PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION IN BLDC MOTOR

Transcription

1 Journal of ELECTRICAL ENGINEERING, VOL. 62, NO. 3, 11, PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION IN BLDC MOTOR Wael A. Salah Dahaman Ishak Khaleel J. Hammadi 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 the next in-coming phase current such that its current rise is slightly delayed during the commutation instant. Experimental results show that the current waveforms of the modified PWM are smoother than that in conventional PWM technique Hence, the output torque exhibits lower ripple contents 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, 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 manent magnet rotor and a wound field stator, which is loop disturbance rejection, high speed current regulators, connected to a power electronic switching circuit. commutation torque minimizations and automated selfcommissioning schemes [4] 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 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 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 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 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 to speed oscillations, resonances in mechanical portions of the drive causing acoustic noise and visible vibration method. Reference [9] discussed the influences of PWM 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 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 School of Electrical and Electronic Engineering, Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Penang, 56 Malaysia. wael sal@eng.usm.my, dahaman@eng.usm.my, khal.dr59@yahoo.com ISSN c 11 FEI STU

2 2 W.A. Salah D. Ishak K.J. Hammadi: PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION where v 02 a i a R S L S e a 03 R s : phase resistance, v an, v bn, v cn : phase voltages, 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 v i c c R S L S e 07 c The equivalent circuit for the BLDC motor is shown in Fig 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 tromagnetic torque of BLDC motor is produced as follows 11 DC Power Power Hall 12 Electric Motor Supply Converter Sensor T e = e ai a + e b i b + e c i c (2) ω m 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 As mentioned above, these were several research works controller as shown in Fig 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 ripples during commutation time. However, in this paper, a modified PWM signal is applied during the start-up of connected in series, and is given by 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 BLDC MOTOR DRIVE SYSTEM 41 where k t is the motor torque constant. 41 BLDC motor produces a trapezoidal back-emf, and 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 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 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 on many parameters in which relating to design parameters [15] 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 v an 54 v bn = R s 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 v cn 0 0 R s i c L s M 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

3 Journal of ELECTRICAL ENGINEERING 62, NO. 3, third phase switch will remain conducting. In this analysis the transition of conduction from Phase A(+)/C( ) to B(+)/C( ) will be considered as shown in Fig. 3. In this case the phase A is the de-energized phase and phase B will be the in-coming energized phase and phase C is the conducting phase Fig. 5. Ideal current commutation in BLDC motors 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 vanishes to zero. This period of commutation between 25 any pair of phases is relatively short comparing to the period of phase conduction At each 60 electrical degree, there will be 2 switches conducting, one from high side of the phase and the other will be from the low side. When phase A and C conducting the high side switch S1 and the low side S4 will be 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 T 2 T 4 PROPOSED METHOD FOR 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 based on the position of rotor, the rotor position is usually sensed by Hall sensors. The Hall sensors generate three 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 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 mained conducting. than conduction region, and 3-phases (rising phase, decaying In this analysis the commutation from phase A to phase, and conducting phase) are all conducted 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 4 W.A. Salah D. Ishak K.J. Hammadi: PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION Based on the commutation events as shown in Fig. 6(a), the modified PWM has been implemented by the microcontroller will be applied speed-up the energized phase current during high-speed region. In this case, the current in the outgoing phase (phase A) would reach zero before the current in in- coming phase (phase B) reaches its max value. The current rates of change can be given by di a dt > di b dt. (6) Fig. 6. Phase currents and torque during commutation event Therefore, the instantaneous phase C current will peak up slightly during this commutation time as shown in Fig. 6(a). On the other hand, phase A current decay time could also be possibly slower than phase B current rise time. Because of this mismatch of decay rate of phase A current i a and rise rate of phase B current i b, small current 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 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 assuming constant back-emf and ignoring the phase resistance, then the phase currents rate of change During commutation can be expressed as 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 to die-off from its value I to zero will be t f = 3L si 43 V dc + 2E. (11) The time i b to build up from zero to its final value I : 47 3L s I Fig. 7. Flow chart of modified PWM signals t r = 2(V 48 dc E). (12) Considering the case of t f = t r, which described in Fig In practice, the rate of current rise is mismatched with where the fall time and rise time are equal, this case could 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) hence a lot of techniques has been introduced to minimize 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) be discussed and analyzed from the perspective of motor 57 control side. t Vdc f =4E = L si 2E. (14)

