is higher at low speed especially at load
operation.
B. Comparison Between DTC-2 and DTC-3
As far as the improvement gained by the proposed DTC
strategy concerns the sector-to-sector commutations, except
those involving sectors II and V, the comparison between
DTC-2 and DTC-3 is based on zoomed views of the currents
ia and ib as well as the overall torque Tem, during the commu-
tation from sector III to sector IV. The obtained measurements
are illustrated in Fig. 17.

8. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 8
(a1) (b1) (c1) (d1)
(a2) (b2) (c2) (d2)
Fig. 12. Steady-state electrical features of the B4-inverter fed BLDC motor drive under DTC-1 (subscript “1”) and DTC-3 (subscript “2”) for a speed
Ω=+120rad/s. Legend: (a) phase-a to phase-b voltage uab (50V/div) and phase-a current ia (10A/div), (b) phase-a and phase-b currents ia and ib (10A/div),
(c) sector succession (2 sectors/div) and phase-a current ia (10A/div), (d) sector succession (2 sectors/div) and phase-c current ic (10A/div).
(a) (b) (c)
(d) (e) (f)
Fig. 13. Steady-state electromagnetic features of the B4-inverter fed BLDC motor drive under DTC-1 for a speed Ω=+120rad/s. Legend: (a) phase-a back-
EMF ea (2V/div) and current ia (10A/div), (b) sector succession (2 sectors/div) and phase-a torque Tema (0.5N.m/div), (c) sector succession (2 sectors/div)
and the sum of phase-a and phase-b torques Tema + Temb (0.5N.m/div), (d) phase-c back-EMF ec (2V/div) and current ic (10A/div), (e) sector succession
(2 sectors/div) and phase-c torque Temc (0.5N.m/div), (f) sector succession (2 sectors/div) and the overall torque Tem (0.5N.m/div).
Referring to Fig. 17.a1, one can clearly notice that the rising
rates |dia/dt| and |dib/dt| under DTC-2 are totally different
during the sector-to-sector commutation, while they are almost
similar under DTC-3 as illustrated in Fig. 17.a2.
Moreover, comparing the results of Figs. 17.b1 and 17.b2,
it is to be noted that the torque dip penalizing DTC-2 during
the sector-to-sector commutation has been damped following
the implementation of DTC-3.

9. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 9
(a) (b) (c)
(d) (e) (f)
Fig. 14. Steady-state electromagnetic features of the B4-inverter fed BLDC motor drive under DTC-3 for a speed Ω=+120rad/s. Legend: same as in Fig. 13.
(a) (b) (c) (d)
Fig. 15. Steady-state electrical features of the B4-inverter fed BLDC motor drive under DTC-3 for a speed Ω=+25rad/s. Legend: (a) ia and ib (10A/div),
(b) sector succession (2 sectors/div) and ia (10A/div), (c) sector succession (2 sectors/div) and ic (10A/div), (d) sector succession (2 sectors/div) and overall
electromagnetic torque Tem (0.5N.m/div).
(a) (b) (c) (d)
Fig. 16. Transient behavior of the B4-inverter fed BLDC motor drive under DTC-3 starting from a steady-state no-load operation at +50rad/s followed by an
increase of the speed to reach +100rad/s, then the application of a load torque Tl proportional to the speed, finally a decrease of the speed to reach +30rad/s
with the load torque maintained. Legend: (a) reference torque (0.2N.m/div) in the top and the estimated speed Ω (50rad/s/div) in the bottom, (b), (c), and
(d) ia in the top and ic in the bottom (10A/div), at no-load operation and Ω=+50rad/s, Tl=+0.3N.m and Ω=+100rad/s, and Tl=+0.06N.m and Ω=+30rad/s,
respectively.

10. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 10
(a1) (b1)
(a2) (b2)
Fig. 17. Zoomed currents ia in phase-a and ib in phase-b as well as the electromagnetic torque Tem of the B4-inverter fed BLDC motor drive under DTC-2
(subscript “1”) and DTC-3 (subscript “2”), during the commutation from sector III to sector IV. Legend: (a) ia in the top and ib in the bottom (10A/div), (b)
sector succession (2 sectors/div) and the electromagnetic torque Tem (0.5N.m/div).
