Journal of ELECTRICAL ENGINEERING, VOL. 62, NO. 3, 11, 1 6 01 01 02 02 03 PWM SWITCHING STRATEGY FOR TORQUE 03 04 04 RIPPLE MINIMIZATION IN BLDC MOTOR 05 05 06 06 07 Wael A. Salah Dahaman Ishak Khaleel J. Hammadi 07 08 08 09 09 This paper describes a new PWM switching strategy to minimize the torque ripples in BLDC motor which is based on sensored rotor position control. The scheme has been implemented using a PIC microcontroller to generate a modified Pulse 11 Width Modulation (PWM) signals for driving power inverter bridge. The modified PWM signals are successfully applied to 11 12 the next in-coming phase current such that its current rise is slightly delayed during the commutation instant. Experimental 12 13 results show that the current waveforms of the modified PWM are smoother than that in conventional PWM technique. 13 14 Hence, the output torque exhibits lower ripple contents. 14 15 K e y w o r d s: permanent magnet, brushless DC, modified PWM, sensored control, torque ripple 15 1 INTRODUCTION could typically be minimized by two techniques, first is 19 by the improved motor designs and the second is by improved 19 In conventional DC motors with brushes, the field control scheme. winding is on the stator and armature winding is on the Improved motor design techniques for pulsating torque rotor. The motor is relatively more expensive and needs minimization include skewing, fractional-slot winding, maintenance due to the brushes and accumulation of the short-pitch winding, increased number of phases, airgap windings, adjusting stator slot opening and wedges, 24 24 brush debris, dust, and commutator surface wear. Moreover in certain hazardous locations, the application of 25 rotor magnetic design through magnet pole arc, width 25 DC brushed motors is limited due to the arcing. This and positions. On the other hand, improved motor control schemes include adaptive control technique, prepro- could be solved by replacing the mechanical switching 28 components ie commutator and brushes by power electronic switches. Brushless DC (BLDC) motor has a pergrammed current waveform control, selective harmonics injection techniques, estimators and observers, speed 29 28 29 30 manent magnet rotor and a wound field stator, which is loop disturbance rejection, high speed current regulators, 30 31 connected to a power electronic switching circuit. commutation torque minimizations and automated selfcommissioning schemes [4]. 32 31 32 The BLDC control drive system is based on the feedback of rotor position, which is obtained at fixed points Minimization of torque ripple in PWM AC drives is typically every 60 electrical degrees for six-step commutations of the phase currents [1]. The BLDC motor drives presented in [5] which proposed a pulse width modulation have high efficiency, low maintenance, longer life span, (PWM) technique for minimizing the RMS torque ripple low noise, control simplicity and compact construction. in inverter-fed induction motor drives. Another study of 38 Based on the shape of the back-emf, the brushless motors can be classified to have either trapezoidal or sinu- PWM methods in permanent magnet brushless DC motor 38 speed control system is given in [6]. The study compared 40 soidal back-emf. In a BLDC motor, the permanent magnets produce an air gap flux density distribution that is methods implemented in voltage inverter PM brushless the efficiency, reliability and torque ripples of six PWM 40 41 41 of trapezoidal shape, hence, resulting in trapezoidal back- motor drives. EMF waveforms. A PWM control algorithm for eliminating torque ripple caused by stator magnetic field jump of brushless DC 43 43 The torque pulsations in PM BLDC motors are generally resulted from the deviation from ideal conditions. It motors is proposed by [7]. Reference [8] proposed a PWM 45 45 can be either related to the design factors of the motor or chopping method to improve the torque ripple for brushless DC miniature motors. The comparison of two types to the power inverter current excitation resulting in nonideal current waveforms [2]. Consequently, the undesired of switching strategies studied to reduce the torque ripple 47 47 48 48 torque pulsation in PM BLDC motor drives may lead shows that the PWM chopping method