5 Journal of ELECTRICAL ENGINEERING 62, NO. 3, 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 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 build-up of current in the in-coming phase at low speed region or speed-up current rate in high-speed region. This will result in overcoming the tips and dips occurred during 31 phase current commutation. This is achieved via the 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 tested motor has been coupled with the torque Lorenz sensor, and the other end of the sensor is coupled to a PM generator 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 And this will be considered as the average commutation technique time between two phases. The total conduction time of The waveform shown in Fig. 9 illustrates the phase phase current will be t total = 2π 3 T current of brushless DC motor using conventional PWM 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 From this, the conduction time of the phase will be the ripple in current waveform is minimized, thus it will t cond = 2π L result in smother output torque with a minimum torque si 2E. (16) ripples. Figure 11 shows a comparison of the generated output 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 6 W.A. Salah D. Ishak K.J. Hammadi: PWM SWITCHING STRATEGY FOR TORQUE RIPPLE MINIMIZATION smoother output torque; result in a visible reduction of [4] HOLTZ, J. SPRINGOB, L.: Identification and Compensation the torque ripples. of Torque Ripple in High-Precision Permanent Magnet Motor 02 Drives, Industrial Electronics, IEEE Transactions on 43 (1996), [5] BASU, K. et al : Minimization of Torque Ripple in PWM AC 05 Drives, Industrial Electronics, IEEE Transactions on 56 (09), [6] QIANG, L. et al : The Study of PWM Methods in Permanent Magnet Brushless DC Motor Speed Control System, in Electrical 08 Machines and Systems, 08. ICEMS 08. International Conference on, 08, pp [7] CUNSHAN, Z. DUNXIN, B.: A PWM Control Algorithm for Eliminating Torque Ripple Caused by Stator Magnetic Field 12 Jump of Brushless DC Motors, in Intelligent Control and Automation, WCICA 08. 7th World Congress on, 08, pp [8] MURAI, Y. et al : Torque Ripple Improvement for Brushless 15 DC Miniature Motors, Industry Applications, IEEE Transactions on 25 (1989), 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, ICEMS 01. Proceedings of the Fifth International Conference 6 CONCLUSION on, 01, pp , 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 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 seen from the measured results of phase currents that the modified PWM signals has managed to reduce the current [12] OH, T.-S.et al : Commutation Time Control for Torque Ripple spike and dips, hence resulting in lower torque ripples. Reduction of BLDC Motors, The Korean Institute of Electrical 30 Engineers, 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, Fourth International Conference on, 1989, pp References 40 [16] BYOUNG-HEE, K. et al : Analysis of Torque Ripple in BLDC Motor with Commutation Time, in Industrial Electronics, [1] TOLIYAT, H. A. CAMPBELL, S. : DSP-Based Electromechanical Motion Control, CRC Press, Boca Raton [Fla.], Proceedings. ISIE 01. IEEE International Symposium on, 42 01,, pp , vol [2] JAHNS, T. M. SOONG, W. L.: Pulsating Torque Minimization 43 Techniques for Permanent Magnet AC Motor Drives a Received December Review, Industrial Electronics, IEEE Transactions on 43 (1996), Wael A. Salah [3] SINGH, B. : Recent Advances in Permanent Magnet Brushless DC Motors, Sadhana Academy Proceedings in Engineering Dahaman Ishak 48 Sciences (1997), Khaleel J. Hammadi