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3436 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 9, SEPTEMBER 2012 Hybrid I-f Starting and Observer-Based Sensorless Control of Single-Phase BLDC-PM Motor Drives Liviu Ioan Iepure, Member, IEEE, Ion Boldea, Fellow, IEEE, and Frede Blaabjerg, Fellow, IEEE Abstract—A motion sensorless control for single-phase perma- nent magnet brushless dc motor based on an I-f starting sequence and a real-time permanent magnet flux estimation is proposed here. The special calculation for extracting the position and speed used here implies the generating of an orthogonal flux system, the atan2 trigonometric function, and a phase-locked loop observer. The influence of the permanent magnet flux harmonic content is presented by analytical expressions and digital simulations. The proposed sensorless control is validated by complete experimental results on a commercial small high-speed blower-motor (40 W, 10 krpm, 12 Vdc). Index Terms—Orthogonal flux system, permanent magnet brushless dc (PM-BLDC), phase-locked loop (PLL) observer, sensorless control. I. I NTRODUCTION I N THE FIELD of small-power (up to 1-Nm torque), small starting torque applications (blowers, pumps), the single- phase BLDC motor presents a growing interest particularly in the residential and automotive industry, where it is more efficient than rival motors and results in motor size reduction [1]–[4]. The main peculiarity of single-phase BLDC motor is the fact that solutions to eliminate the dead points in torque waveform are required. Methods to study and eliminate this drawback by electromagnetic analysis, modeling, and then by a proper design and/or by an adequate control have been addressed extensively [5]–[9]. Typically, one Hall sensor is used to control the current commutation to maximize the torque output by keeping the back EMF and the current in phase. For high speed, the advance commutation angle techniques as assessed in [10], [11] have to be used. Also, in [12]–[14], adaptive commutation angle methods for efficiency and torque improvement, requiring some extra hardware, are proposed. Under open-loop pulse width modulation (PWM) control, a current spike during each commutation appears. This results in acoustic noise, increased electronic cost, torque pulsations, and low efficiency. One solution is to use the aforementioned Manuscript received March 25, 2011; revised June 13, 2011; accepted August 12, 2011. Date of publication October 14, 2011; date of current version April 13, 2012. L. I. Iepure is with the AVL Trimerics GmbH, 70794 Filderstadt, Germany (e-mail: [email protected]). I. Boldea is with the Department of Electrical Engineering, University Po- litehnica of Timisoara, 300223 Timisoara, Romania (e-mail: boldea@lselinux. upt.ro). F. Blaabjerg is with the Institute of Energy Technology, Aalborg University, 9220 Aalborg, Denmark (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2011.2172176 phase advance technique, while [15] proposes a tail end current control. Also, in [16], current shape control for improving the efficiency and to avoid the oversizing of power electronics devices was investigated. In [17], [18], another current shape solution, for smoothing the torque, was determined based on a prior finite-element method (FEM) analysis. In [19], using the Lagrange multiplier, an optimal current waveform for low copper losses and low torque ripple was introduced. For this purpose, high-resolution position information and a microcon- troller are needed. While several publications on single-phase permanent mag- net brushless dc (PM-BLDC) motor control have appeared, few so far considered the elimination of position sensor. One solution for sensorless control of single-phase BLDC motor drives is based on back EMF sensing via the winding time- sharing method, as described in [20]. In this paper, a second solution, based on real-time flux estimation, is adopted. Though apparently very simple sensorless control techniques should be used in single-phase BLDC motors, good performance in terms of speed regulation, torque pulsations, and losses require more involved control solutions, such as those that follow, which still may be implemented on reasonable cost DSP systems. In view of the above, the present paper’s main contributions aim to: introduce a voltage-model proportional integrator con- troller (PI) compensated observer-based sensorless control for single-phase PM-BLDC motor drives; develop a special calculation method for estimating the rotor position from the permanent magnet (PM) flux ob- server by generating an orthogonal flux system and by using the atan2 special trigonometric function; analyze the peculiarity of using a flux waveform with harmonic content in the proposed position observer; improve the estimated position, by using a phase-locked loop (PLL) observer, which can give also the estimated speed, and so the noise produced by position differentia- tion is eliminated; validate the proposed sensorless control under both motor- ing and regenerative braking operation modes; combine the flux voltage-model observer-based proposed sensorless control with an open-loop current-frequency (I-f) starting strategy with a simple transition to closed- loop sensorless control. The paper is structured as follows: Introduction (Section I), Proposed state observer (Section II), I-f starting and proposed sensorless control diagram (Section III), Experimental results (Section IV), and Conclusions (Section V). 0278-0046/$26.00 © 2011 IEEE

