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A novel position-sensorless control method for brushless DC motors
Energy Conversion and Management 52 (2011) 1669–1676
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
A novel position-sensorless control method for brushless DC motors X.Z. Zhang a,b,⇑, Y.N. Wang a a b
School of Electrical and Information Engineering, Hunan University, Changsha, People’s Republic of China School of Computer and Communication, Hunan Institute of Engineering, Xiangtan, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 29 November 2009 Received in revised form 30 September 2010 Accepted 15 October 2010 Available online 10 November 2010 Keywords: Brushless DC (BLDC) motor Sensorless control Back EMF zero-crossing point detection PWM
a b s t r a c t This paper presents the design and implementation of a high performance position-sensorless control scheme for the extensively used brushless DC (BLDC) motors. In the proposed method, with proper PWM strategy, instead of detecting the zero-crossing point (ZCP) of the nonexcited motor back electromagnetic force (EMF) or the average motor terminal to neutral voltage, the true zero-crossing points of back EMF are extracted directly from the difference of the specific average line-to-line voltages with simple RC circuits and comparators. In contrast to conventional methods, the neutral voltage is not needed and the diode freewheeling currents in the nonconducted phase are eliminated completely; therefore, the commutation signals are more accurate and insensitive to the common-mode noise. Moreover, 100% pulse-width-modulation (PWM) duty ratio control of BLDC motors is provided with the presented method. As a result, the proposed method makes it possible to achieve good motor performance over a wide speed range and to simplify the starting procedure. The detailed circuit model is analyzed and some experimental results obtained from a sensorless prototype are shown to verify the analysis and confirm the validity of the proposed method. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Permanent magnet brushless DC (BLDC) motors offer many advantages including compact form, high efficiency, easy of control and low maintenance. A BLDC motor needs an inverter and a position sensor to commutate so that the motor line current is in phase with the corresponding back electromotive (EMF). However, the position sensor presents several disadvantages because of its negative impact on drive cost and system reliability. Sensorless control techniques for BLDC motors have been a research topic for the last two decades [1]. These schemes are based on using back EMF of the BLDC motor [2], detection of freewheeling diode conduction in the open phase [3], detection of the stator third harmonic voltage components [4], estimation by observer [5] and so on [6]. Among the various techniques, the zero crossing detection of back EMF is the most popular one. Many indirect and direct back EMF detection methods, which sense the back EMF ZCP of the open phase, have been published in the last decades. One well-known back EMF detection method is to build a motor neutral point and then to sense voltage difference between the open phase terminal and the motor neutral point [2]. Since this method will introduce a high common-mode noise in the motor neutral point, low pass filters are required to eliminate the noise; ⇑ Corresponding author at. School of Electrical and Information Engineering, Hunan University, Changsha, People’s Republic of China. Tel.: +86 13574084952. E-mail address: [email protected] (X.Z. Zhang). 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.10.030
however, usage of low pass filters will introduce a phase delay, especially at high speed [7]. Compensation for the filter phase delay is reported in [8] by using a frequency independent phase shifter. The back EMF integration and third harmonic voltage integration are introduced in [4] to reduce the common-mode noises. But the works in [2,4,7,8] still require building a motor neutral point. An approach to sense back EMF by detection of freewheeling diode conduction in the open phase is presented in [3]. This method requires special PWM strategy that tends to introduce open phase current, which definitely results in unexpected torque pulsation. Moreover, its sensing circuit requires extra power supplies, which increase system cost. A direct back EMF detection method is proposed in [9], in which the voltage difference between the open phase terminal and 0 V (the power ground of DC-link) is detected. As the sensing circuit can only work during the freewheeling period (off time of PWM) in this method, a minimum off time (3 ls) is required to do sampling, this leads to a result that the maximum duty ratio of PWM is less than 100%. Another direct back EMF detection technique to perform wide duty ratio control, from 5% to 95%, is proposed in [10]. It is the first paper which eliminates duty cycle limitation by changing the sampling point of back EMF according to duty ratio. However, the ZCP of back EMF is derived by logic comparison rather than by calculation. The another problem in [10] is that the use of two reference voltages increases the cost of the sensing circuit. Under the ideal assumption that no freewheeling current exists in the nonconducted phase, a simple position-sensorless method to
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detect the back EMF ZCP in [11] and start the machine in [12] are proposed. These methods rely on a difference of line voltages measured at the terminals of the motor, and the difference can provide an amplified version of back EMF at its ZCPs. Unfortunately, this ideal assumption does not always hold. Actually, when using the method in [11,12], there is likely to have freewheeling current in the nonconducted phase both during normal commutation period and un-commutated period. As a result, the sum of two conducted phase currents is not equal to zero; therefore, the obtained ZCPs are not accurate and cannot to be used to compute the commutation points. Moreover, the adjustable range of the PWM duty ratio is not wide and far less than 100%. Therefore, in this paper, our motivation is to design a novel position-sensorless scheme for BLDC motors based on back EMF detection with the purpose of overcoming the disadvantages of the aforementioned sensorless scheme. Unlike the method in [11,12], the proper PWM strategy is adopted and it is proved that the motor neutral voltage equals to half DC-link voltage (0.5Udc), and the diode freewheeling currents in the nonconducted phase are eliminated completely. Hence, the true back EMF ZCP can be directly extracted by detecting the difference of line-to-line voltages measured at the terminals of the motor without sensing the motor neutral voltage, and no filtering circuit is required. It is shown that this difference of line-to-line voltages provides an amplified version of an appropriate back EMF at its zero crossings. Compensating 30° offset, the required commutation positions can be calculated and determined. Moreover, compared with [9–12], the adjustable range of the PWM duty ratio is more wider and can reach 100%. Also, no extra power supplies are required for sensing circuit. As a result, the proposed back EMF detection method makes it possible for this sensorless BLDC motor control system to achieve good motor performance over a much wider speed range and the starting procedure is simplified.
