1_review of position-sensorless operation of brushless permanent-magnet machines

352 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 2, APRIL 2006

Review of Position-Sensorless Operation ofBrushless Permanent-Magnet Machines

Paul P. Acarnley and John F. Watson, Senior Member, IEEE

AbstractThe operation of a brushless permanent-magnet ma-chine requires rotor-position information, which is used to controlthe frequency and phase angle of the machines winding currents.Sensorless techniques for estimating rotor position from measure-ments of voltage and current have been the subject of intensiveresearch. This paper reviews the state of the art in these sensorlesstechniques, which are broadly classified into three types: motionalelectromotive force, inductance, and flux linkage.

Index TermsBrushless machines, estimation, permanent-magnet (PM) machines, position measurement, reviews.

I. INTRODUCTION

THE CURRENT flow in the windings of a brushlesspermanent-magnet (PM) machine must be synchronizedto the instantaneous position of the rotor, and therefore, thecurrent controller must receive information about the positionof the machines rotor. An auxiliary device (e.g., an opticalencoder or resolver) may be used to measure rotor position,but there has been much interest in sensorless schemes, inwhich position information is derived by on-line analysis of thevoltages and currents in the machine windings. Fig. 1 showsa schematic sensorless scheme with a position estimationfunctional block receiving measurements of machine voltagesand currents and supplying rotor-position data to the current andcommutation controller. The sensorless approach has severaladvantages: 1) only electrical connections to the machine arethe main phase windings, so installation costs are minimized;2) position-sensing function can be located with the othercontrol electronics: it does not need to be sited adjacent to themachine, and therefore does not inhibit the operating tempera-ture range; 3) absence of connecting leads prevents corruptionof position data by electromagnetic interference; and 4) cost ofa position-encoding device is avoided.

The idea of position-sensorless operation of brushless ma-chines was first advanced by Frus and Kuo [1] using a techniqueknown as waveform detection for deducing rotor position involtage-fed variable-reluctance stepping motors by analysis ofcurrent waveforms. Since that time, a number of titles havebeen used to describe this area of technology. Following closeon waveform detection came the term indirect positionsensing, which was justified by the observation that position

Manuscript received June 16, 2004; revised October 12, 2004. Abstractpublished on the Internet January 25, 2006.

P. P. Acarnley is with the School of Electrical, Electronic and ComputerEngineering, University of Newcastle, Newcastle upon Tyne, NE1 7RU, U.K.(e-mail: [email protected]).

J. F. Watson is with the School of Engineering, Robert Gordon University,Aberdeen, AB10 1FR, U.K.

Digital Object Identifier 10.1109/TIE.2006.870868

Fig. 1. Position estimation from measurements of voltage and current in themachine supply.

sensing came indirectly from voltage and current waveforms.Other authors have used the term direct position sensing, be-cause rotor position was obtained directly from the machine andnot from a separate encoder. Even the generic term sensorlesscould be considered misleading: the techniques are positionsensorless, but usually require sensing of current and sometimesvoltage.

This paper reviews the extensive research on sensorlessoperation of brushless PM machines, emphasizing particularlyrecent journal publications. Section II describes the characteris-tics of PM machines and their specific position-information re-quirements. Sensorless techniques may be broadly categorizedas: motional electromotive force (EMF), inductance or flux-linkage sensing, each of which is described in Sections IIIV.

II. CHARACTERISTICS AND POSITION-SENSINGREQUIREMENTS OF BRUSHLESS PM MACHINES

The purpose of this section is to outline the basic character-istics of brushless PM machines with particular reference to therequirements for rotor-position information.

A. Categories of Brushless PM MachineBrushless PM machine drives can be divided into two subcat-

egories [2]. The first uses continuous rotor-position feedbackto supply the motor with sinusoidal voltages and currents bypulsewidth modulation of the dc supply voltage. The ideal mo-tional EMF is sinusoidal, so that the interaction with sinusoidalcurrents produces constant torque with very low ripple. Thistype of drive system is called a PM ac drive, brushless ac drive,sinusoidal-fed PM drive, or sinusoidal brushless dc drive.