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3436 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 9, SEPTEMBER 2012

Hybrid I-f Starting and Observer-Based SensorlessControl of Single-Phase BLDC-PM Motor Drives

Liviu Ioan Iepure, Member, IEEE, Ion Boldea, Fellow, IEEE, and Frede Blaabjerg, Fellow, IEEE

Abstract—A motion sensorless control for single-phase perma-nent magnet brushless dc motor based on an I-f starting sequenceand a real-time permanent magnet flux estimation is proposedhere. The special calculation for extracting the position and speedused here implies the generating of an orthogonal flux system, theatan2 trigonometric function, and a phase-locked loop observer.The influence of the permanent magnet flux harmonic content ispresented by analytical expressions and digital simulations. Theproposed sensorless control is validated by complete experimentalresults on a commercial small high-speed blower-motor (40 W,10 krpm, 12 Vdc).

Index Terms—Orthogonal flux system, permanent magnetbrushless dc (PM-BLDC), phase-locked loop (PLL) observer,sensorless control.

I. INTRODUCTION

IN THE FIELD of small-power (up to 1-Nm torque), smallstarting torque applications (blowers, pumps), the single-

phase BLDC motor presents a growing interest particularlyin the residential and automotive industry, where it is moreefficient than rival motors and results in motor size reduction[1]–[4].

The main peculiarity of single-phase BLDC motor is the factthat solutions to eliminate the dead points in torque waveformare required. Methods to study and eliminate this drawbackby electromagnetic analysis, modeling, and then by a properdesign and/or by an adequate control have been addressedextensively [5]–[9].

Typically, one Hall sensor is used to control the currentcommutation to maximize the torque output by keeping theback EMF and the current in phase. For high speed, the advancecommutation angle techniques as assessed in [10], [11] haveto be used. Also, in [12]–[14], adaptive commutation anglemethods for efficiency and torque improvement, requiring someextra hardware, are proposed.

Under open-loop pulse width modulation (PWM) control, acurrent spike during each commutation appears. This resultsin acoustic noise, increased electronic cost, torque pulsations,and low efficiency. One solution is to use the aforementioned

Manuscript received March 25, 2011; revised June 13, 2011; acceptedAugust 12, 2011. Date of publication October 14, 2011; date of current versionApril 13, 2012.

L. I. Iepure is with the AVL Trimerics GmbH, 70794 Filderstadt, Germany(e-mail: [email protected]).

I. Boldea is with the Department of Electrical Engineering, University Po-litehnica of Timisoara, 300223 Timisoara, Romania (e-mail: [email protected]).

F. Blaabjerg is with the Institute of Energy Technology, Aalborg University,9220 Aalborg, Denmark (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/TIE.2011.2172176

phase advance technique, while [15] proposes a tail end currentcontrol. Also, in [16], current shape control for improving theefficiency and to avoid the oversizing of power electronicsdevices was investigated. In [17], [18], another current shapesolution, for smoothing the torque, was determined based ona prior finite-element method (FEM) analysis. In [19], usingthe Lagrange multiplier, an optimal current waveform for lowcopper losses and low torque ripple was introduced. For thispurpose, high-resolution position information and a microcon-troller are needed.