TABLE XII
COMPARISON BETWEEN THE CONTROL SCHEME COMPLEXITY AND THE
TORQUE RIPPLE OF THE THREE DTC STRATEGIES
comparison criteria
control torque ripple
scheme in sectors into sectors
I,III,IV&VI II&V I,III,IV&VI II&V
DTC-1 simple low high medium high
DTC-2 +/-complex low low medium medium
DTC-3 +/-complex low low low medium
C. Comparison Study: a Synthesis
Accounting for the results discussed in the two preceding
sections, one can make a synthesis regarding the compari-
son between the three developed DTC strategies. From the
hardware point of view, these involve the same topology. The
differences concern exclusively the control system. For the
sake of their classification in terms of control scheme and
torque quality, three major criteria have been selected, such
that:
• the control scheme complexity,
• the torque ripple amplitude with two distinguished cases:
– operation within a sector,
– operation during sector-to-sector commutation.
The obtained results are given in Table XII.
V. CONCLUSION
The paper was aimed at a comparative study between three
direct torque control (DTC) strategies dedicated to BLDC
motor drives fed by a four-switch inverter, also known asB4-
inverter. The considered DTC strategies are described as
follows:
• DTC-1 which is inspired from the one intended to the
control of B6-inverter fed BLDC motor drives,
• DTC-2 that considers a dedicated vector selection sub-
table in order to independently control the torques de-
veloped by the phases connected to the B4-inverter legs
during their simultaneous conduction,
• DTC-3 which has been proposed in this work, in order
to eradicate the torque dips, penalizing DTC-2 during
sector-to-sector commutations. This has been achieved by
balancing the rising rates of the two controlled currents
of the BLDC motor.
Within the study background, the operation basis of the
BLDC motor have been recalled considering both cases of B6-
and B4-inverters in the armature with emphasis on the two-
and three-phase conduction modes. Then, the vector selection
tables and sub-tables (if any) of the three DTC strategies under
comparison have been synthesized as optimally as possible in
an attempt to reduce the torque ripple.

11. Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
IEEE TRANSACTIONS ON POWER ELECTRONICS , VOL.29, NO. , 2014 11
The study has been achieved by an experimentally-based
comparison considering, in a first step, the BLDC motor
steady-state operation under DTC-1 and DTC-3. Then, a spe-
cial attention has been paid to the comparison of the BLDC
motor performance under DTC-2 and DTC-3, during sector-
to-sector commutations. It has been clearly shown that B4-
inverter fed BLDC motor drives exhibit, under DTC-3, high
performance with reduced torque ripple. Further comparison
criteria shall be considered in the future. Of particular interest
are acoustic noise and vibration which are of great importance
in many applications such as electric and hybrid propulsion
systems in so far as the passenger comfort is concerned.
REFERENCES
[1] I. Takahashi, and T. Noguchi, “A new quick-response and high-efficiency
control strategy of an induction motor”, IEEE Trans. Ind. Appl., vol. 22,
no. 5, pp. 820-827, 1986.
[2] A. Taheri, A. Rahmati, and S. Kaboli, “Efficiency improvement in DTC
of six-phase induction machine by adaptive gradient descent of flux”,
IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1552-1562, 2012.
[3] A. B. Jidin, N. R. B. N. Idris, A. H. B. M. Yatim, M. E. Elbuluk, and T.
Sutikno, “A wide-speed high torque capability utilizing overmodulation
strategy in DTC of induction machines with constant switching frequency
controller”, IEEE Trans. Power Electron., vol. 27, no. 5, pp. 2566-2575,
2012.
[4] B. Metidji, N. Taib, L. Baghli, T. Rekioua, and S. Bacha, “Low-cost direct
torque control algorithm for induction motor without AC phase current
sensors”, IEEE Trans. Power Electron., vol. 27, no. 9, pp. 4132-4139,
2012.