Fig. 2. Ideal back EMF and phase current waveforms.
must be in phase with the corresponding phase back EMF, which have a trapezoidal waveform, as shown in Fig. 2. In permitted scope, the assumption is as follows. (1) The stator winding is a concentrative winding with 120° equi-spacing. (2) The winding is distributed equably on the smooth surface of the stator. (3) The magnetic saturation is neglected. Vortex and magnetic hysteresis losses are neglected. (4) The armature reaction is neglected and the distribution of air–gap field is uniform. The voltage equation of the three-phase BLDC motor is
0 2. Proposed sensorless commutation scheme 2.1. Mathematical model of BLDC motor Consider a BLDC motor having three stator phase windings connected in star. PMs are mounted on the rotor. The BLDC motor is driven by a three-phase inverter with what is called six-step commutation. Fig. 1 shows the equivalent circuit of a BLDC motor and the inverter topology, and Fig. 2 illustrates the relationship among the back-EMF waveform of an ideal BLDC motor and the armature current, where E, I denotes the amplitude of back EMF and current, respectively. The currents should have a rectangular waveform and
Fig. 1. Inverter topology and equivalent circuit of a BLDC motor.
1 0 ra ua B C B @ ub A ¼ @ 0 0 uc 0
1 0 La ia CB C B r b 0 A@ ib A þ p@ 0 0 rc 0 ic 1 0 1 un ea B C B C þ @ eb A þ @ un A ec un 0
0
10
0 Lb 0
1 ia CB C 0 A@ ib A Lc ic
0
10
ð1Þ
where ‘‘p” denotes the derivative operation, and ua, ub, uc the phase winding voltage of stator (in volts); ea, eb, ec phase winding back EMF of the stator (in volts); ia, ib, ic phase winding current of stator (in amperes); ra, rb, rc phase winding resistance of stator (in ohms);
Fig. 3. Timing diagram of H_PWM–L_PWM control signals.
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La, Lb, Lc phase winding inductance of stator (in henrys); un is the neutral voltage of motor (in volts); um is the mid DC-link voltage (in volts). Because the motor’s three phases are similar, in permitted scope, ra = rb = rc = r, La = Lb = Lc = L, and (1) can be simplified as ux = rix + Lpix + ex + un, where x = a, b, c. In the two-phase conduction mode, there are six combinations of the stator excitation in one cycle and each combination lasts for 60 electrical degrees. In order to produce maximum torque, the inverter commutation should be performed every 60 electrical degrees, which is called commutation period. In order to regulate the conduction current so that the motor will faithfully follow the given velocity or torque command, the power switches of the three-phase inverter are generally controlled via a high frequency pulse width modulation signal. In this paper, for easily detecting the back EMF ZCP, two side chopping mode (H_PWM–L_PWM scheme) is adopted. Fig. 3 illustrates the gating sequence of the electronic switches’ waveforms in this typical PWM strategy in which both the active switches in the lower half bridge and upper half bridge are modulated simultaneously [13]. 2.2. Proposed back EMF detection method Since the neutral point of the BLDC motor is always not offered, it is difficult to construct the terminal voltage Eq. (1) for one phase. Therefore, the line voltages are considered and may be determined as
8 > < uab ¼ rðia ib Þ þ Lpðia ib Þ þ ðea eb Þ ubc ¼ rðib ic Þ þ Lpðib ic Þ þ ðeb ec Þ > : uca ¼ rðic ia Þ þ Lpðic ia Þ þ ðec ea Þ
ð2Þ
These line voltages can, however, be estimated without the need for star point by taking the difference of terminal voltages measured with respect to the negative DC bus. Subtracting Eq. (2)-2 from Eq. (2)-1 gives
uabbc ¼ uab ubc ¼ rðia þ ic 2ib Þ þ Lpðia þ ic 2ib Þ þ ðea þ ec 2eb Þ
ð3Þ
Consider the interval when phases A and C are conducting and phase B is open as indicated by the shaded region in Fig. 2. In this interval, phase A winding is connected to the +Udc of the DC supply, phase C to the Udc of the DC supply and phase B is open. Therefore, for a BLDC motor having three stator phase windings connected in star, ea = ec and ia + ib + ic = 0. It can be seen from Fig. 2 (shaded region) that the back EMF in phases A and C are equal and opposite. Therefore in that interval Eq. (3) may be simplified as
uabbc ¼ 3rib 3Lpib 2eb
ð4Þ
Rearranging,
eb ¼
uabbc 3rib 3Lpib 2 2 2
ð5Þ
Obviously, the back EMF value of phase B would be the linear summation of the line voltage difference (uabbc) and the voltage drop on the stator impedance (rib and Lpib). It is again evident from Fig. 2 that during this interval the back EMF eb transits from one polarity to another crossing zero. Thus, if the unexcited phase B current ib is always equal to zero, there is no freewheeling current flowing in the phase B winding, the voltage drop on the stator impedance will not exit, and the back EMF calculation of phase B will be simplified.In terms of the brushless DC motor, all three-phase windings generally have current flowing due to the armature inductance in the commutation state, thus the current ib of unexcited phase B is not strictly equal to zero, as shown in Fig. 2 nearby he = 90°, 150°, 270°, and 330°, and the voltage drop on the stator
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impedance cannot be ignored. However, it can be seen from Fig. 2 that the back EMF ZCPs are far away from the commutation points when phase B is open. In other words, in the vicinity of back EMF ZCPs of unexcited phase during the non-commutation interval, the proper approximation that ea = ec = E and ia = ic = I is established. In the normal conduction period, only two phases conduct. Assuming at a particular step, phase A and phase C are conducting while phase B is open. Referring to Fig. 2, it shows that switches T1 and T6 or T2 and T5 are chopping, separately. As an example, the situation with T1 and T6 chopped is analyzed, where current flows into phase A and then out phase C. Since T1 and T6 are modulated simultaneously, there are two cases, PWM ON time and PWM OFF time, for the different state of T1 and T6. Case 1: PWM ON time This case corresponds to the selected intervals when switches T1 and T6 are the only two active switches. Fig. 4 illustrates the equivalent circuit. If the conduction voltage caused by the power switches and the diodes is negligible, then the terminal voltage can be obtained as
8 > < ua ¼ ud ¼ ria þ Lpia þ ea þ un ub ¼ eb þ un > : uc ¼ 0 ¼ ric þ Lpic þ ec þ un
ð6Þ
In this condition, from phase A and phase C and noting that ea = ec = E and ia = ic = I, then the neutral voltage equals the half DC-link voltage, namely un ¼ 12 ud ¼ um . Accordingly, from phase A, its back EMF can be expressed as
ea ¼ ud ria Lpia un Since un ¼
1 u 2 d
ð7Þ
and ia > 0, one will have
ud ud ea ¼ E ¼ ria Lpia < 2 2
ð8Þ
Since E < eb < E, then ud/2 < eb < ud/2. From Eq. (6)-2, we obtain 0 < ub < ud, this means that there is no current flowing in phase B winding and there is not exits freewheeling current through the anti-parallel diode VD3 and VD4, ib = 0. Therefore, the back EMF in Eq. (5) can be simplified as
eb ¼
uabbc ubc uab ¼ 2 2
ð9Þ
Case 2: PWM OFF time This case corresponds to the selected intervals when switches T1 and T6 are PWM off, and the anti-parallel diode VD2 and VD5 work in freewheeling states. The terminal voltage can be obtained according to the switching status of the power switches as
8 > < ua ¼ 0 ¼ ria þ Lpia þ ea þ un ub ¼ eb þ un > : uc ¼ ud ¼ ric þ Lpic þ ec þ un
ð10Þ
In this condition, from phase A and phase C and noting that ea = ec = E and ia = ic = I, then the neutral voltage also equals to the half DC-link voltage, un ¼ 12 ud ¼ um . From phase C, we also obtain
ec ¼ ud ric Lpic un Now that un ¼
1 u 2 d
ð11Þ
¼ um and ic > 0, one can obtain
ud ud ec ¼ E ¼ ric Lpic < 2 2
ð12Þ
Since E < eb < E, then ud/2 < eb < ud/2, so we obtain 0 < ub < ud, this means that there is no current flowing in phase B winding and there is not exits freewheeling current through the anti-parallel
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(a) PWM ON state
(b) PWM OFF state
Fig. 4. Different state of VT1 and VT6. (a) PWM ON state; and (b) PWM OFF state.