While several publications on single-phase permanent mag-net brushless dc (PM-BLDC) motor control have appeared,few so far considered the elimination of position sensor. Onesolution for sensorless control of single-phase BLDC motordrives is based on back EMF sensing via the winding time-sharing method, as described in [20]. In this paper, a secondsolution, based on real-time flux estimation, is adopted. Thoughapparently very simple sensorless control techniques should beused in single-phase BLDC motors, good performance in termsof speed regulation, torque pulsations, and losses require moreinvolved control solutions, such as those that follow, which stillmay be implemented on reasonable cost DSP systems.

In view of the above, the present paper’s main contributionsaim to:

• introduce a voltage-model proportional integrator con-troller (PI) compensated observer-based sensorless controlfor single-phase PM-BLDC motor drives;

• develop a special calculation method for estimating therotor position from the permanent magnet (PM) flux ob-server by generating an orthogonal flux system and byusing the atan2 special trigonometric function;

• analyze the peculiarity of using a flux waveform withharmonic content in the proposed position observer;

• improve the estimated position, by using a phase-lockedloop (PLL) observer, which can give also the estimatedspeed, and so the noise produced by position differentia-tion is eliminated;

• validate the proposed sensorless control under both motor-ing and regenerative braking operation modes;

• combine the flux voltage-model observer-based proposedsensorless control with an open-loop current-frequency(I-f) starting strategy with a simple transition to closed-loop sensorless control.

The paper is structured as follows: Introduction (Section I),Proposed state observer (Section II), I-f starting and proposedsensorless control diagram (Section III), Experimental results(Section IV), and Conclusions (Section V).

0278-0046/$26.00 © 2011 IEEE

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Fig. 1. Structure of the proposed state observer.

II. THE PROPOSED STATE OBSERVER

A rotor position and speed observer, based on a generatedorthogonal flux system, is proposed and explored further. Fig. 1shows the proposed estimation diagram. The state observer iscomposed of a PM flux estimator, an orthogonal flux systemgenerator, and a PLL observer.

A. PM Flux Estimator

The implemented PM flux estimator is using as inputs theapplied voltage and the winding current. Instead of using themeasured phase voltage, the PI current controller output isused as a voltage estimator. This will reduce the cost and willimprove the drive robustness to noise and so a LPF whichcan delay the signal is not needed as in the case of measuredvoltage. In this case, the power switch voltage drops and thedead time have to be considered, particularly at low-speedoperation.

Starting from machine voltage (1), the PM flux linkage isdetermined by voltage integration, using (2)

V =R · i + L · di

dt+ e; e =

dψPM

dt= ke(θ) · ω (1)

Ψs =

t∫0

(V − Ri − Vcomp)dt;

ΨPM = Ψs − Li; Vcomp = (kp + ki/s) · Ψs (2)

where V is the input voltage, i is the current, R is the resistance,e is the back EMF, ω is the rotor speed, L is the windinginductance, and Ψs, ΨPM are the total flux and the permanentmagnet flux, respectively.

In practice, the implementation of an integrator for motorflux estimation is problematic because of the ramp drift and thedc offset produced on the output signal. A PI correction feed-back (Vcomp) was used here, together with an ideal integrator.

Considering that complementary PWM signals were usedfor controlling the power switches, thus allowing controlledregenerative braking also, the reconstructed voltage is ob-tained from

V = (2 · D − 1) · Vdc (3)

where D is the reference duty cycle, and Vdc is the dc linkvoltage.

Fig. 2 shows as an example the estimated total flux andPM flux, obtained by simulation from the shown input voltagesignal and phase current, at 5000-rpm speed.

The estimated flux was approximated by Fourier series asfunction of electrical position θ through a curve fitting algo-

Fig. 2. PM flux estimator inputs and output. (a) Applied voltage. (b) Phasecurrent. (c) Estimated total flux and PM flux, at 5000 rpm, by digitalsimulations.

rithm to analytically illustrate the peculiarity of using nonsi-nusoidal flux distribution in the proposed position and speedestimation.