The second category of PM motor drive is referred toas the brushless dc drive, trapezoidal brushless dc drive, orrectangular-fed drive. In the three-phase form, rectangular cur-rent blocks of duration 120 electrical are supplied to themachine, in which the ideal motional EMF is trapezoidal, with

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ACARNLEY AND WATSON: POSITION-SENSORLESS OPERATION OF BRUSHLESS PERMANENT-MAGNET MACHINES 353

Fig. 2. Equivalent circuit for one phase of a brushless PM machine.

the constant part of the waveform timed to coincide with theintervals of constant phase current. For this type of machine,rotor-position information is needed only at the commutationpoints, e.g., every 60 electrical in the three-phase machine.

Both the trapezoidal and sinusoidal machines can be repre-sented by the same equivalent circuit for each phase winding(Fig. 2), in which the source voltage v supplies current i tothe phase circuit consisting of series-connected resistance R,inductance L, and motional EMF e. The motional EMF iscaused by the movement of the PM rotor and is thereforedependent on rotor position, as well as being proportional torotor velocity. Power supplied to the EMF e by the current iis converted into mechanical output power when the machineis acting as a motor. The rotor-position dependence of theinductance and motional EMF impacts on the machine voltageand current waveforms. This inter-relationship is utilized insensorless schemes with the voltage and current waveformsbeing analyzed to extract the EMF or inductance (or a com-bination of the two), from which the rotor position is deduced.

The torque output of a brushless PM motor is constant over aspeed range limited by the power electronic converters abilityto maintain the phase currents at the demanded levels. Fast andaccurate control of phase-winding current is possible only if theavailable supply voltage from the dc link is substantially greaterthan the motional EMF, so that a surplus voltage is available toforce current changes. The speed at which the surplus voltage isno longer adequate is referred to as the base speed. The machinecan run above base speed in the field-weakening mode, in whicha component of the armature current produces a field opposingthe magnet field and reduces the effective motional EMF. Fieldweakening is accomplished in both sinusoidal and trapezoidalmachines by increasing the phase angle by which the currentleads the motional EMF [3]. This requirement has importantimplications for position sensing: If the machines torque-producing capability is to be fully utilized over a broad rangeof speeds in the field-weakening region, then high-resolutionposition sensing is needed, even for trapezoidal machines.

B. PM Machine CongurationsPosition variation of inductance and motional EMF in the

PM machine depends on the magnetic structure. Brushless PMmachines are characterized by having a field produced by thepermanent magnet on the rotor and the armature winding on

the stator. For the conventional inner rotor radial-field machine,there are four possible rotor structures, as shown in Fig. 3. In thesurface-mounted magnet arrangement [Fig. 3(a)], using modernrare-earth materials with magnetic relative permeability closeto unity, the effective air gap is equal to the sum of the physicalairgap between rotor and stator plus the magnet depth. Conse-quently, current flowing in armature conductors produces onlya small magnetic-flux component, and therefore, the inductanceof the phase winding is small. Furthermore, if the entire rotorsurface is covered by a permanent magnet, there is negligiblevariation in winding inductance with rotor position.

The inset magnet configuration [Fig. 3(b)] is often preferredfor trapezoidal machines, because the magnet pole arc can beadjusted to assist in shaping the motional-EMF waveform. Thepresence of soft-magnetic material at the physical airgap in theregions between the magnet poles causes a substantial variationin winding inductance, with maximum inductance occurring atrotor positions where the magnet pole arcs are misaligned fromthe winding axis.

The two other configurations [Fig. 3(c) and (d)] have magnetsburied in the rotor body. For the interior magnet structure[Fig. 3(c)], the direction of magnetization is radial. This struc-ture is preferred for sinusoidal PM machines, because it is easierto achieve the necessary sinusoidal variation of flux densityaround the airgap periphery. The high-permeability magneticmaterial adjacent to the airgap leads to higher values of machineinductances than those that occur in the first two configurations.Finally, the flux-concentrating type [Fig. 3(d)] has magnetslocated with their axes in the circumferential direction, so thatthe flux over a rotor pole arc is contributed by two separatemagnets. This configuration also exhibits significant saliencyeffects, causing a substantial variation of winding inductancewith rotor position.