has a higher output torque and lower ripples comparing to the overlapping 49 49 to speed oscillations, resonances in mechanical portions 50 50 of the drive causing acoustic noise and visible vibration method. Reference [9] discussed the influences of PWM 51 51 patterns in high precision machines [3]. Therefore, the mode on the current generated by back-emf of switchoff phase in BLDC motor. A low cost digital control tech- 52 52 torque ripple minimization or elimination is a considerable issue in BLDC motor drives. The torque pulsations nique is proposed in [10] with a constant frequency digital 53 53 54 54 55 55 56 School of Electrical and Electronic Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang, 56 Malaysia. wael sal@eng.usm.my, dahaman@eng.usm.my, khal.dr59@yahoo.com 57 57 ISSN 13-32 c 11 FEI STU
2 W.A. Salah D. Ishak K.J. Hammadi: PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION... 01 where 01 02 v 02 a i a R S L S e a 03 R s : phase resistance, v an, v bn, v cn : phase voltages, 03 04 L s : self-inductance, i a, i b, i c : phase currents, v 04 b i b R S L S e b 05 0 n M : mutual inductance, e a, e b, e c : phase back-emfs. 05 06 06 v i c c R S L S e 07 c The equivalent circuit for the BLDC motor is shown 07 08 in Fig. 1. 08 09 Fig. 1. Brushless DC motor equivalent circuit Due to the interaction of the currents in stator windings and the magnetic field from rotor magnets, the elec- 10 09 10 11 tromagnetic torque of BLDC motor is produced as follows 11 DC Power Power Hall 12 Electric Motor Supply Converter Sensor 12 13 T e = e ai a + e b i b + e c i c (2) 13 14 ω m 14 15 15 Position / Speed Feedback 16 Controller where ω m is the mechanical speed of the rotor. The equation of motion is given by 16 Fig. 2. BLDC drive system components dω m 19 = T e T L Bω m (3) 19 dt J PWM controller, simulated and experimentally verified where for a BLDC motor drive system. T L : load torque, In [11], commutation torque ripple reduction in BLDC B : damping constant, 24 motor using PWM ON PWM mode. Reference [12] 24 J : moment of inertia of rotor shaft and load [14]. 25 presents a new method on reducing commutation torque 25 ripples generated in brushless DC motor drives based on BLDC drive system typically consists of BLDC motor, power electronics converter, hall-effect sensors and Commutation Time Control. 28 28 As mentioned above, these were several research works controller as shown in Fig. 2. 29 29 in the past decade which focused on minimizing torque For six-step motor control, at each step the instantaneous output power will be will be deliver from two phases 30 30 ripples during commutation time. However, in this paper, 31 31 a modified PWM signal is applied during the start-up of connected in series, and is given by 32 32 the commutation sequence for the incoming phase current P such that it will gradually build up and reach the targeted o = ω m T e = 2EI (4) value in order to minimize the torque ripples in BLDC where I is the current amplitude and E is the induced motor drives. The proposed method does not require any back-emf. From equations (2) and (4), the output torque additional hardware modification. can also be expressed as T e = 2kφI = 2k t I (5) 2 MATHEMATICAL MODEL OF 40 40 BLDC MOTOR DRIVE SYSTEM 41 where k t is the motor torque constant. 41 BLDC motor produces a trapezoidal back-emf, and 43 43 therefore the excited current waveform is preferably 3 ANALYSIS OF BLDC TORQUE RIPPLES rectangular-shaped. The phase resistances of the stator MOTORS DUE CURRENT COMMUTATION 45 45 windings are assumed to be equal. The self and mutual inductances are constant irrespectively of rotor position In order to minimize the torque ripples in Brushless 47 47 due to surface mounted permanent magnet rotor topology. The rotor-induced currents are neglected and the DC machines the analysis of torque curves to be performed. The constant current torque waveforms depend 48 48 49 on many parameters in which relating to design parameters [15]. 50 49 damper windings are also not present. The three phase 50 voltage equation can be expressed as in equation (1) [13]. 51 The common used commutation in 3 phase BLDC motor is the six-step, in which each phase voltage is energized 51 52 52 53 53 v an 54 v bn = R s 0 0 0 R s 0 i a for interval of 1 degree electrical according to the rotor i b + electrical position. At any sector, only one phase is energized as positive and one of the other phases is energized 54 55 v cn 0 0 R s i c 55 56 56 57 L s M 0 0 0 L s M 0 d i a i b + e a as negative in order to maintain a current path. For control the BLDC motor a typical 3 phase full bridge will be 57 e b (1) dt 0 0 L s M used for drive the motor. i c e c