Equation (4) shows the obtained analytical approximation

ψPM =∑

k=1,3,5

Ak cos(k · θ) + B1 · sin θ (4)

where ψPM is the instantaneous estimated PM flux, and theterms Ak, B1 are the coefficients of the Fourier series, listed inAppendix, Table I.

B. The Proposed Orthogonal PM Flux System Generator

In single-phase BLDC-PM motors, there is less informationthan in three phase motors, and thus, some special calculationshave to be done to estimate the rotor position. The idea ofthis sensorless drive is to create an orthogonal PM flux linkagesystem to employ it in rotor position/speed estimation. In theliterature, the solution of generating two orthogonal signals isapplied in the field of single-phase grid connected systems,where the delayed signal is the measured voltage [21]–[23], butno such a solution for one-phase BLDC motor sensorless driveis encountered.

Considering an ideal sinusoidal flux distribution as in (5),a flux phasor as in (6) can be assigned, where the estimatedPM flux is Re{Ψ}

ψ(θ) = Ψ · cos θ (5)

Ψ = Ψ · ejθ = Ψ · cos θ + j · Ψ · sin θ. (6)

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3438 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 9, SEPTEMBER 2012

Fig. 3. Locus of PM flux phasor. (a) Ideal sinusoidal shape. (b) Real fluxshape.

Where ψ(θ) is the instantaneous value of PM flux in statorframe coordinates, and Ψ is the PM flux amplitude. From(6), the phasor phase angle, and so the PM position, can bedetermined by using (7), which, under steady-state conditions,equals ωt

θ = arctan(

Im{Ψ}Re{Ψ}

). (7)

Now, in the case of the real PM flux of a BLDC motor, due tothe harmonic content in its shape, the PM flux phasor amplitudeis not constant with its position, and it is not always equal withthe PM flux amplitude as Fig. 3 shows. Due to this aspect, aFourier series analytical approach is employed here to outlinethe peculiarity of using a PM flux with harmonic content, whenextracting the position by the above presented method.

Hence, starting from (5)–(7), the nonsinusoidal PM fluxshape is implied further in estimating the rotor. By using anidentical flux shape delayed with π/2, the imaginary com-ponent of the PM flux phasor is obtained. Having the PMflux approximation from (4), the delayed PM flux analyticalapproximation is expressed by

ψPMd =∑

k=1,3,5

Ak cos(k · θ − π

2

)+ B1 · sin

(θ − π

2

).

(8)

Fig. 3 shows the flux locus of the ideal sinusoidal flux,respectively, of the real PM flux determined using (4) and (8).

Thus, having two orthogonal fluxes as the real and imaginarycomponents of a flux phasor given in (9), the rotor position canbe extracted using the special function atan2 as in (10)

ΨPM =ψPM + j · ψPMd (9)

θatan = arctan(

Im{ΨPM}Re{ΨPM}

)= atan2

(ψPMd

ψPM

). (10)

To avoid the complex mathematics for an analytical expres-sion of rotor position, (10) was numerically computed usingthe fluxes from (4) and (8), and the result was also expressedusing the Fourier series. Equation (11) represents the Fourierseries-based approximation of the calculated position. Somefourth-order harmonics are noticed additionally to the lineardependency with speed. The C0, C1, and C2 are the coefficientsof the Fourier series, listed in Appendix, Table I. Equation (11)is valid for a flux waveform varying from a triangular shape to

Fig. 4. (a) Orthogonal fluxes and (b) estimated position at 5000 rpm by digitalsimulations.

Fig. 5. Simulink implementation of position estimator.

a sinusoidal one, with the C0, C1, C2 tending to zero as the PMflux waveform is approaching to a sinusoidal shape

θatan =∫

ω · dt + C0 + C1 · cos(4ωt) + C2 · sin(4ωt).