diode VD3 and VD4, ib = 0. Then, the back EMF in Eq. (5) can also be simplified as Eq. (9).Therefore, from the above analysis, with H_PWM–L_PWM scheme there exits no freewheeling current in the unexcited phase winding during the un-commutated interval, and the operation uab ubc (uabbc) enables the detection of the back EMF ZCP of the phase B. In Section 4, it will further prove that the difference of line-to-line voltage waveforms is an inverted representation of the back-EMF waveform. It may also be noted that the subtraction operation provides a gain of two to the back-EMF waveform, thus amplifying it. In this method, the maximum duty
(1) Block diagram of the overall system
ratio of PWM can reach 100% since the sensing circuit can work whether T1 and T6 are ON or OFF.Similarly, the difference of lineto-line voltage ubcca enables the detection of zero crossing of phase C back-EMF when phases B and C back-EMF are equal and opposite. The difference of line-to-line voltage ucaab waveform gives the zero crossing of phase A back-EMF, where phases C and B have equal and opposite back-EMF. Therefore the zero crossing instants of the back-EMF waveforms may be estimated indirectly from measurements of only the three terminal voltages of the motor. This is true even for a small rotation of the rotor, as shown in Section 4.
(2) Experimental equipment and its components
(3) Proposed back EMF detection circuit. Fig. 5. The block diagram and prototype of sensorless BLDC motor control system.
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(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , rotor position signal sb and phase current ib Fig. 6. Simulation waveforms at 100 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, rotor position signal sb and phase current ib.
3. System implementation and starting method 3.1. System structure A prototype of sensorless BLDC motor control system is built in the lab. Fig. 5-1 and -2 shows the functional diagram and its experimental equipment, respectively. A DC motor is used as a mechanical load of the BLDC motor. Ratings and parameters of the BLDC motor are listed as power = 180 W; current = 0.94 A; voltage = 220 V; number of poles = 4. The power supply that the back EMF detection circuit requires is from IGBT driving and protecting circuits. The protection signal of IGBT driving and protecting circuit is fed to DSP directly. A proportional–integral (PI) regulator is used for current regulation. From the sensed terminal voltages and subsequently their differences are determined. Indeed, only two lineto-line voltages are needed, and the third line-to-line voltage is determined according to uab + ubc + uca = 0. For simplicity, no speed control loop is provided. The entire drive system is controlled by a low-cost, fixed-point digital signal processor (DSP), dsPIC30F6010. To ascertain the effectiveness of the scheme, there are two commutation methods in Fig. 5. So, we can compare the commutation signals from the proposed technique and the HALL sensor. The carrier frequency of the inverter is 16 kHz. The detailed circuit of the proposed back EMF detection method is shown in Fig. 5-3. It is noted that the power supplies the driving and protecting circuit used are also provided to the back EMF sensing circuit, so no extra power supplies are needed. Comparators are
used to amplify the back EMF signals and to compare the line-toline voltage differences. The output signal of each phase back EMF detection circuit is sent to analogy Multiplexer. Under the action of DSP, Multiplexer selects which signal to be used according to which phase is the open phase. The PWM signal from DSP is used as the clock signal of D-type Flip-Flop, which will latch the output of Multiplexer. To mask the abnormal level-shift of open phase voltage, the first output samples of Multiplexer is discarded by appling a customized delay, which produced in GAL once a new phase commutation occurs, to Flip-Flop at the beginning of the commutation interval. Then, the output of Flip-Flop is the detected back EMF zero-crossing signal.
3.2. Starting procedure As the amplitude of back EMF is proportional to the rotor speed, it is impossible to detect the back EMF ZCP when the motor is at standstill. Therefore, a suitable starting procedure is necessary to the sensorless BLDC motor drive. In this control system, the starting procedure is divided into three stages [2,14,15]. In stage 1, two phases of the motor are energized for enough time; the rotor will be locked into a predefined position. In stage 2, a commutation signal advancing the switching pattern by 120 electrical degrees will be applied to the motor, and then, the frequency of the commutation signals is increasing gradually when the rotor rotates up by the adding currents. In stage 3, the operation mode of the motor
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(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , rotor position signal sb and phase current ib Fig. 7. Simulation waveforms at 1000 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, rotor position signal sb and phase current ib.
is changed to self-controlled mode when the speed of the rotor reaches a certain value, that is to say, the back EMF value reaches a detectable level. 4. Simulation and experimental results To verify the feasibility of the proposed method, computer simulations are first realized by MATLAB/SIMULIN software [16]. The four poles motor parameters used for simulation and hardware implementation are given as R = 2.875 X, Lm = 1.6 mH, Ls = 8.5 mH.
ubc
uab eb
Figs. 6a and 7a show the simulated back-EMF waveform of phase B and the line-to-line voltage difference uab, ubc at speed reference 100 rpm and 1000 rpm, respectively. The corresponding back EMF zero-crossings signal Seb, the calculated rotor position signal Scb and phase B current ib are depicted in Figs. 6b and 7b, respectively. It can be seen that the plots validate Eq. (9) in the region of zero crossing of the back EMF, and there exits no freewheeling current in unexcited phase B. Therefore we conclude that the method of detection of zero crossings of line-to-line voltage difference, as described in the previous section, is valid for a wide speed
Seb Scb
Shb ib
(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , calculated rotor position signal scb , Hall signal shb and phase current ib
Fig. 8. Experimental results at 100 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, calculated rotor position signal scb, Hall signal shb and phase current ib.
