A new cost effective sensorless commutation

644 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 2, MARCH 2007

A New Cost Effective Sensorless CommutationMethod for Brushless DC Motors Without

Phase Shift Circuit and Neutral VoltageCheng-Hu Chen and Ming-Yang Cheng, Member, IEEE

Abstract—This paper presents the analysis, design, and imple-mentation of a high performance and cost effective sensorless con-trol scheme for the extensively used brushless dc motors. In an ef-fort to decrease cost and increase ease of implementation, the com-mutation signals are obtained without the motor neutral voltage,multistage analog filters, A/D converters, or the complex digitalphase shift (delay) circuits which are indispensable in the conven-tional sensorless control algorithms. In the proposed method, in-stead of detecting the zero crossing point of the nonexcited motorback electromagnetic force (EMF) or the average motor terminalto neutral voltage, the commutation signals are extracted directlyfrom the specific average line to line voltages with simple RC cir-cuits and comparators. In contrast to conventional methods, theneutral voltage is not needed; therefore, the commutation signalsare insensitive to the common mode noise. Moreover, the complexphase shift circuit can be eliminated. As a result, the proposed con-trol algorithm can be easily interfaced with the cost effective com-mercial Hall effect sensor based commutation integrated circuits.Due to its inherent low cost, the proposed control algorithm is par-ticularly suitable for cost sensitive products such as air purifiers,air blowers, cooling fans, and related home appliances. Theoret-ical analysis and experiments are conducted over a wide operatingspeed range and different back EMF waveforms to justify the ef-fectiveness of the proposed method.

Index Terms—Brushless dc motor (BLDCM), neutral voltage,phase shift circuit, sensorless control.

I. INTRODUCTION

DURING the last two decades, a lot of research on sensor-less control techniques for brushless dc motors (BLDCMs)

have been conducted. This research can be divided into four cat-egories [1]–[3]. 1) Detection of the zero crossing point (ZCP)of the motor terminal to neutral voltage with a precise phaseshift circuit [4]–[7]. 2) Back electromagnetic force (EMF) in-tegration method [8]. 3) Sensing of the third harmonic of theback EMF [9]. 4) Detection of freewheeling diode conductionand related extended strategies [10]. Among the various tech-niques, the back EMF zero crossing detection method is themost popular. In fact, many commercial sensorless integrated

Manuscript received December 13, 2005; revised May 4, 2006. This paperwas presented in part at the IEEE PEDS’05,Kuala Lumpur, Malaysia, Nov.28–Dec. 1, 2005. This work was supported by the Electric Motor TechnologyCenter, National Cheng Kung University. Recommended for publication by As-sociate Editor M. G. Simoes.

The authors are with the Department of Electrical Engineering, NationalCheng Kung University, Tainan 701, Taiwan, R.O.C. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2006.890006

circuits (ICs) such as Fairchild ML4425, Allegro 8904, etc. [11],[12] have been designed using this method. Unfortunately, thereare several practical implementation problems when using thephase to neutral zero crossing detection method. Firstly, the neu-tral voltage is required for comparison with the non-conductedback EMF or the average terminal voltage, in which it will in-troduce a high common-mode noise [6]. The other problem isthe requirement of the phase shift (delay time) circuit. Since thezero crossing points of the conventional back EMF method areinherently leading 30 electric degrees of the ideal commutationpoints, a precise velocity estimator and a phase shift circuit (al-gorithm) are needed to process the zero crossing signals so thataccurate commutation points can be determined. The additionalopen loop starting process and a complex phase shift circuit ac-companied with a precise velocity estimator make the sensorlesscommutation much more complex than the Hall effect sensorbased commutation. As a result, it is not surprising that the costof the commercial sensorless commutation ICs is usually severaltimes higher than that of the Hall effect sensor based commuta-tion ICs.