III. POSITION SENSING USING MOTIONAL EMF

A. Principles

In brushless PM machines, movement of the magnets relativeto the armature windings causes a motional EMF to be induced.Since the instantaneous magnitude of the EMF is a function ofrotor position relative to the winding, information about posi-tion is contained in the EMF waveform. In practice, however,it is difficult to extract the information about EMF, because themachine windings are carrying rapidly changing currents andexperience substantial induced voltages from phase switching.A further obstacle is that the motional EMF is proportional torotor speed. When the machine is to operate from standstill,position sensing is possible only when a threshold speed isattained, so it is usual practice to make the initial accelera-tion under open-loop control using a ramped frequency signal[4], [5], the parameters of which must be chosen to match driveand load parameters. Acceleration from rest at an arbitrary startposition for the rotor is particularly problematic, as it is possiblefor the motor to run initially in the reverse direction, andso, some schemes involve auxiliary sensors or high-frequencyexcitation tests to establish the rotor position and define theappropriate initial winding excitation pattern.

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Fig. 3. Rotor configurations of four-pole radial-field machines. (a) Surface mounted. (b) Inset. (c) Interior. (d) Flux concentrating.

The simplest form of this sensing arrangement, reported byIizuka et al. [6], can be understood by referring to the excitationtiming diagram for a trapezoidal machine in the upper partof Fig. 4. The zero-crossing values of the motional EMF ineach phase are an attractive feature to use for sensing, becausethey are independent of speed and because they occur at rotorpositions where the phase winding is not excited. However, asshown in Fig. 4, the EMF zero crossings do not correspondto those rotor positions where commutation between phasesshould take place. Therefore, the signals must be phase shiftedby 90 electrical before they can be used for commutation. Forexample, in Fig. 4, the shifted positive-going zero crossing ofthe phase-a motional EMF is used to trigger commutation ofnegative current from phase b to c.

The simple motional-EMF sensing scheme described abovehas a number of limitations that prevent its general application.

1) In common with all motional-EMF schemes, sensing isnot possible at low speeds. There are two restrictionson low-speed operation. First is the absence of motionalEMF at zero speed, which can be addressed by accelerat-ing the motor to a suitable speed with a preset sequenceof excitation. A second factor is the requirement to phaseshift the zero-crossing signals by 90 electrical. In theoriginal work [6], the phase shifting was implementedusing three separate RC networks that produce thenecessary phase shift only when the working frequencyis sufficiently high. The heavy filtering inherent in thesignal processing limits the dynamic performance of theposition-sensing scheme.

2) It is assumed that there is a very rapid decay of currentwhen a phase is switched off, so the voltage appearingacross the terminals of the unexcited phase is equal to themotional EMF. This assumption may not be true at speedsapproaching the base speed, or in the field-weakeningregion. Therefore, there is an upper limit on the usefulspeed range obtainable with this form of motional-EMFsensing.

3) The motional EMF is measured across the terminals ofeach of the three machine phases in turn. For a star-connected machine, it is necessary to have a connectionto the machines star point, and therefore there are four,rather than the conventional three, machine connections.

Despite these restrictions, the method has been success-fully applied in special-purpose low-cost applications forfans and pumps with unidirectional operation. For example,

Fig. 4. Derivation of current commutation signals from motional EMF (e) ina trapezoidal PM motor.

Iizuka et al. [6] described a 1.2-kW four-pole brushless dcmotor for an air-conditioning unit with motional-EMF positionsensing over a speed range from 1950 to 5700 r/min. An

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Fig. 5. Voltage reference points and current variables in a three-phase star-connected machine.

application of motional-EMF sensing in a brushless drive foran automotive fuel pump has been presented by Shao et al.[7], who overcame the starting problem with an experimen-tally determined open-loop excitation ramp. Toliyat et al. [8]described position sensing in a surface-mount magnet machinewith insignificant saliency. This development involved a tappedmachine winding that facilitated cancellation of both the third-harmonic component of motional EMF and the resistive voltagedrop, so there were no errors caused by changes in the windingresistance due to heating. Sensorless operation at excitationfrequencies as low as 2 Hz was described. A digital phase-locked loop has been used by Amano et al. [9] to tacklethe phase-shifting problem, though the dynamic range of sen-sorless operation was limited by the low-pass characteristicsof the loop filter. A similar limitation has been experiencedby others tackling the same problem [10][12]. For interiormagnet machines, armature reaction may cause distortion ofthe airgap flux distribution and consequent errors in rotor-position detection. Shen and Tseng [13] have analyzed the errormechanism and developed a technique for armature-reactioncompensation.