(11)

In this paper, the adopted solution for real-time generationof the imaginary PM flux component is based on delayingthe estimated PM flux with a number of sampling periods,equivalent to 90 electrical degrees. The number of samplingperiods used for the delay is obtained from the estimated speedusing

N =2π

4 · ω · p · Ts(12)

where ω is the estimated speed in [rad/s], p is the number ofpole pairs, and Ts is the sampling time

Fig. 4 shows the estimated and the delayed PM fluxes,respectively, and the estimated position obtained by simulationat a speed of 5000 rpm, while Fig. 5 illustrates the Simulinkimplemented block diagram of the position estimator.

The above determined harmonics from (11) are visible assmall oscillations in the estimated position. They may causefurther problems in prescribing a proper current shape, andsome measures must be taken.

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Fig. 6. Equivalent PLL-based position and speed estimator.

Fig. 7. Simulation results at 3000 rpm. (a) Estimated position. (b) Positionerror with equivalent PLL system.

C. PLL-Based Position Refining and Speed Observer

In general, the calculation of speed from the estimated rotorposition by differentiation is problematic because it results insignificant noise. Here, a PLL is used to estimate the speed andto filter the estimated position.

So far, PLL observers have been widely used in high perfor-mance servo drives for speed calculation from resolver or en-coder signals or for position and speed estimation in sensorlesscontrol of three-phase motors [24]–[26]. Regarding the single-phase PLL observer, various structures were usually used forsingle-phase grid-connected applications [27], [28], but no ap-plications for single-phase PM-BLDC motor sensorless drivesare known to us so far.

Fig. 6 presents the PLL structure which improves the atan2-based estimated position (θatan). The error between the pre-vious atan2 position and the estimated position is the input toa PI controller, while the output from the PI controller is theestimated speed. The essential relations are given by

ε = sin(θ̂a tan − θ̂PLL); ω̂PLL =(

Kp +Ki

s

)· ε;

θ̂PLL = ω̂PLL/s. (13)

Fig. 7 shows by simulation results how the PLL output posi-tion tracks the input position and behaves like a very efficientLPF for the noticed position oscillations.

Fig. 8. Proposed sensorless control block diagram.

III. I-f STARTING AND PROPOSED SENSORLESS

CONTROL DIAGRAM

Fig. 8 shows the proposed sensorless control diagram. Basi-cally, the control contains two PI controllers, a state observer,and an I-f starting sequence.

During the I-f starting sequence, the applied reference cur-rent frequency is ramped by using a first-order delay filter,while the reference current amplitude is maintained constant.From this frequency, an imposed position is obtained, and theprescribed phase current is commutated by using this feedfor-ward signal.

When running on this starting sequence, the speed con-troller is kept with zero input error by flagi/f to avoid erroraccumulation in the integral component (which would causeproblems when crossing to the closed-loop sensorless control).When the I-f frequency exceeds a certain threshold value, theflagi/f signal will make the transition to the state observer-basedsensorless control.

A closed-speed loop containing the inner current loop isused further for state-observer-based sensorless control. Theoutput from the PI speed controller represents the referencecurrent for the current controller. The current control loop alsoemploys a PI controller, which has the purpose to minimizethe current error. The current control is made through themeasurement of the phase current which is forced to follow awaveform template. The current shape is now prescribed usingthe estimated position, obtained as described in the previoussections.

IV. EXPERIMENTAL RESULTS

The proposed motion sensorless control was validated byexperiments. The experimental motor is an outer rotor four-pole single-phase tapered airgap PM-BLDC motor with theelectrical specification given in Appendix, Table II. The imple-mentation of the digital sensorless control was carried out withthe rapid prototyping and real-time interface system dSpace1103 (Fig. 9). It goes without saying that an industrial im-plementation should be done on a low-cost DSP, and in ourexperience, a dsPIC30F2010 (Microchip) should satisfy thecomputation requirements. However, this is beyond our scopehere. A full-bridge single-phase PWM converter is used. It

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3440 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 9, SEPTEMBER 2012

Fig. 9. Experimental rig.