In order to cope with the aforementioned problems, a newcost effective sensorless commutation method is proposed. In-stead of detecting the motor terminal to neutral voltage, theestimated commutation signals are extracted directly from thespecific average line to line voltage of a BLDCM using simplesingle-stage low pass filters and low cost comparators [13]. Theoutput signals of the new detection circuit can be directly ap-plied to the conventional commutation table, as if they were ob-tained from the real Hall effect sensors. That is, the estimatedcommutation signals are well in phase with the ideal commuta-tion points. Unlike conventional solutions, the proposed methoddoes not require additional virtual motor neutral voltage, com-plex phase shift circuits, or precise speed estimators. Therefore,in terms of cost and reliability, the proposed approach has ob-vious advantages over conventional solutions. Theoretical anal-ysis and several experiments have been conducted to demon-strate the feasibility of the proposed approach. The results indi-cate that the proposed method exhibits satisfactory performanceover a wide speed range under varying load conditions and dif-ferent back EMF waveforms. These characteristics suggest thatthe proposed method is very suitable for cost sensitive applica-tions such as home appliances, computer peripherals, automo-tive components, etc.

The remainder of the paper is organized as follows. Section IIderives mathematical models for each commutation state of aBLDCM, where the switching statuses of the power devices

0885-8993/$25.00 © 2007 IEEE

CHEN AND CHENG: NEW COST EFFECTIVE SENSORLESS COMMUTATION METHOD 645

Fig. 1. Inverter topology and equivalent circuit of a BLDCM.

are considered. The principle and the commutation error of thenew sensorless commutation method based on the specific av-erage line to line voltage are explained in Sections III and IV.Section V discusses the practical implementation and the exper-imental results. Conclusions are given in Section VI.

II. MATHEMATICAL MODELS OF EACH COMMUTATION STATE

Fig. 1 shows the equivalent circuit of a BLDCM and the in-verter topology. Fig. 2 illustrates the relationship among theback EMF waveform of an ideal BLDCM, the armature cur-rent, the commutation signals (H1–H3), and the switching sig-nals (S1–S6) for the inverter. It can be seen that the fundamentalcharacteristics of a BLDCM during each commutation state issimilar to that of a dc brush motor. Since the back EMF and thearmature current are not perfectly sinusoidal, the dynamic equa-tion of a BLDCM is preferably expressed by the per phase vari-able method rather than the two axes variable method [1]–[3]

(1)

(2)

where is the phase voltage, is the armature resistance,is the armature inductance, is the armature current, and

is the armature back EMF.In order to regulate the conduction current so that the motor

will faithfully follow the given velocity or torque command, thepower switches are generally controlled via a high frequencyPWM signal (5–15 KHz for small to mid-sized motors). Theswitching signal can be injected on the high side, low side, orboth sides of the inverter legs. However, in order to reduce thecost of the gate drive circuit, the boost strap circuit is accompa-nied with switching on the high side (as shown in Fig. 2). Thismethod is widely used in many home appliances and industrialapplications [6], [13]. In what follows, the terminal voltages arederived according to the status of the conduction current and theswitching signal. According to the polarity of the armature cur-rent as illustrated in Fig. 2, the terminal voltage of each phasecan be divided into three sub-sections, i.e., positive, negative,and nonconducted. Fig. 3 illustrates the equivalent circuits ofeach commutation state for phase-“ ” over one electric cycle,and the same results can be obtained for the other two phases.

States I and II: Armature Current is Positive: Fig. 3(a) and (b)illustrate the equivalent circuit of the commutation states (I andII) where the armature current is positive. If the conduction

Fig. 2. Ideal back EMF, conduction current, commutation signals, andswitching signals of a BLDCM.

voltage caused by the power switches and the diodes is negli-gible, then the terminal voltage can be obtained according tothe switching status of the power switch S1

conducted states

freewheeling states (3)

States IV and V: Armature Current is Negative:Fig. 3(c) and (d) illustrate the equivalent circuit of thecommutation states (IV and V) where the armature current isnegative. Since the switch S2 is turned on, the motor terminal isconnected to the power ground. Therefore, the terminal voltagewill be kept low despite the switching status of the upper legs

conducted & freewheeling states (4)

States III and VI: Armature is Open (Nonconducted):Fig. 3(e) and (f) illustrate the equivalent circuit of the commu-tation states (III and VI) where the armature is open. Since thearmature is disconnected from the voltage source, the terminalvoltage can be expressed as the summation of the armatureback EMF and the neutral voltage

(5)


Fig. 3. Equivalent circuits of each commutation state for phase “a.” (a) Ar-mature current is “+,” conducted, states I and II. (b) Armature current is “+”,freewheeling, states I and II. (c) Armature current is “�,” conducted, states IVand V. (d) Armature current is “�,” freewheeling, states IV and V. (e) Armatureis open, conducted, states III and VI. (f) Armature is open, freewheeling, statesIII and VI.