Most of the work on motional-EMF sensorless operationhas been implemented in a laboratory environment using eitherhard-wired analog/digital circuits or digital signal processors(DSPs). However, Cheng and Tzou [5] have designed andtested a mixed-mode integrated circuit, in a standard 0.35-msingle-poly four-metal CMOS process, to perform all aspectsof motional-EMF detection. In addition, several commercialintegrated circuits are available, e.g., those in [14].

B. Sensing From the Third Harmonic of Motional EMFMoriera [15] introduced an improved method for position

sensing using motional EMF, which utilizes the third-harmoniccomponent in the EMF waveform of a trapezoidal PM machine,and thus reduces the phase-shifting problem outlined above.Fig. 5 shows the three windings of a star-connected machinewith star point s. An additional star connection of three identicalresistors is connected between the phase ends a, b, c, and aseparate star point n.

Assuming that the resistances I and inductances (L) ofthe three machine windings are identical and that the phasemotional EMFs are as shown in Fig. 6, it can be shown thatthe voltage between the two star points n and s is equal to themean of the three phase EMFs.

Fig. 6 shows the voltage vns and its relationship to the rotorpositions for switching between phases. The vns waveform hasa frequency three times that of the fundamental component

Fig. 6. Derivation of current commutation signals from third harmonic ofmotional EMF (e) in a trapezoidal PM motor.

of any of the phase motional EMFs, and therefore, it is re-ferred to as the third harmonic of motional EMF, thoughit also contains harmonics of higher orders. The waveform isshifted through a rotor position of 30 by integration. The zerocrossings of the integrated waveform correspond to the rotorpositions at which excitation must be switched between thephases, and therefore, the zero crossings are suitable excitationswitching signals.


Fig. 7. Principles of a closed-loop observer.

During each cycle of excitation, the vns waveform passesthrough three cycles. Therefore, the excitation trigger signalsmust be synchronized to the appropriate phase excitationchange, depending on the required directions of torque andspeed. The trigger signals are synchronized once per excitationcycle by identifying a suitable reference position, such as thepositive-going zero crossing of motional EMF in phase a.In comparison to the basic method of position sensing usingmotional EMF (Section III-A), the third-harmonic method hasthe following advantages.

1) There is a reduced filtering requirement, because theintegration (low-pass filtering) function is performed ona signal, which has a frequency three times that of thefundamental signal. The lighter filtering improves thedynamic performance.

2) Operation at higher speeds is possible in principle, be-cause the voltage vns can be recovered even if cur-rent continues to flow in the third (unexcited) phase.Shen et al. [16] have successfully applied third harmonicof back EMF sensing in the high-speed flux-weakeningregion with current flowing continuously in all threephases of the machine.

An important limitation on the third-harmonic approach isthe initial assumption in the analysis that the inductance isequal in all three phases. This assumption is usually valid forsurface-mounted magnet machines, but is not correct for rotorconfigurations that cause the machine to exhibit significantsaliency. In the latter case, errors in position estimation arisedue to rapidly changing phase currents and extra low-passfiltering may be needed.

C. Observer-Based Methods

Observer principles (Fig. 7) have been applied to sensorlessoperation of PM machines. A machine and power converterare supplied with one or more inputs (e.g., voltages) and pro-duce several measured outputs (e.g., currents). A mathematicalmodel of the converter/machine combination is supplied withthe same inputs and produces estimates of the outputs. Theseestimated outputs are compared with the measured outputs toyield an estimation error, which is fed back to the model toassist in correcting the estimates. If the estimation error issmall, the model replicates the behavior of the real converter

and machine. All of the states in the mathematical model areaccessible, so estimates of all physical quantities are available,including those which are difficult or expensive to measure(e.g., rotor position or phase flux linkage).

Closed-loop observers have been used to address positionsensing in PM machines [17][25]. Solsana et al. [17] describedthe application of the principle to a sinusoidal PM machineand presented simulation results showing how the machinecan start successfully even when there were initial errors inestimated speed and rotor position. A later paper by the sameauthors [18] discussed the impact of modeling errors, suchas space harmonics of the magnet field, on the estimation ofrotor speed. Two alternative models (a voltage model anda current model) for a PM machine with significant rotorsaliency have been used for position estimation by Matsui andco-worker [19], [20]. However, the starting problem remained,and for consistent starting, a separate technique was needed[21], often using the inductance-variation approach describedin Section IV. In applications where erratic initial motion canbe tolerated, modified control laws have been proposed [22] forrobust sensorless control at low speeds.