Journal of ELECTRICAL ENGINEERING 62, NO. 3, 11 3 01 third phase switch will remain conducting. In this analysis 01 02 the transition of conduction from Phase A(+)/C( ) 02 03 to B(+)/C( ) will be considered as shown in Fig. 3. In 03 04 this case the phase A is the de-energized phase and phase 04 05 B will be the in-coming energized phase and phase C is 05 06 the conducting phase. 06 07 07 08 08 09 09 11 11 12 12 13 13 14 14 15 15 Fig. 5. Ideal current commutation in BLDC motors 19 19 Ideally the current in BLDC motor with trapezoidal back-emf is square in shape. Figure 4 shows the ideal current waveforms, yet practically the current in the upcoming phase takes a finite time to settle to its maximum 24 value, also the die-off phase takes a finite time to get 24 25 vanishes to zero. This period of commutation between 25 any pair of phases is relatively short comparing to the period of phase conduction. 28 28 At each 60 electrical degree, there will be 2 switches 29 29 conducting, one from high side of the phase and the other 30 30 will be from the low side. When phase A and C conducting the high side switch S1 and the low side S4 will be 31 31 32 Fig. 3. Transition of conduction from phase A to B (a) Phase 32 in ON state and current will start build up. Yet, when A conducts, (b) During commutation time between phase A,B, switch S1 turned OFF, the current will decayed through (c) Phase B conducts the freewheeling diode D0 and the switch S4, this will take i a a short time which will occur at each step. In the next I a sequence where phase B high-side with phase C low- side, the switches S1 and S4 will be in ON state. I b i b 40 0 40 T 2 T 4 PROPOSED METHOD FOR 41 41 3 3 T TORQUE RIPPLE MINIMIZATION 43 I c The commutation between the 3 phases occurred six 43 i c times per electrical revolution. As a result current ripple 45 t generated in commutation period which is the main 45 drawback of BLDC Motor. 47 Fig. 4. Ideal current waveform of 3-phase BLDC Motor In the conduction region, 2-phases are conducted 47 48 based on the position of rotor, the rotor position is usually 48 49 sensed by Hall sensors. The Hall sensors generate three 49 50 For the analysis of commutation time, the commutation signals corresponding to six states of rotor position. On 50 of the current through two phases to be considered, 51 the other hand commutation region is to be transient re- 51 52 one phase will be switched off, the second phase will replace gion which converts from the current conduction from one 52 the switched off phase and the third phase will re- 53 phase into the next one, commutation is relatively shorter 53 54 mained conducting. than conduction region, and 3-phases (rising phase, decaying 54 55 In this analysis the commutation from phase A to phase, and conducting phase) are all conducted. 55 56 phase B will be considered. The current transfer happens Conduction and commutation appears six times per one 56 during the six-step, since there is one phase to be 57 electrical rotation of the rotor [16]. The current waveform 57 switched ON while other switch will be OFF, and the during commutation is shown as in Fig. 5.
4 W.A. Salah D. Ishak K.J. Hammadi: PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION... 01 Based on the commutation events as shown in Fig. 6(a), 01 02 the modified PWM has been implemented by the microcontroller 02 03 will be applied speed-up the energized phase 03 04 current during high-speed region. In this case, the current 04 05 in the outgoing phase (phase A) would reach zero 05 06 before the current in in- coming phase (phase B) reaches 06 07 its max value. The current rates of change can be given 07 08 by 08 09 di a 09 10 dt > di b dt. (6) Fig. 6. Phase currents and torque during commutation event 10 11 Therefore, the instantaneous phase C current will peak 11 12 