If the switch of the upper leg is conducted (e.g., S3 is on), theneutral voltage can be expressed as

(6)

(7)

According to (6) and (7), the neutral voltage can be written as

(8)

If the switch of the upper leg is not conducted (e.g., S3 is off),the neutral voltage can be expressed as

(9)

(10)

(11)

As illustrated in Fig. 2, the amplitudes of the back EMF for theconduction phases during each commutation state are equal, andtheir polarities are opposite, namely 0. Accordingly,the neutral voltage can be rewritten as

conducted states (12)


If the waveform of the back EMF is perfectly sinusoidal, onewill have

(14)

Fig. 4. Measured instantaneous terminal voltage and corresponding switchingsignals (from top to bottom: terminal voltage V , switching signal for S1,switching signal for S2).

Substituting (14) into (8) and (11), the motor neutral voltage canbe rewritten as

conducted states (15)


Substituting (12) and (13) into (5), the terminal voltage of aBLDCM which has an ideal trapezoidal back EMF waveformcan be expressed as

conducted states

and


Equation (18) represents the case where the back EMF wave-form is perfectly sinusoidal

and conducted states

and


Note that each motor terminal is placed between the upperdiodes, which are connected to the dc source, and the lowerdiodesof the inverter, which are connected to the ground. It canbeexpected that the maximum and minimum terminal voltages willbe fixed between and 0. Fig. 4 shows the measured terminalvoltage and the corresponding switching signals. It is found thatthe waveforms are in accordance with the theoretical analysis.

III. PROPOSED ZCP DETECTION APPROACH BY

AVERAGE LINE TO LINE VOLTAGE

The major problem of the conventional back EMF sensingtechniques is that they require noisy motor neutral voltage and


Fig. 5. Ideal average terminal voltages under different duty ratios.

a fixed phase shift circuit. Since the noisy motor neutral voltagewill introduce the common mode noise into the sensorless cir-cuit, a low pass filter is indispensable. On the other hand, thefixed phase shift function over a wide speed range is hard to im-plement with analog circuits. Although the digital phase shiftalgorithm may provide better performance over a wide speedrange application, it is more complex than the analogue solu-tion and the cost will therefore be increased significantly. Inorder to cope with the aforementioned problems, the proposedmethod extracts the commutation points directly from the motorterminal voltages with simple comparators and a single stagelow pass filter. While conventional methods focus on the phaseto motor neutral voltage, namely the phase back EMF voltage,the key issue for the proposed approach is the specific line toline voltage.

If the terminal voltages are expressed in the average form (i.e.,duty ratio), the switching states in (3), (4), (17), and (18) can beeliminated. The terminal voltages are rewritten as follows.

States I and II: Armature Current is Positive:

(19)

States III and VI: Armature is Open (Nonconducted):

(20)

States IV and V: Armature Current is Negative:

(21)

According to (19)–(21), the ideal average terminal voltages forall three phases with different duty ratios are illustrated in Fig. 5.The measured instantaneous (upper trace) and average (lowertrace) terminal voltages as the duty ratio is increased from 10%,to 50%, to 100% are shown in Fig. 6. It is observed that the av-erage terminal voltage can be divided into three sub-sections asabovementioned. Moreover, the amplitude is proportional to the

Fig. 6. Measured instantaneous (first trace) and average (second trace) terminalvoltages under different duty ratios. (a) Duty ratio = 10%. (b) Duty ratio =50%. (c) Duty ratio = 100%.

duty-ratio as predicted by the theoretical analysis. The voltagespikes shown in the upper trace of Fig. 6 are caused by the


Fig. 7. Phase relationship among the back EMF, the average terminal voltage,and the average line to line voltage.

residual current during the commutation transition, in whichtheir effect will be discussed in Section IV.