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Seb
ubc
Scb
uab
Shb
eb
ib
(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , calculated rotor position signal scb , Hall signal shb and phase current ib
Fig. 9. Experimental results at 1000 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, calculated rotor position signal scb, Hall signal shb and phase current ib.
ib
Scb
Fig. 10. B-Phase current, calculated commutation signal at 98% duty cycle.
Stage 1
Stage 2
Stage 3
ib Scb
Shb
Fig. 11. Starting process of BLDC motors with three stages. (From top to bottom: phase current, commutation signal after time shift, ZCP signal of phase B).
range.Figs. 8 and 9 present the experimental results for two speed references, which are 100 rpm and 1000 rpm, respectively. At 100 rpm, Fig. 8a illustrates the measured line-to-line voltage differences for ubc and uab, and the calculated back EMF signal by using the proposed method. Fig. 8b shows the corresponding ZCP of back EMF Seb, calculated rotor position Scb, measured Hall signal Shband the current of phase B. It is clear that each trigger edge of ZCP signal corresponds to 60°, 120°, 180°, 240°, 300°, 360° rotor position of back EMF of the unconducting phase. At 1000 rpm, Fig. 9 gives the experimental results of our sensorless method. As shown in Figs. 8 and 9, the calculated commutation signals coincide with those determined by HALL sensor. The experimental waveforms of phase A in Figs. 8 and 9 show a good agreement with the waveforms of simulation in Figs. 6 and 7. It can be observed that the estimated rotor position is in agreement with what is measured directly by the position sensor. These experimental results therefore confirm those obtained in simulation. To validate the system performance at high duty ratio, Fig. 10 shows the phase current and the estimated rotor position at 98% duty cycle. From this waveform, it can be seen that the commuta-
tion instant happens at trigger edge of phase current. Thus, the commutation process works well both in PWM on time and PWM off time even in high duty ratio. Compared with sensorless methods in [9,11,12], which can only work either in PWM off time or low PWM duty ratio, the proposed method exhibits better performance. Fig. 11 shows the current waveform and commutation signals of the experimental BLDCM drive implemented using the propose technique starting form standstill (stage 1) to closed-loop operation. It can be seen that the stage 2 lasts four electric cycles to assure the rotor aligning with the rotating magnetic field. When the input voltage is higher than, that is, if the back EMF is high enough for the detection circuit, the sensorless commutation signals will be sent to the commutation table and the motor is changed to the self commutation mode (stage 3). Moreover, the starting procedure from standstill to closed-loop operation is smooth and has no serious distortion of phase current. Experimental results show that the proposed method is feasible and efficient. With this sensorless method based on line-to-line back EMF, the motor can run smoothly in a wide speed range. 5. Conclusion Unlike conventional back EMF based sensorless commutation methods which focus on detection of the ZCP of the motor terminal to neutral voltage, a novel sensorless commutation method based on the difference of line-to-line voltage is proposed in this study. Both theoretical analysis and experimental results verify that satisfactory performance can be achieved with the proposed sensorless commutation method. Compared with the existing solutions, the proposed method has several improvements or characteristics, including the followings. 1. The neutral voltage is not required in the proposed method, only the three motor terminal voltages need to be detected. 2. With H_PWM–L_PWM scheme, it is proved that there exits no freewheeling current in the unexcited phase winding during the un-commutated interval, thus, the estimated ZCP is reliable and accurate. The process of estimating ZCP is implemented by the detection circuit, and so this method does not need position sensor. 3. Since the amplitude of the line-to-line voltage is significantly larger than the phase voltage, even a small back EMF can be effectively detected. Namely, a lower open loop starting speed can be achieved. 4. The maximum duty ratio of PWM can reach 100% since the sensing circuit can work whether the switches are PWM ON or PWM OFF.
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5. The special PWM scheme, H_PWM–L_PWM, is used in this method, which will result in higher switch losses when compared with the conventional single-bridge modulated PWM scheme. Torque ripple in this method is bigger than that in the conventional method in which PWM scheme is H_PWM– L_ON or L_PWM–H_ON. Acknowledgements The authors are grateful to the anonymous reviewers and to the National Natural Science Foundation of China Key Program for supporting this work through research Grant NSFC-60835004 and Hunan Natural Science Foundation through research Grant JJ076111. Reference [1] Acarnley PP, Watson JF. Review of position-sensorless operation of brushless permanent-magnet machines. IEEE Trans Ind Electron 2006;53(2):352–62. [2] Iizuka K, Uzuhashi H, Kano M, Endo T, Mohri K, et al. Microcomputer control for sensorless brushless motor. IEEE Trans Ind Appl 1985;27:595–601. [3] Ogasawara S, Suzuki K, Akagi H. A sensorless brushless dc motor system. Electr Eng Jpn 2007;112(5):109–18. [4] Jiang Q, Bi C, Hung R. A new phase-delay-free method to detect back EMF zerocrossing points for sensorless control of spindle motors. IEEE Trans Magn 2005;41(7):2287–94.
[5] Alireza R, Asaei Behzad. A novel method for estimating the initial rotor position of PM motors without the position sensor. Energy Convers Manage 2009;50(8):1879–83. [6] Song ZQ, Hou ZJ, Jiang CW, et al. Sensorless control of surface permanent magnet synchronous motor using a new method. Energy Convers Manage 2006;47(15–16):2451–60. [7] Shen JX, Tseng KJ. Analyses and compensation of rotor position detection error in sensorless PM brushless DC motor drives. IEEE Trans Energy Convers 2003;18(1):87–93. [8] Jung DH, Ha IJ. Low-cost sensorless control of brushless DC motors using a frequency-independent phase shifter. IEEE Trans Power Electron 2000;15(4):744–52. [9] Shao JW, Nolan D, Hopkins T. Improved direct back EMF detection sensorless brushless DC (BLDC) motor drives for automotive fuel pumps. IEEE Trans Ind Appl 2003;39(6):1734–40. [10] Lai YS, Lin YK. A new cost effective sensorless commutation method for brushless DC motors without using phase shift circuit and neutral voltage. IEEE Trans Power Electron 2007;22(2):644–53. [11] Damodharan P, Vasudevan K. Sensorless brushless DC motor drive based on the zero-crossing detection of back electromotive force (EMF) from the line voltage difference. IEEE Trans Energy Convers 2010;25(3):661–8. [12] Damodharan P, Sandeep R, Vasudevan K. Simple position sensorless startig method for brushless DC motor. IEE Proc Electr Power Appl 2008;2(1):49–55. [13] Lai YS, Lin YK. Assessment of pulse-width modulation techniques for brushless dc motor drives. In: Proc IEEE IAS annu meet, October 2006. p. 1629–36. [14] Lee W-J, Sul S-K. A new starting method of BLDC motors without position sensor. IEEE Trans Ind Appl 2006;42(6):1532–8. [15] Behzad A, Rostami Alireza. A novel starting method for BLDC motors without the position sensors. Energy Convers Manage 2009;50(2):337–43. [16] Matlab Company, Matlab user guide: version R2010b. Matlab Company: USA; 2010.