up slightly during this commutation time as shown in 12 13 Fig. 6(a). On the other hand, phase A current decay time 13 14 could also be possibly slower than phase B current rise 14 15 time. Because of this mismatch of decay rate of phase A 15 16 current i a and rise rate of phase B current i b, small current 16 17 dip appears in phase C current. Consequently, the 17 net torque will exhibit torque spike during the commutation 19 instances. The current rates of change are given 19 by di a dt < di b dt. (7) The proposed PWM scheme will slow-down the energized 24 phase current during low-speed region so that it 24 25 will minimize the associated torque ripple which appear 25 during the commutation interval. Referring to the two current loops during commutation, 28 which is the diode loop and the switch loop. By 28 29 assuming constant back-emf and ignoring the phase resistance, 29 30 then the phase currents rate of change During 30 31 commutation can be expressed as 31 32 32 di a dt = V dc + 2E, (8) 3L s di b dt = 2(V dc E), (9) 3L s di c dt = V dc 4E, (10) 3L s 40 where V dc is the dc link voltage. The time taken for i a 40 41 to die-off from its value I to zero will be 41 43 t f = 3L si 43 V dc + 2E. (11) 45 45 The time i b to build up from zero to its final value I : 47 3L s I 47 48 Fig. 7. Flow chart of modified PWM signals t r = 2(V 48 dc E). (12) 49 49 50 Considering the case of t f = t r, which described in Fig. 5 50 51 In practice, the rate of current rise is mismatched with where the fall time and rise time are equal, this case could 51 52 the rate of the current decay which produces torque ripples. happen when dc link voltage (V dc ) equal to 4 times of the 52 The torque ripples are critical issue in BLDC drives; 53 induced BEMF (E). 53 54 hence a lot of techniques has been introduced to minimize 54 55 the torque ripples. In this paper, a proposed technique 55 t Vdc 56 used to minimize the torque ripples in BLDC motors will r =4E = 3L s I 2(V dc E) = 3L s I 2(4E E) = L si 2E, (13) 56 57 be discussed and analyzed from the perspective of motor 57 control side. t Vdc f =4E = L si 2E. (14)
Journal of ELECTRICAL ENGINEERING 62, NO. 3, 11 5 01 01 02 02 03 03 04 04 05 05 06 06 07 07 08 08 09 09 11 11 12 12 13 13 14 14 15 15 19 19 Fig. 8. Experimental test bench the value of step time to the value of commutation time ratio. The commutation time in much smaller if compared 24 with the total phase conduction time. Figure 7 describes 24 25 the flow chart used to generate the modified PWM signals 25 implemented in the PIC microcontroller. As can clearly be seen from Fig. 7, Assign Step 28 Startup Duty block will be used to gradually delay the 28 29 build-up of current in the in-coming phase at low speed 29 30 region or speed-up current rate in high-speed region. This 30 31 will result in overcoming the tips and dips occurred during 31 phase current commutation. This is achieved via the 32 32 Fig. 9. Normal PWM control motor current and line voltage modified PWM signals preprogrammed to execute only during the commutation instants. 5 RESULTS Figure 8 shows the experimental test bench, where the 40 40 tested motor has been coupled with the torque Lorenz 41 41 sensor, and the other end of the sensor is coupled to a PM generator. 43 43 Figure 9 shows the output current and the line voltage 45 Fig. 10. Modified PWM control motor current and line voltage using the normal PWM control. While the waveforms 45 shown in Fig. 10 show the output current and line voltage 47 of the BLDC motor under the modified PWM control 47 48 And this will be considered as the average commutation technique. 48 49 time between two phases. The total conduction time of The waveform shown in Fig. 9 illustrates the phase 49 50 phase current will be t total = 2π 3 T current of brushless DC motor using conventional PWM 50 51 switching. Comparing with the waveform of the modified 51 t 52 total = t r + t cond. (15) PWM switching shown in Fig. 10, it clearly shows that 52 53 From this, the conduction time of the phase will be the ripple in current waveform is minimized, thus it will 53 54 54 55 t cond = 2π 55 56 3 L result in smother output torque with a minimum torque si 2E. (16) ripples. Figure 11 shows a comparison of the generated output 56 57 The proposed method will be based on applying the torque using both types of control. It is obvious that by 57 modified PWM at the interval whereas it proportional to adopting the modified PWM technique will produce a