Fig. 10. Experimental results at 3000 rpm. (a) Estimated and delayed flux.(b) Measured and PLL-based estimated position. (c) Position error. (d) Speed.

should be mentioned that the motor was provided with itsblower, and thus it was under its “natural” load all the time.

A. Steady-State Tests

Fig. 10 shows the experimental results at a given constantspeed of 3000 rpm. The measured and estimated positions areintentionally shifted with 1 radian to avoid overlaps.

A good agreement between measured (calculated from Hallsignal) and estimated position can be observed, and the filtering

Fig. 11. Experimental results for speed transient. (a) Measured speed.(b) Estimated speed. (c) Current. (d) Estimated flux. (e) Current and Hall signalsunder speed transient. (f) Current and Hall signals at constant speed.

behavior of the PLL observer can be also noticed if we analyzethe position error.

The offset value noticed in position error from Fig. 10 is com-pensated when running on speed closed-loop sensorless control,and moreover, a speed-dependent phase advance commutationangle was applied at higher speeds, to obtain an always positivetorque.

B. Dynamics

Having a commercial blower-1 phase BLDC motor blockunit, the measured position was obtained only from the Hallsignal. Consequently, the position feedback may perhaps notbe very precise. The relation between the Hall sensor outputand the current is used also to validate the sensorless controleffectiveness.

Fig. 11 shows a transient behavior for speed steps of1000 rpm. Comparing Fig. 11(e) and (f), a small delay betweenthe current and the Hall signal is noticed under transients. Sincethe current is prescribed using this estimated position, it meansthat the error between the estimated and the real position isincreasing under speed transients but not alarming (a maximumvalue of 20 electric degrees was calculated). This delay can be

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IEPURE et al.: HYBRID I-f STARTING AND OBSERVER-BASED SENSORLESS CONTROL OF BLDC-PM MOTOR DRIVES 3441

Fig. 12. Experimental results for 5000 to 3000 rpm speed transient.(a) Measured speed. (b) Estimated speed. (c) Estimated flux. (d) Current.

reduced more by a better PLL observer tuning, or it can also becompensated by a distinctive phase commutation advance angleunder acceleration.

C. Regenerative Braking

For rapid and controlled braking, the regenerative braking isapplied here. Fig. 12 shows a regenerative braking from 5000to 3000 rpm.

A drop in the estimated flux amplitude during brakingprocess is noticed. This flux decrease can be explained bythe fact that during the braking time interval, the dc linkvoltage increases, and since no voltage measurement is done,the estimated flux is affected by this phenomenon. A propertyof the proposed sensorless control reveals: in spite of thisphenomenon, the sensorless speed control remains effectivebecause the position from the PLL observer is not affectedby PM flux amplitude. The estimated position which remainsclose to the measured one and the current waveform which hasopposite sign compared with the BEMF (Fig. 13) confirms thecontrol effectiveness during regenerative braking.

D. I-f Starting Tests

Fig. 14 presents a detailed view over the crossing momentfrom the I-f sequence to closed-loop sensorless control. Asexplained above, the PI speed controller sees zero speed errorat the input, and so the imposed reference current from it

Fig. 13. Representative signals during braking. (a) Estimated and measuredposition. (b) Estimated voltage versus BEMF. (c) Phase current.

will be zero during I-f sequence. During this sequence, aconstant current is commutated based on a feedforward positioninformation.

When the reference frequency from I-f control is greaterthan the imposed threshold, the sensorless control passes to theclosed-loop sensorless control, and the current commutation isthen done based on the estimated position [Fig. 14(c)], whilethe I-f position and speed become zero.

After the transition to closed-loop sensorless control, thespeed controller produces a nonzero signal output as referencecurrent [Fig. 14(e)]. In Fig. 14(b), good speed estimation is ob-tained, with some oscillations at the start around the prescribedI-f speed. Fig. 14(c) shows that for both the estimated and I-fpositions, the initial position is considered to be the parkingposition. As shown in [29], by applying a proper positivepulse before I-f sequence, the starting position will alwaysbe appropriate for starting with positive current as used here[Fig. 14(d)].