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
A novel position-sensorless control method for brushless DC motors X.Z. Zhang a,b,⇑, Y.N. Wang a a b
School of Electrical and Information Engineering, Hunan University, Changsha, People’s Republic of China School of Computer and Communication, Hunan Institute of Engineering, Xiangtan, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 29 November 2009 Received in revised form 30 September 2010 Accepted 15 October 2010 Available online 10 November 2010 Keywords: Brushless DC (BLDC) motor Sensorless control Back EMF zero-crossing point detection PWM
a b s t r a c t This paper presents the design and implementation of a high performance position-sensorless control scheme for the extensively used brushless DC (BLDC) motors. In the proposed method, with proper PWM strategy, instead of detecting the zero-crossing point (ZCP) of the nonexcited motor back electromagnetic force (EMF) or the average motor terminal to neutral voltage, the true zero-crossing points of back EMF are extracted directly from the difference of the specific average line-to-line voltages with simple RC circuits and comparators. In contrast to conventional methods, the neutral voltage is not needed and the diode freewheeling currents in the nonconducted phase are eliminated completely; therefore, the commutation signals are more accurate and insensitive to the common-mode noise. Moreover, 100% pulse-width-modulation (PWM) duty ratio control of BLDC motors is provided with the presented method. As a result, the proposed method makes it possible to achieve good motor performance over a wide speed range and to simplify the starting procedure. The detailed circuit model is analyzed and some experimental results obtained from a sensorless prototype are shown to verify the analysis and confirm the validity of the proposed method. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Permanent magnet brushless DC (BLDC) motors offer many advantages including compact form, high efficiency, easy of control and low maintenance. A BLDC motor needs an inverter and a position sensor to commutate so that the motor line current is in phase with the corresponding back electromotive (EMF). However, the position sensor presents several disadvantages because of its negative impact on drive cost and system reliability. Sensorless control techniques for BLDC motors have been a research topic for the last two decades [1]. These schemes are based on using back EMF of the BLDC motor [2], detection of freewheeling diode conduction in the open phase [3], detection of the stator third harmonic voltage components [4], estimation by observer [5] and so on [6]. Among the various techniques, the zero crossing detection of back EMF is the most popular one. Many indirect and direct back EMF detection methods, which sense the back EMF ZCP of the open phase, have been published in the last decades. One well-known back EMF detection method is to build a motor neutral point and then to sense voltage difference between the open phase terminal and the motor neutral point [2]. Since this method will introduce a high common-mode noise in the motor neutral point, low pass filters are required to eliminate the noise; ⇑ Corresponding author at. School of Electrical and Information Engineering, Hunan University, Changsha, People’s Republic of China. Tel.: +86 13574084952. E-mail address: [email protected] (X.Z. Zhang). 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.10.030
however, usage of low pass filters will introduce a phase delay, especially at high speed [7]. Compensation for the filter phase delay is reported in [8] by using a frequency independent phase shifter. The back EMF integration and third harmonic voltage integration are introduced in [4] to reduce the common-mode noises. But the works in [2,4,7,8] still require building a motor neutral point. An approach to sense back EMF by detection of freewheeling diode conduction in the open phase is presented in [3]. This method requires special PWM strategy that tends to introduce open phase current, which definitely results in unexpected torque pulsation. Moreover, its sensing circuit requires extra power supplies, which increase system cost. A direct back EMF detection method is proposed in [9], in which the voltage difference between the open phase terminal and 0 V (the power ground of DC-link) is detected. As the sensing circuit can only work during the freewheeling period (off time of PWM) in this method, a minimum off time (3 ls) is required to do sampling, this leads to a result that the maximum duty ratio of PWM is less than 100%. Another direct back EMF detection technique to perform wide duty ratio control, from 5% to 95%, is proposed in [10]. It is the first paper which eliminates duty cycle limitation by changing the sampling point of back EMF according to duty ratio. However, the ZCP of back EMF is derived by logic comparison rather than by calculation. The another problem in [10] is that the use of two reference voltages increases the cost of the sensing circuit. Under the ideal assumption that no freewheeling current exists in the nonconducted phase, a simple position-sensorless method to
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detect the back EMF ZCP in [11] and start the machine in [12] are proposed. These methods rely on a difference of line voltages measured at the terminals of the motor, and the difference can provide an amplified version of back EMF at its ZCPs. Unfortunately, this ideal assumption does not always hold. Actually, when using the method in [11,12], there is likely to have freewheeling current in the nonconducted phase both during normal commutation period and un-commutated period. As a result, the sum of two conducted phase currents is not equal to zero; therefore, the obtained ZCPs are not accurate and cannot to be used to compute the commutation points. Moreover, the adjustable range of the PWM duty ratio is not wide and far less than 100%. Therefore, in this paper, our motivation is to design a novel position-sensorless scheme for BLDC motors based on back EMF detection with the purpose of overcoming the disadvantages of the aforementioned sensorless scheme. Unlike the method in [11,12], the proper PWM strategy is adopted and it is proved that the motor neutral voltage equals to half DC-link voltage (0.5Udc), and the diode freewheeling currents in the nonconducted phase are eliminated completely. Hence, the true back EMF ZCP can be directly extracted by detecting the difference of line-to-line voltages measured at the terminals of the motor without sensing the motor neutral voltage, and no filtering circuit is required. It is shown that this difference of line-to-line voltages provides an amplified version of an appropriate back EMF at its zero crossings. Compensating 30° offset, the required commutation positions can be calculated and determined. Moreover, compared with [9–12], the adjustable range of the PWM duty ratio is more wider and can reach 100%. Also, no extra power supplies are required for sensing circuit. As a result, the proposed back EMF detection method makes it possible for this sensorless BLDC motor control system to achieve good motor performance over a much wider speed range and the starting procedure is simplified.