6 W.A. Salah D. Ishak K.J. Hammadi: PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION... 01 smoother output torque; result in a visible reduction of [4] HOLTZ, J. SPRINGOB, L.: Identification and Compensation 01 02 the torque ripples. of Torque Ripple in High-Precision Permanent Magnet Motor 02 Drives, Industrial Electronics, IEEE Transactions on 43 (1996), 03 03 309 3. 04 04 [5] BASU, K. et al : Minimization of Torque Ripple in PWM AC 05 Drives, Industrial Electronics, IEEE Transactions on 56 (09), 05 06 553 5. 06 07 [6] QIANG, L. et al : The Study of PWM Methods in Permanent 07 08 Magnet Brushless DC Motor Speed Control System, in Electrical 08 Machines and Systems, 08. ICEMS 08. International 09 09 Conference on, 08, pp. 3897 00. [7] CUNSHAN, Z. DUNXIN, B.: A PWM Control Algorithm for 11 11 Eliminating Torque Ripple Caused by Stator Magnetic Field 12 Jump of Brushless DC Motors, in Intelligent Control and Automation, 12 13 08. WCICA 08. 7th World Congress on, 08, 13 14 pp. 6547 6549. 14 15 [8] MURAI, Y. et al : Torque Ripple Improvement for Brushless 15 DC Miniature Motors, Industry Applications, IEEE Transactions on 25 (1989), 1 450. Fig. 11. Motor output torque 41 Hz [9] ZHANG, X. CHEN, B. : Influences of PWM Mode on the Current Generated by BEMF of Switch-Off Phase in Control Sys- 19 tem of BLDC Motor, in Electrical Machines and Systems, 01. 19 ICEMS 01. Proceedings of the Fifth International Conference 6 CONCLUSION on, 01, pp. 579 2, vol. 1. [10] SATHYAN, A.et al : A Low-Cost Digital Control Scheme for The modified Pulse Width Modulation (PWM) signals for driving the power inverter bridge for BLDC motric Machines and Drives Conference, 09. IEMDC 09. IEEE Brushless DC Motor Drives in Domestic Applications, in Elec- 24 International, 09, pp. 76 82. 24 25 tor drives have been successfully implemented using PIC [11] GUANGWEI, M.et al : Commutation Torque Ripple Reduction in BLDC Motor using PWM ON PWM Mode, in Electrical 25 microcontroller. The BLDC motor control based on rotor position sensing scheme been discussed. It can clearly be Machines and Systems, 09. ICEMS 09. International Conference on, 09,, pp. 1 6. seen from the measured results of phase currents that the 28 28 modified PWM signals has managed to reduce the current [12] OH, T.-S.et al : Commutation Time Control for Torque Ripple 29 29 spike and dips, hence resulting in lower torque ripples. Reduction of BLDC Motors, The Korean Institute of Electrical 30 Engineers, 08. 30 31 31 Acknowledgment [13] PILLAY, P. KRISHNAN, R.: Modeling, Simulation, and 32 Analysis of Permanent-Magnet Motor Drives. II. The Brushless 32 The authors wish to thank Ministry of Science, Technology DC Motor Drive, Industry Applications, IEEE Transactions on and Innovation Malaysia (MOSTI) under grant 25 (1989), 4 9. No. 305/PELECT/60130 and Universiti Sains Malaysia for providing research fellowship and funding for this [14] EMADI, A. ANDREAS, J. C.: Energy-Efficient Electric Motors, Marcel Dekker, New York, 05. [15] LAJOIE-MAZENC, M.et al : Analysis of Torque Ripple in research. Electronically Commutated Permanent Magnet Machines and 38 Minimization Methods, in Electrical Machines and Drives, 1989. 38 Fourth International Conference on, 1989, pp. 85 89. References 40 [16] BYOUNG-HEE, K. et al : Analysis of Torque Ripple in BLDC 40 41 Motor with Commutation Time, in Industrial Electronics, 01. 41 [1] TOLIYAT, H. A. CAMPBELL, S. : DSP-Based Electromechanical Motion Control, CRC Press, Boca Raton [Fla.], 04. 42 Proceedings. ISIE 01. IEEE International Symposium on, 42 01,, pp. 10 1048, vol. 2. 43 [2] JAHNS, T. M. SOONG, W. L.: Pulsating Torque Minimization 43 Techniques for Permanent Magnet AC Motor Drives a Received December 10 45 Review, Industrial Electronics, IEEE Transactions on 43 (1996), 45 3 0. Wael A. Salah [3] SINGH, B. : Recent Advances in Permanent Magnet Brushless 47 47 DC Motors, Sadhana Academy Proceedings in Engineering Dahaman Ishak 48 Sciences (1997), 8 853. Khaleel J. Hammadi 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57