According to the average terminal voltage derived in(19)–(21), the average line to line voltage can be expressedas

(22)

(23)

Equation (23) reveals that the zero crossing points of the averageline to line voltage will occur at 30 and 210 electric degrees.According to (22) and (23), Fig. 7 shows the phase relationshipamong the ideal back EMF, the average terminal voltage, and theaverage line to line voltage of phase “ ” and phase “ .” It is clearto see that the average line to line voltage lags 30 electric de-grees compared with the back EMF , namely the zero crossingpoints of the line to line voltage are in phase with the ideal com-mutation signals. Fig. 8(a) illustrates the practical circuit for

Fig. 8. Proposed and conventional sensorless commutation circuits. (a) Pro-posed cost effective sensorless commutation circuit. (b) Conventional sensor-less commutation circuit.

TABLE IINPUT FOR THE PROPOSED SENSORLESS COMMUTATION

CIRCUIT AND THE CORRESPONDING OUTPUT SIGNALS

implementing the proposed approach to obtain the commuta-tion signals (namely the virtual Hall effect signals ).Table I summarizes the three specific line to line voltages forthe proposed sensorless commutation approach. According tothe properties of the average line to line voltage, the ideal com-mutation points can be obtained directly from the three motorterminal voltages without the knowledge of the neutral voltage.Moreover, the obtained zero crossing points are inherently inphase with the ideal commutation points, that is, the complexphase shift circuit/algorithm can be eliminated. Consequently,the circuit needed in the proposed approach is much simplercompared with that needed in the conventional circuit shown inFig. 8(b).


Fig. 9. Illustration of various commutation errors. (a) Low pass filter. (b) Ar-mature impedance. (c) Effect of the voltage spike.

IV. ANALYSIS OF THE COMMUTATION ERROR

A. Phase Delay by the Low Pass Filter and the ArmatureImpedance

The phase delay angles caused by the input low pass filterand the armature impedance shown in Fig. 9(a) and (b) can beexpressed as

(24)

(25)

Since the 30 (or 90 ) phase shift circuit shown in Fig. 8(b)is not required in the proposed approach, the corner frequency

of the input low pass filter can be easily determined by themaximum motor speed and the switching frequency

, in which the value of can be chosen as

(26)

where 120, and is the pole number ofthe BLDCM.

The phase delay caused by the armature impedance can beneglected in most small to mid-sized BLDCMs due to the factthat the value of the resistance is usually much larger than theinductance. The current loop compensator can be used to over-come the delay caused by the armature impedance, however, itis not needed in most home appliance applications since it isonly required in very high speed applications.

B. Voltage Spikes by the Residual Current

The voltage spikes shown in Figs. 4 and 6 are created by theresidual current when the armature current is blocked by thepower switches. The voltage spike is the main cause for thecommutation error in the conventional back EMF integrationmethod and the window-captured back EMF method (detectingback EMF during the silent period) [7]. In these methods, theback EMF is compared with the motor neutral voltage or a fixeddc level, therefore the non-continuous voltage spikes will resultin noisy (virtual) ZCPs. In order to deal with these noisy ZCPs,additional complex digital filters are indispensable, which willdefinitely increase the complexity of the algorithm. Fig. 9(c) il-lustrates a close look at the effect of the voltage spike in the ter-minal voltage and the line to line voltage when a proper low passfilter is added. It can be seen that the polarity of the line to linevoltage is not sensitive to the voltage spike, that is the noisy ZCPwill not occur during the switching transition. In other words,the proposed method is more robust and easier to implementcompared with the conventional solutions.

V. EXPERIMENTAL EVALUATION

Fig. 10 shows the block diagram of the proposed sensorlesscontrol method. The system can be divided into several sub-blocks, including a velocity command generator, an open loopstarting process, a line to line voltage based virtual Hall effectsignal circuit, an electric commutation table, and a PWM gen-erator. The reference voltage determines the duty ratio for thePWM circuit, and the output speed of the motor is proportionalto the duty ratio. The speed command is implemented usinga variable resistor, while a simple RC circuit can be added toregulate a required acceleration/deceleration rate to achieve asmooth start. If the reference speed is too low, namely the refer-ence voltage is not high enough, the preprogrammed Hall effectsignals will be sent to the commutation table sequentially. It isknown as the open loop starting procedure, where the BLDCMis operated as a synchronous motor during this process. Theopen loop starting procedure lasts 1.5 s to assure that the rotorwill align with the rotating magnetic field generated from themulti-phase stator coils. The open loop starting speed is set to


Fig. 10. Block diagram of the overall system.

Fig. 11. Structure of the employed BLDCMs. (a) Type I (segmented magnet),trapezoidal back EMF. (b) Type II (ring magnet), sinusoidal back EMF.