To further validate this proposed sensorless control, a shortanalysis of developed torque is done. Based on a previous FEManalysis and laboratory measurements [30], the BEMF and thecogging torque characteristic of the motor are used as look-up tables. The input to these look-up tables is the calculatedposition from the Hall signal. Using this information, the torquewas calculated using (13) under steady state (dω/dt = 0)

J · dω

dt= ke · i + Tcogg − Tload. (14)

Fig. 15 shows the experimental results for a constant speedof 4000 rpm. At this speed, no commutation phase advanceangle was used. It can be noticed that the current is almost inphase with the BEMF (only a small delay time of approximately2–3 sampling times, needed for the current to rise, is noticed),

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3442 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 9, SEPTEMBER 2012

Fig. 14. Experimental results for starting. (a) Estimated speed. (b) Speedcomparison. (c) Position. (d) Current. (e) Output from speed controller. (f) Hallsignal.

and so, the obtained instantaneous torque is always positive.Fig. 15 shows the possibility of evaluating torque waveformwithout using any online measurement and shows fairly smalltorque pulsations for a single-phase PMBLDC, due to the factthat the current is correctly prescribed using the estimatedposition.

Due to the errors that can appear when calculating the posi-tion from the Hall sensor in dynamics, only the torque estimatedunder steady-state speed is reliable and presented.

V. CONCLUSION

A hybrid I-f starting and observer-based motion sensorlesscontrol, which can handle both motoring and regenerativebraking operation modes for a single-phase PM BLDC motor,

Fig. 15. Experimental results at 4000 rpm. (a) Position. (b) BEMF andcurrent. (c) Calculated torque.

was introduced here. No regenerative braking under sensorlesscontrol for a single-phase PM-BLDC motor is known to usso far.

The proposed sensorless control is based on the estimationof a continuous position starting from a real-time referencevoltage-model PM flux estimator. In author’s knowledge, nosensorless control for single-phase PM-BLDC motor drivewhich does not use any voltage measurement and allows foradvanced control solutions (i.e., current shaping based on highresolution position information) was referred in the literatureso far.

Starting from the estimated PM flux, some special calcula-tions are done to extract the position/speed information. Theseimply a generated orthogonal PM flux system and the atan2function for a first step position calculation. Then, a PLLobserver is used for speed estimation and position filtering.Such a sensorless control solution for a single-phase PM-BLDCmotor drive is considered new.

The peculiarity of using a PM flux with harmonic contentfor extracting the position in this way is explained and detailedby Fourier series analytical approximation and by simulations.In spite of the harmonic content in the estimated PM flux, theeffectiveness of this method was proven by exhaustive exper-imental results under both motoring and regenerative brakingoperation modes.

Also, the proposed sensorless control proved to be effec-tive, in spite of the estimated PM flux amplitude variations(Section IV-C). Here, the estimated flux amplitude decreaseis mainly caused by the experimental setup which allows thereverse current in the dc link to flow only in the dc link capacitorduring regenerative braking. However, in a real application, theestimated PM flux amplitude changing can be caused by both dcvoltage variation (i.e., when a battery supply is used) and phaseresistance variation. This encourages the authors to say that theuse of a simple reference voltage-model PM flux estimator, in

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IEPURE et al.: HYBRID I-f STARTING AND OBSERVER-BASED SENSORLESS CONTROL OF BLDC-PM MOTOR DRIVES 3443

TABLE IFOURIER SERIES COEFFICIENTS

TABLE IIMOTOR PARAMETERS

spite of its susceptibility to parameter variations, should sufficefor this solution of sensorless control.

Also, the aforementioned property allowed the sensor-less control implementation without being necessary to useany voltage measurement (dc link voltage or terminal phasevoltage).

APPENDIX

See Tables I and II.

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Liviu Ioan Iepure (M’11) received the Ph.D. degreefrom University Politehnica of Timisoara, Romania,in 2010.

