2014 dtc of b4 inverter fed bldc motor

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2014 dtc of b4 inverter fed bldc motor

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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.

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