150 RPM in this study. 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

Fig. 12. Measured back EMF waveforms of employed BLDCMs. (a) Type Imotor. (b) Type II motor.

commutation table and the motor is changed to the self com-mutation mode. That is, the synchronous motor is changed to abrushless dc motor. Unlike conventional solutions, the complexspeed estimation algorithm and the phase shift algorithm are notrequired in the proposed method. Therefore, the proposed sen-sorless commutation circuit can be easily interfaced with the lowcost Hall effect sensor based commutation ICs.

Fig. 11 shows the assembly of the two BLDCMs employed inthis study, Fig. 12 shows their corresponding back EMF wave-forms, which are trapezoidal and sinusoidal. Fig. 13(a)–(c) showthe experimental results for a wide speed operation range, from10% 100% full speed with the type I motor. Fig. 13(d) showsthe low speed performance of the proposed algorithm with thetype II motor. It is found that the proposed algorithm is in-sensitive to the back EMF waveform and the operating speeds.


Fig. 13. Measured commutation signals under different duty ratios and back EMF waveforms (from top to bottom: average terminal voltage V , average terminalvoltage V , average line to line voltage V , estimated commutation signal, signal from Hall effect sensor). (a) Duty ratio = 10%, type I motor. (b) Duty ratio= 50%, type I motor. (c) Duty ratio = 100%, type I motor. (d) Duty ratio = 10%, type II motor.

Since the required speed ratio for fans and ventilations are usu-ally around 3 5, the experimental results reveal that the pro-posed sensorless commutation approach can be applied to mosthome appliance applications. Fig. 14 shows the experimentalresults when compared with the conventional method shown inFig. 8(b). It can be seen that the signal from the conventionalsolution strongly depends on the operating speed; the mismatchangle is leading 21.8 in 10% full-speed, lagging 14.4 in 50%full-speed, and lagging 22.8 in full speed. The large commu-tation error is mainly caused by the multistage filters; thereforea speed dependent phase compensation algorithm is usually in-dispensable. Compared with the conventional solution, the pro-posed method is not only easier to design and implement, butalso exhibits better performance.

VI. CONCLUSION

Unlike conventional back EMF based sensorless commuta-tion methods which focus on detection of the ZCP of the motorterminal to neutral voltage, a novel sensorless commutationmethod based on the average line to line voltage is proposed inthis study. Both theoretical analysis and experimental resultsverify that satisfactory performance can be achieved with theproposed sensorless commutation method. Compared withthe conventional solutions, the proposed method has severaladvantages, including the following.

1) Elimination of the motor neutral voltage: The neutralvoltage is not required in the proposed method, only thethree motor terminal voltages need to be detected.


Fig. 14. Performance evaluation, compared with the conventional circuit (fromtop to bottom: instantaneous motor terminal voltage, signal from Hall effectsensor, signal from the proposed “line voltage method”, signal from the conven-tional “phase voltage method”). (a) Duty ratio = 10%. (b) Duty ratio = 50%.(c) Duty ratio = 100%.

2) Elimination of the fixed phase shift circuit: The proposedspecific average line to line voltage inherently lags 30electric degrees compared with the phase back EMF.Moreover, experimental results have revealed that thephase relationship is insensitive to operating speed andload conditions.

3) Low starting speed: Since the amplitude of the line to linevoltage is significantly larger than the phase voltage, evena small back EMF can be effectively detected. Namely, alower open loop starting speed can be achieved.

4) Insensitive to the back EMF waveform: Compared withthe third-harmonic detection method, the proposed methodcan be used for a BLDCM with nonideally trapezoidal orsinusoidal back EMF waveforms, since most BLDCMs donot have ideal back EMF waveforms.

5) Cost effective: Because the speed estimation algorithmand the complex phase shift circuits are not required, thecostly digital signal processor controller is not needed.Using a simple starting process, the proposed method canbe easily interfaced with the low cost commercial Halleffect sensor based commutation ICs. Consequently, theproposed method is particularly suitable for cost sensitiveapplications such as home appliances and related com-puter peripherals.

ACKNOWLEDGMENT

The authors wish to thank B. Liao for his assistance with thiswork.