He was a Guest Researcher at the Institute ofEnergy Technology, Aalborg University, AalborgEast, Denmark, in 2009, and at the EBM-PAPSTSt. Georgen GmbH & Co., St. Georgen, Germany,in 2008. He is currently an electric machinedevelopment engineer at AVL-Trimerics GmbH,Filderstadt, Germany. His current research interestsinclude design, modeling, testing, and control of

electric machines, sensors, and actuators.

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3444 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 9, SEPTEMBER 2012

Ion Boldea (M’77–SM’81–F’96) received the M.S.and Ph.D. degrees from the University Politehnica ofTimisoara, Romania, in 1967 and 1973, respectively.

He is currently a Full Professor at the UniversityPolitehnica of Timisoara, Timisoara, Romania. Hehas visited universities in the U.S. and the U.K.repeatedly and has published extensively on lin-ear and rotary electric machines, drives, and powerelectronics. His latest books (with S. A. Nasar) areElectric Drives (2nd Edition), Boca Raton: CRCPress, 2005; The Induction Machine Handbook,

Boca Raton: CRC Press, 2001; and The Electric Generator Handbook (parts 1and 2), Boca Raton: CRC Taylor & Francis, 2005. He is an Associate Editorof Electric Power Components and Systems and Director of the Internet-onlyJournal of Electric Engineering (www.jee.ro).

Dr. Boldea is a member of the Industrial Drives and the Electric MachinesCommittees of the IEEE Industry Applications Society (IAS) and was Chair-man of the OPTIM International Conferences (IEEE-IAS sponsored) in 1996,1998, 2000, 2002, 2004, 2006, 2008, and 2010.

Frede Blaabjerg (S’86–M’88–SM’97–F’03) wasborn in Erslev, Denmark, on May 6, 1963. He re-ceived the M.Sc.E.E. and Ph.D. degrees from theInstitute of Energy Technology, Aalborg University,Aalborg, Denmark, in 1987 and 1995, respectively.

He was with ABB-Scandia, Randers, Denmark,from 1987 to 1988. He became an Assistant Pro-fessor in 1992 at Aalborg University, in 1996, anAssociate Professor, and in 1998, a Full Professorin power electronics and drives. Today, he is alsothe Dean of the Faculty of Engineering, Science, and

Medicine. In 2000, he was a Visiting Professor with the University of Padova,Padova, Italy, as well as a part-time Program Research Leader in wind turbinesat the Research Center Risoe. In 2002, he was a Visiting Professor at CurtinUniversity of Technology, Perth, Australia. He has been involved in manyresearch projects within the industry. Among them is the Danfoss ProfessorProgram in Power Electronics and Drives. He is the author or coauthor ofmore than 500 publications in his research fields including Control in PowerElectronics (New York: Academic, 2002). He is an Associate Editor for theJournal of Power Electronics and Elteknik. He has been very involved inDanish Research policy in the last ten years. His research interests are in powerelectronics, static power converters, ac drives, switched reluctance drives,modeling, characterization of power semiconductor devices and simulation,wind turbines, and green power inverters.

Dr. Blaabjerg is a member of the Danish Academy of Technical Science, theEuropean Power Electronics and Drives Association, and the IEEE IndustryApplications Society. Finally, he has served as Distinguished Lecturer forthe IEEE Power Electronics Society from 2005 to 2007. He is the Editor-in-Chief of the IEEE TRANSACTIONS ON POWER ELECTRONICS. He receivedthe 1995 Angelos Award for his contribution in modulation technique andcontrol of electric drives, the Annual Teacher Prize from Aalborg University,in 1995, the Outstanding Young Power Electronics Engineer Award from theIEEE Power Electronics Society, in 1998, eight IEEE Prize paper awards, theC. Y. O’Connor fellowship from Perth, Australia, in 2002, the Statoil-Prize forhis contributions in power electronics, in 2003, and the Grundfos-prize for hiscontributions in power electronics and drives, in 2004.