Fig. 2. Ideal back EMF and phase current waveforms.
must be in phase with the corresponding phase back EMF, which have a trapezoidal waveform, as shown in Fig. 2. In permitted scope, the assumption is as follows. (1) The stator winding is a concentrative winding with 120° equi-spacing. (2) The winding is distributed equably on the smooth surface of the stator. (3) The magnetic saturation is neglected. Vortex and magnetic hysteresis losses are neglected. (4) The armature reaction is neglected and the distribution of air–gap field is uniform. The voltage equation of the three-phase BLDC motor is
0 2. Proposed sensorless commutation scheme 2.1. Mathematical model of BLDC motor Consider a BLDC motor having three stator phase windings connected in star. PMs are mounted on the rotor. The BLDC motor is driven by a three-phase inverter with what is called six-step commutation. Fig. 1 shows the equivalent circuit of a BLDC motor and the inverter topology, and Fig. 2 illustrates the relationship among the back-EMF waveform of an ideal BLDC motor and the armature current, where E, I denotes the amplitude of back EMF and current, respectively. The currents should have a rectangular waveform and
Fig. 1. Inverter topology and equivalent circuit of a BLDC motor.
1 0 ra ua B C B @ ub A ¼ @ 0 0 uc 0
1 0 La ia CB C B r b 0 A@ ib A þ p@ 0 0 rc 0 ic 1 0 1 un ea B C B C þ @ eb A þ @ un A ec un 0
0
10
0 Lb 0
1 ia CB C 0 A@ ib A Lc ic
0
10
ð1Þ
where ‘‘p” denotes the derivative operation, and ua, ub, uc the phase winding voltage of stator (in volts); ea, eb, ec phase winding back EMF of the stator (in volts); ia, ib, ic phase winding current of stator (in amperes); ra, rb, rc phase winding resistance of stator (in ohms);
Fig. 3. Timing diagram of H_PWM–L_PWM control signals.
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La, Lb, Lc phase winding inductance of stator (in henrys); un is the neutral voltage of motor (in volts); um is the mid DC-link voltage (in volts). Because the motor’s three phases are similar, in permitted scope, ra = rb = rc = r, La = Lb = Lc = L, and (1) can be simplified as ux = rix + Lpix + ex + un, where x = a, b, c. In the two-phase conduction mode, there are six combinations of the stator excitation in one cycle and each combination lasts for 60 electrical degrees. In order to produce maximum torque, the inverter commutation should be performed every 60 electrical degrees, which is called commutation period. In order to regulate the conduction current so that the motor will faithfully follow the given velocity or torque command, the power switches of the three-phase inverter are generally controlled via a high frequency pulse width modulation signal. In this paper, for easily detecting the back EMF ZCP, two side chopping mode (H_PWM–L_PWM scheme) is adopted. Fig. 3 illustrates the gating sequence of the electronic switches’ waveforms in this typical PWM strategy in which both the active switches in the lower half bridge and upper half bridge are modulated simultaneously [13]. 2.2. Proposed back EMF detection method Since the neutral point of the BLDC motor is always not offered, it is difficult to construct the terminal voltage Eq. (1) for one phase. Therefore, the line voltages are considered and may be determined as
8 > < uab ¼ rðia ib Þ þ Lpðia ib Þ þ ðea eb Þ ubc ¼ rðib ic Þ þ Lpðib ic Þ þ ðeb ec Þ > : uca ¼ rðic ia Þ þ Lpðic ia Þ þ ðec ea Þ
ð2Þ
These line voltages can, however, be estimated without the need for star point by taking the difference of terminal voltages measured with respect to the negative DC bus. Subtracting Eq. (2)-2 from Eq. (2)-1 gives
uabbc ¼ uab ubc ¼ rðia þ ic 2ib Þ þ Lpðia þ ic 2ib Þ þ ðea þ ec 2eb Þ
ð3Þ
Consider the interval when phases A and C are conducting and phase B is open as indicated by the shaded region in Fig. 2. In this interval, phase A winding is connected to the +Udc of the DC supply, phase C to the Udc of the DC supply and phase B is open. Therefore, for a BLDC motor having three stator phase windings connected in star, ea = ec and ia + ib + ic = 0. It can be seen from Fig. 2 (shaded region) that the back EMF in phases A and C are equal and opposite. Therefore in that interval Eq. (3) may be simplified as
uabbc ¼ 3rib 3Lpib 2eb
ð4Þ
Rearranging,
eb ¼
uabbc 3rib 3Lpib 2 2 2
ð5Þ
Obviously, the back EMF value of phase B would be the linear summation of the line voltage difference (uabbc) and the voltage drop on the stator impedance (rib and Lpib). It is again evident from Fig. 2 that during this interval the back EMF eb transits from one polarity to another crossing zero. Thus, if the unexcited phase B current ib is always equal to zero, there is no freewheeling current flowing in the phase B winding, the voltage drop on the stator impedance will not exit, and the back EMF calculation of phase B will be simplified.In terms of the brushless DC motor, all three-phase windings generally have current flowing due to the armature inductance in the commutation state, thus the current ib of unexcited phase B is not strictly equal to zero, as shown in Fig. 2 nearby he = 90°, 150°, 270°, and 330°, and the voltage drop on the stator
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impedance cannot be ignored. However, it can be seen from Fig. 2 that the back EMF ZCPs are far away from the commutation points when phase B is open. In other words, in the vicinity of back EMF ZCPs of unexcited phase during the non-commutation interval, the proper approximation that ea = ec = E and ia = ic = I is established. In the normal conduction period, only two phases conduct. Assuming at a particular step, phase A and phase C are conducting while phase B is open. Referring to Fig. 2, it shows that switches T1 and T6 or T2 and T5 are chopping, separately. As an example, the situation with T1 and T6 chopped is analyzed, where current flows into phase A and then out phase C. Since T1 and T6 are modulated simultaneously, there are two cases, PWM ON time and PWM OFF time, for the different state of T1 and T6. Case 1: PWM ON time This case corresponds to the selected intervals when switches T1 and T6 are the only two active switches. Fig. 4 illustrates the equivalent circuit. If the conduction voltage caused by the power switches and the diodes is negligible, then the terminal voltage can be obtained as