REFERENCES

[1] K. Rajashekara, A. Kawamura, and K. Matsuse, Sensorless Control ofAC Motor Drives. Piscataway, NJ: IEEE Press, 1996.

[2] J. P. Jahnson, M. Ehsani, and Y. Guzelaunler, “Review of sensorlessmethods for brushless DC,” in Proc. IEEE IAS Annu. Meeting Conf.,Phoenix, AZ, 1999, pp. 143–150.

[3] R. Krishnan, Electric Motor Drives, Modeling, Analysis, and Con-trol. Englewood Cliffs, NJ: Prentice-Hall, 2001.

[4] K. Lizuka, H. Uzuhashi, M. Kano, T. Endo, and K. Mohri, “Microcom-puter control for sensorless brushless motor,” IEEE Trans. Ind. Appl.,vol. IA-21, no. 4, pp. 595–601, May/Jun. 1985.

[5] H. Chen, Y. Chang, S. Lin, C. Huang, Y. Chen, and K. Liang, “Sensor-less control for dc inverter-fed compressors,” in Proc. APEC’04, Ana-heim, CA, 2004, pp. 1100–1106.

[6] J. Shao, D. Nolan, M. Teissier, and D. Swanson, “A novel microcon-troller-based sensorless brushless dc (BLDC) motor drive for automo-tive fuel pumps,” IEEE Trans. Ind. Appl., vol. 39, no. 6, pp. 1730–1740,Nov./Dec. 2003.

[7] Q. Jiang, C. Bi, and R. Huang, “A new phase-delay method to detectback EMF zero-crossing points for sensorless control of spindlemotors,” IEEE Trans. Magnetics, vol. 41, no. 7, pp. 2287–2594, Jul.2005.

[8] R. C. Becerra, T. M. Jahns, and M. Ehsani, “Four-quadrant sensorlessbrushless ECM drive,” in Proc. APEC’91, 1991, pp. 202–209.

[9] J. Moreira, “Indirect sensing for rotor flux position of permanentmagnet AC motors operating over a wide speed range,” IEEE Trans.Ind. Appl., vol. 32, no. 6, pp. 1394–1401, Nov./Dec. 1996.

[10] S. Ogasawara and H. Akagi, “An approach to position sensorless drivefor brushless dc motors,” IEEE Trans. Ind. Appl., vol. 27, no. 5, pp.928–923, Sep./Oct. 1991.

[11] Fairchild Semiconductor, “Datasheet of ML 4425,” Tech. Rep., 2001.[12] Allegro Micro Systems, “Datasheet of Allegro 8904,” Tech. Rep., 2003.[13] C.-H. Chen and M.-Y. Cheng, “A new sensorless control scheme for

brushless dc motors without phase shift circuit,” in Proc. 6th IEEE Int.Conf. Power Electron. Drive Syst., 2005, pp. 1084–1089, K. L..


Cheng-Hu Chen was born in I-Lan, Taiwan, R.O.C.,in 1974. He received the B.S. degree in mechanicalengineering from the National Taiwan University ofScience and Technology, Taipei, Taiwan, R.O.C., in1997, and the M.S. and Ph.D. degrees in mechanicalengineering and electrical engineering from NationalCheng Kung University, Tainan, Taiwan, R.O.C., in1999 and 2006, respectively.

Currently, he is a Post-Doctoral Fellow at the Na-tional Cheng Kung University. His current researchinterests include sensorless BLDC motor/alternator

control, power factor control, hybrid electric vehicles, and automotive powersystems.

Ming-Yang Cheng (M’97) was born in Taiwan,R.O.C., in 1963. He received the B.S. degree incontrol engineering from the National Chiao-TungUniversity, Hsinchu, Taiwan, R.O.C., in 1986 andthe M.S. and Ph.D. degrees in electrical engineeringfrom the University of Missouri, Columbia, in 1991and 1996, respectively.

From 1997 to 2002, he held several teaching po-sitions at the Kao Yuan Institute of Technology, theDayeh University, and the National Kaohsiung FirstUniversity of Science and Technology. In 2002, he

joined the Department of Electrical Engineering, National Cheng Kung Univer-sity, Tainan, Taiwan, where he is currently an Associate Professor. His researchinterests include motion control, motor drives, visual servoing, and biped loco-motion.

A new cost effective sensorless commutation

Education

Transcript of A new cost effective sensorless commutation