[5] B. El Badsi, B. Bouzidi, and A. Masmoudi, “Bus-clamping-based DTC:
an attempt to reduce harmonic distortion and switching losses”, IEEE
Trans. Ind. Electron., vol. 60, no. 3, pp. 873-884, 2013.
[6] S. Ziaeinejad, Y. Sangsefidi, H. P. Nabi, and A. Shoulaie, “Direct torque
control of two-phase induction and synchronous motors”, IEEE Trans.
Power Electron., vol. 28, no. 8, pp. 4041-4050, 2013.
[7] K. B. Lee, and F. Blaabjerg, “Sensorless DTC-SVM for induction motor
driven by a matrix converter using a parameter estimation strategy”, IEEE
Trans. Ind. Electron., vol. 55, no. 2, pp. 512-521, 2008.
[8] K. D. Hoang, Z. Q. Zhu, and M. P. Foster, “Influence and compensation of
inverter voltage drop in direct torque-controlled four-switch three-phase
PM brushless AC drives”, IEEE Trans. Power Electron., vol. 26, no. 8,
pp. 2343-2357, 2011.
[9] Y. Zhang, J. Zhu, Z. Zhao, W. Xu, and D. G. Dorrell, “An improved direct
torque control for three-level inverter-fed induction motor sensorless
drive”, IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1502-1513, 2012.
[10] B. El Badsi, “Six-switch inverter emulation based DTC strategy dedi-
cated to three-switch inverter-fed induction motor drives”, Computation
and Mathematics in Electrical and Electronic Engineering (COMPEL),
vol. 32, no. 1, pp. 289-301, 2013.
[11] B. El Badsi, B. Bouzidi, and A. Masmoudi, “DTC scheme for a four-
switch inverter fed induction motor emulating the six-switch inverter
operation”, IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3528-3538,
2013.
[12] H. W. Van der Breock, and J. D. Van der Wyk, “A comparative
investigation of a three-phase induction machine drive with a component
minimized voltage-fed inverter under different control options”, IEEE
Trans. Ind. Appl., vol. IA-20, no. 2, pp. 309-320, 1984.
[13] F. Blaabjerg, S. Freysson, H. H. Hansen, and S. Hansen, “A new
optimized space-vector modulation strategy for a component-minimized
voltage source inverter”, IEEE Trans. Power Electron., vol. 12, no. 4, pp.
704-714, 1997.
[14] T. S. Lee, and J. H. Liu, “Modeling and control of a three-phase four-
switch PWM voltage-source rectifier in d-q synchronous frame”, IEEE
Trans. Power Electron., vol. 26, no. 9, pp. 2476-2489, 2011.
[15] R. Wang, J. Zhao, and Y. Liu, “A comprehensive investigation of four-
switch three-phase voltage source inverter based on double fourier integral
analysis”, IEEE Trans. Power Electron., vol. 26, no. 10, pp. 2774-2787,
2011.
[16] F. Aghili, “Fault-tolerant torque control of BLDC motors”, IEEE Trans.
Power. Electron., vol. 26, no. 2, pp. 355-363, 2011.
[17] A. Stirban, I. Boldea, and G. Andreescu, “Motion-sensorless control
of BLDC-PM motor with offline FEM-information-assisted position and
speed observer”, IEEE Trans. Ind. Appl., vol. 48, no. 6, pp. 1950-1958,
2012.
[18] J. Fang, X. Zhou, and G. Liu, “Instantaneous torque control of small
inductance brushless DC motor”, IEEE Trans. Power. Electron., vol. 27,
no. 12, pp. 4952-4964, 2012.
[19] C. S. Joice, S. R. Paranjothi, and V. J. S. Kumar, “Digital control
strategy for four quadrant operation of three phase BLDC motor with
load variations”, IEEE Trans. Ind. Appl., vol. 9, no. 2, pp. 974-982, 2013.