8 > < ua ¼ ud ¼ ria þ Lpia þ ea þ un ub ¼ eb þ un > : uc ¼ 0 ¼ ric þ Lpic þ ec þ un
ð6Þ
In this condition, from phase A and phase C and noting that ea = ec = E and ia = ic = I, then the neutral voltage equals the half DC-link voltage, namely un ¼ 12 ud ¼ um . Accordingly, from phase A, its back EMF can be expressed as
ea ¼ ud ria Lpia un Since un ¼
1 u 2 d
ð7Þ
and ia > 0, one will have
ud ud ea ¼ E ¼ ria Lpia < 2 2
ð8Þ
Since E < eb < E, then ud/2 < eb < ud/2. From Eq. (6)-2, we obtain 0 < ub < ud, this means that there is no current flowing in phase B winding and there is not exits freewheeling current through the anti-parallel diode VD3 and VD4, ib = 0. Therefore, the back EMF in Eq. (5) can be simplified as
eb ¼
uabbc ubc uab ¼ 2 2
ð9Þ
Case 2: PWM OFF time This case corresponds to the selected intervals when switches T1 and T6 are PWM off, and the anti-parallel diode VD2 and VD5 work in freewheeling states. The terminal voltage can be obtained according to the switching status of the power switches as
8 > < ua ¼ 0 ¼ ria þ Lpia þ ea þ un ub ¼ eb þ un > : uc ¼ ud ¼ ric þ Lpic þ ec þ un
ð10Þ
In this condition, from phase A and phase C and noting that ea = ec = E and ia = ic = I, then the neutral voltage also equals to the half DC-link voltage, un ¼ 12 ud ¼ um . From phase C, we also obtain
ec ¼ ud ric Lpic un Now that un ¼
1 u 2 d
ð11Þ
¼ um and ic > 0, one can obtain
ud ud ec ¼ E ¼ ric Lpic < 2 2
ð12Þ
Since E < eb < E, then ud/2 < eb < ud/2, so we obtain 0 < ub < ud, this means that there is no current flowing in phase B winding and there is not exits freewheeling current through the anti-parallel
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(a) PWM ON state
(b) PWM OFF state
Fig. 4. Different state of VT1 and VT6. (a) PWM ON state; and (b) PWM OFF state.
diode VD3 and VD4, ib = 0. Then, the back EMF in Eq. (5) can also be simplified as Eq. (9).Therefore, from the above analysis, with H_PWM–L_PWM scheme there exits no freewheeling current in the unexcited phase winding during the un-commutated interval, and the operation uab ubc (uabbc) enables the detection of the back EMF ZCP of the phase B. In Section 4, it will further prove that the difference of line-to-line voltage waveforms is an inverted representation of the back-EMF waveform. It may also be noted that the subtraction operation provides a gain of two to the back-EMF waveform, thus amplifying it. In this method, the maximum duty
(1) Block diagram of the overall system
ratio of PWM can reach 100% since the sensing circuit can work whether T1 and T6 are ON or OFF.Similarly, the difference of lineto-line voltage ubcca enables the detection of zero crossing of phase C back-EMF when phases B and C back-EMF are equal and opposite. The difference of line-to-line voltage ucaab waveform gives the zero crossing of phase A back-EMF, where phases C and B have equal and opposite back-EMF. Therefore the zero crossing instants of the back-EMF waveforms may be estimated indirectly from measurements of only the three terminal voltages of the motor. This is true even for a small rotation of the rotor, as shown in Section 4.
(2) Experimental equipment and its components
(3) Proposed back EMF detection circuit. Fig. 5. The block diagram and prototype of sensorless BLDC motor control system.
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(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , rotor position signal sb and phase current ib Fig. 6. Simulation waveforms at 100 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, rotor position signal sb and phase current ib.
3. System implementation and starting method 3.1. System structure A prototype of sensorless BLDC motor control system is built in the lab. Fig. 5-1 and -2 shows the functional diagram and its experimental equipment, respectively. A DC motor is used as a mechanical load of the BLDC motor. Ratings and parameters of the BLDC motor are listed as power = 180 W; current = 0.94 A; voltage = 220 V; number of poles = 4. The power supply that the back EMF detection circuit requires is from IGBT driving and protecting circuits. The protection signal of IGBT driving and protecting circuit is fed to DSP directly. A proportional–integral (PI) regulator is used for current regulation. From the sensed terminal voltages and subsequently their differences are determined. Indeed, only two lineto-line voltages are needed, and the third line-to-line voltage is determined according to uab + ubc + uca = 0. For simplicity, no speed control loop is provided. The entire drive system is controlled by a low-cost, fixed-point digital signal processor (DSP), dsPIC30F6010. To ascertain the effectiveness of the scheme, there are two commutation methods in Fig. 5. So, we can compare the commutation signals from the proposed technique and the HALL sensor. The carrier frequency of the inverter is 16 kHz. The detailed circuit of the proposed back EMF detection method is shown in Fig. 5-3. It is noted that the power supplies the driving and protecting circuit used are also provided to the back EMF sensing circuit, so no extra power supplies are needed. Comparators are
used to amplify the back EMF signals and to compare the line-toline voltage differences. The output signal of each phase back EMF detection circuit is sent to analogy Multiplexer. Under the action of DSP, Multiplexer selects which signal to be used according to which phase is the open phase. The PWM signal from DSP is used as the clock signal of D-type Flip-Flop, which will latch the output of Multiplexer. To mask the abnormal level-shift of open phase voltage, the first output samples of Multiplexer is discarded by appling a customized delay, which produced in GAL once a new phase commutation occurs, to Flip-Flop at the beginning of the commutation interval. Then, the output of Flip-Flop is the detected back EMF zero-crossing signal.
3.2. Starting procedure As the amplitude of back EMF is proportional to the rotor speed, it is impossible to detect the back EMF ZCP when the motor is at standstill. Therefore, a suitable starting procedure is necessary to the sensorless BLDC motor drive. In this control system, the starting procedure is divided into three stages [2,14,15]. In stage 1, two phases of the motor are energized for enough time; the rotor will be locked into a predefined position. In stage 2, a commutation signal advancing the switching pattern by 120 electrical degrees will be applied to the motor, and then, the frequency of the commutation signals is increasing gradually when the rotor rotates up by the adding currents. In stage 3, the operation mode of the motor
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(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , rotor position signal sb and phase current ib Fig. 7. Simulation waveforms at 1000 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, rotor position signal sb and phase current ib.
is changed to self-controlled mode when the speed of the rotor reaches a certain value, that is to say, the back EMF value reaches a detectable level. 4. Simulation and experimental results To verify the feasibility of the proposed method, computer simulations are first realized by MATLAB/SIMULIN software [16]. The four poles motor parameters used for simulation and hardware implementation are given as R = 2.875 X, Lm = 1.6 mH, Ls = 8.5 mH.
ubc
uab eb
Figs. 6a and 7a show the simulated back-EMF waveform of phase B and the line-to-line voltage difference uab, ubc at speed reference 100 rpm and 1000 rpm, respectively. The corresponding back EMF zero-crossings signal Seb, the calculated rotor position signal Scb and phase B current ib are depicted in Figs. 6b and 7b, respectively. It can be seen that the plots validate Eq. (9) in the region of zero crossing of the back EMF, and there exits no freewheeling current in unexcited phase B. Therefore we conclude that the method of detection of zero crossings of line-to-line voltage difference, as described in the previous section, is valid for a wide speed
Seb Scb
Shb ib
(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , calculated rotor position signal scb , Hall signal shb and phase current ib
Fig. 8. Experimental results at 100 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, calculated rotor position signal scb, Hall signal shb and phase current ib.
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Seb
ubc
Scb
uab
Shb
eb
ib
(a) Voltage difference ubc , uab and back EMF of phase B
(b) Zero crossing signal seb , calculated rotor position signal scb , Hall signal shb and phase current ib
Fig. 9. Experimental results at 1000 rpm. (a) Voltage difference ubc, uab and back EMF of phase B; and (b) zero-crossing signal seb, calculated rotor position signal scb, Hall signal shb and phase current ib.
ib
Scb
Fig. 10. B-Phase current, calculated commutation signal at 98% duty cycle.
Stage 1
Stage 2
Stage 3
ib Scb
Shb
Fig. 11. Starting process of BLDC motors with three stages. (From top to bottom: phase current, commutation signal after time shift, ZCP signal of phase B).
range.Figs. 8 and 9 present the experimental results for two speed references, which are 100 rpm and 1000 rpm, respectively. At 100 rpm, Fig. 8a illustrates the measured line-to-line voltage differences for ubc and uab, and the calculated back EMF signal by using the proposed method. Fig. 8b shows the corresponding ZCP of back EMF Seb, calculated rotor position Scb, measured Hall signal Shband the current of phase B. It is clear that each trigger edge of ZCP signal corresponds to 60°, 120°, 180°, 240°, 300°, 360° rotor position of back EMF of the unconducting phase. At 1000 rpm, Fig. 9 gives the experimental results of our sensorless method. As shown in Figs. 8 and 9, the calculated commutation signals coincide with those determined by HALL sensor. The experimental waveforms of phase A in Figs. 8 and 9 show a good agreement with the waveforms of simulation in Figs. 6 and 7. It can be observed that the estimated rotor position is in agreement with what is measured directly by the position sensor. These experimental results therefore confirm those obtained in simulation. To validate the system performance at high duty ratio, Fig. 10 shows the phase current and the estimated rotor position at 98% duty cycle. From this waveform, it can be seen that the commuta-
tion instant happens at trigger edge of phase current. Thus, the commutation process works well both in PWM on time and PWM off time even in high duty ratio. Compared with sensorless methods in [9,11,12], which can only work either in PWM off time or low PWM duty ratio, the proposed method exhibits better performance. Fig. 11 shows the current waveform and commutation signals of the experimental BLDCM drive implemented using the propose technique starting form standstill (stage 1) to closed-loop operation. It can be seen that the stage 2 lasts four electric cycles to assure the rotor aligning with the rotating magnetic field. When the input voltage is higher than, that is, if the back EMF is high enough for the detection circuit, the sensorless commutation signals will be sent to the commutation table and the motor is changed to the self commutation mode (stage 3). Moreover, the starting procedure from standstill to closed-loop operation is smooth and has no serious distortion of phase current. Experimental results show that the proposed method is feasible and efficient. With this sensorless method based on line-to-line back EMF, the motor can run smoothly in a wide speed range. 5. Conclusion Unlike conventional back EMF based sensorless commutation methods which focus on detection of the ZCP of the motor terminal to neutral voltage, a novel sensorless commutation method based on the difference of line-to-line voltage is proposed in this study. Both theoretical analysis and experimental results verify that satisfactory performance can be achieved with the proposed sensorless commutation method. Compared with the existing solutions, the proposed method has several improvements or characteristics, including the followings. 1. The neutral voltage is not required in the proposed method, only the three motor terminal voltages need to be detected. 2. With H_PWM–L_PWM scheme, it is proved that there exits no freewheeling current in the unexcited phase winding during the un-commutated interval, thus, the estimated ZCP is reliable and accurate. The process of estimating ZCP is implemented by the detection circuit, and so this method does not need position sensor. 3. Since the amplitude of the line-to-line voltage is significantly larger than the phase voltage, even a small back EMF can be effectively detected. Namely, a lower open loop starting speed can be achieved. 4. The maximum duty ratio of PWM can reach 100% since the sensing circuit can work whether the switches are PWM ON or PWM OFF.
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5. The special PWM scheme, H_PWM–L_PWM, is used in this method, which will result in higher switch losses when compared with the conventional single-bridge modulated PWM scheme. Torque ripple in this method is bigger than that in the conventional method in which PWM scheme is H_PWM– L_ON or L_PWM–H_ON. Acknowledgements The authors are grateful to the anonymous reviewers and to the National Natural Science Foundation of China Key Program for supporting this work through research Grant NSFC-60835004 and Hunan Natural Science Foundation through research Grant JJ076111. Reference [1] Acarnley PP, Watson JF. Review of position-sensorless operation of brushless permanent-magnet machines. IEEE Trans Ind Electron 2006;53(2):352–62. [2] Iizuka K, Uzuhashi H, Kano M, Endo T, Mohri K, et al. Microcomputer control for sensorless brushless motor. IEEE Trans Ind Appl 1985;27:595–601. [3] Ogasawara S, Suzuki K, Akagi H. A sensorless brushless dc motor system. Electr Eng Jpn 2007;112(5):109–18. [4] Jiang Q, Bi C, Hung R. A new phase-delay-free method to detect back EMF zerocrossing points for sensorless control of spindle motors. IEEE Trans Magn 2005;41(7):2287–94.
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