[20] D. Grenier, L. A. Dessaint, O. Akhrif, and J. P. Louis, “A Park-
like transformation for the study and the control of a nonsinusoidal
brushless DC motor”, Proc. IEEE IECON, Industrial Electron. Control,
and Instrumentation, vol. 2, no. 2, pp. 836-843, Nov. 6-10, 1995.
[21] F. Bodin, and S. Siala, “New reference frame for brushless DC motor
drive”, Proc. IEEE PEVD Annu. Meeting, Power Electronics and Variable
Speed Drives, Conf. Publ. no. 456, pp. 554-559, 1998.
[22] P. J. Sung, W. P. Han, L. H. Man, and F. Harashima, “A new approach for
minimum-torque-ripple maximum-effeciency control of BLDC motor”,
IEEE Trans. Ind. Electron., vol. 47, no. 1, pp. 109-114, 2000.
[23] S. B. Ozturk, and H. A. Toliyat, “Direct torque and indirect flux control
of brushless DC motor”, IEEE Trans. Mechatronics, vol. 16, no. 2, pp.
351-360, 2011.
[24] Z. Q. Zhu, and J. H. Leong, “Analysis and mitigation of torsional
vibration of PM brushless AC/DC drives with direct torque controller”,
IEEE Trans. Ind. Appl., vol. 48, no. 4, pp. 1296-1306, 2012.
[25] F. Jiancheng, L. Haitao, and H. Bangcheng, “Torque ripple reduction
in BLDC torque motor with nonideal back EMF”, IEEE Trans. Power
Electron., vol. 27, no. 11, pp. 4630-4637, 2012.
[26] M. Masmoudi, B. El Badsi, and A. Masmoudi, “Direct torque control
of brushless DC motor drives with improved reliability”, in Conf. Rec.
8th Inter. Conf. and Exhibition on Ecological Vehicles and Renewable
Energies (IEEE Digital Object Identifier: 10.1109/EVER.2013.6521562),
Monte Carlo, Monaco, March 2013.
[27] S. B. Ozturk, W. C. Alexander, and H. A. Toliyat, “Direct torque control
of four-switch brushless DC motor with non-sinusoidal back EMF”, IEEE
Trans. Power Electron., vol. 25, no. 2, pp. 263-271, 2010.
Mourad Masmoudi received the BS in 1993 from the
Ecole Normale Suprieure de l’Enseignement Technique
of Tunis, Tunisia, and the MS in 2004 from the Sfax
Engineering National School, University of Sfax, Tunisia,
both in electrical engineering. He has been a technologist
at the Sfax Higher Institute of Technology, Tunisia, since
2004. Mr Mourad Masmoudi is a member of the Research
Laboratory of Renewable Energies and Electric Vehicles
of the University of Sfax where he is preparing his PhD in electrical
engineering. His major interests are reduced structure inverter fed brushless
motor drives applied in automotive systems.
Bassem El Badsi received the BS degree in 2004 in
Electromechanical Engineering, the MS in 2005 and the
PhD in 2009 all in Electrical Engineering, from the Sfax
Engineering National School (SENS), University of Sfax,
Tunisia. He is currently an Associate Professor of power
electronics and drives at SENS since 2009. Mr El Badsi
is a member of the Research Laboratory of Renewable
Energies and Electric Vehicles of the University of Sfax.
His major interests are the analysis and the implementation of advanced
control strategies in AC motor drives applied to automotive systems.
Ahmed Masmoudi received the BS degree from Sfax
Engineering National School (SENS), University of Sfax,
Tunisia, in 1984, the PhD from Pierre and Marie Curie
University, Paris, France, in 1994, and the Research
Management Ability degree from SES, in 2001, all in
electrical engineering. In 1988, he joined the Tunisian
University where he held different positions involved in
both education and research activities. He is currently a
professor of electric power engineering at SENS and the director of the
Research Laboratory of Renewable Energies and Electric Vehicles. His main
interests include the design of new topologies of AC machines allied to the
implementation of advanced and efficient control strategies in drives and
generators, applied to automotive as well as in renewable energy systems.