A model-based approach to EMF sensing has been describedby Cho et al. [23] for a surface-mounted magnet machinefor a direct drive in a washing machine. In this application,the machine was subjected to large temperature variations,which impacted on both the stator resistance and the rem-nant flux density of the ferrite magnets. Therefore, the ma-chines temperature was estimated, via the stator resistance,at those parts of the wash cycle where the rotor speed waszero, and appropriate corrections were applied to the modelparameters. An alternative approach to temperature-dependentparameter tracking [24] involved the injection of a currentperturbation signal when the machine was operating at steady-state speed.

IV. POSITION SENSING USING INDUCTANCE VARIATION

An alternative method of position sensing involves moni-toring rates of change of winding current. Since the rate ofcurrent change depends on the inductance of the winding, andthis inductance is a function of rotor position and windingcurrent, then rotor position can be deduced from windingcurrent and its rate of change. Such a scheme has the importantadvantage that it is useful even at zero speed where there isno motional EMF. Sensing of rotor position by inductancevariation in the brushless PM machine is complicated because:1) in a machine with surface-mounted magnets, there is noinherent saliency, so any variation of winding inductance withrotor position arises only from magnetic saturation; 2) therate of change of current in the PM machine is dominated bythe motional EMF; 3) the variation of incremental inductancewith rotor position undergoes two cycles per single electricalcycle of the PM machine, causing an ambiguity in sensedposition. The final point is illustrated in Fig. 8, which showsthe variation of the various components of flux linkage overtwo cycles of a two-pole PM machine. The minimum valueof incremental inductance occurs at rotor positions of both0 and 180, but the magnet flux linkage is maximum positive at

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Fig. 8. Flux linkages and incremental inductance as a function of rotorposition in a PM machine with saliency.

the position of 0 and maximum negative at the 180 position.Despite these obvious difficulties, there have been numerousattempts to use inductance variation to detect rotor position inPM machines.

The first application of inductance methods addresses theproblem of starting, including identification of the rotor po-sition before full excitation is applied to the machine. Initialposition identification is particularly important in applicationssuch as traction, where any reverse motion caused by incorrectexcitation is unacceptable. Exploratory voltage signals havebeen applied to the phase windings of a salient PM machinethat was stationary [20], [26][29]. The resulting current am-plitudes depended on the incremental inductance, and thereforethe rotor position. However, the sensed position spanned arange of 180 electrical and there remained the problem ofresolving the orientation of the rotor over the full 360 elec-trical range.

The universally adopted solution to the issue of rotor orien-tation ambiguity is to consider the effect of magnetic saturationon the incremental inductance. The principles of this methodcan be understood by referring to the flux-linkage characteris-tics in Fig. 8. Suppose the rotor position has been determined aseither 0 or 180, by observing that the incremental inductanceof a phase is at its minimum value. Now, consider the effectof a positive pulse of current. If the rotor is aligned at the 0

Fig. 9. Current pulse amplitude as a function of rotor position in a machinewith magnetic saturation.

position, the effect of the pulse is to increase the total positiveflux linked with the phase, but if the rotor is at the 180 position,the current reduces the total negative flux linkage. Therefore,there is a difference between the flux amplitudes for the twoalternative rotor positions and, consequently, a difference in thelevel of magnetic saturation. If magnetic saturation increases,the incremental inductance is lower and so the amplitude ofthe current pulse is larger at one of the two possible rotorpositions, as illustrated in Fig. 9. Magnetic saturation has asmall but significant influence on incremental inductance evenin a surface magnet machine with no inherent saliency effect.The study by Nakashima et al. [30] has been successful inutilizing saturation effects to estimate initial rotor position insuch machines, albeit with reduced accuracy: a maximum errorof 18 electrical was reported.

The initial starting position of a salient PM motor can beinvestigated by high-frequency injection methods that effec-tively detect the position-dependent incremental inductance[31], [32], [34][36]. For example, Noguchi et al. [31] eval-uated the winding impedance with the pulsewidth-modulatedvoltage controller producing a low-amplitude output at a fre-quency of 50 Hz. Ambiguity in the magnet direction wasresolved by adjusting the parameters of the closed-loop currentcontroller so that an oscillatory current response was obtainedfor the lowest values of incremental inductance, correspondingto maximum saturation. Aihara et al. [32] used a higher fre-quency (500 Hz) for signal injection and discriminated betweenmagnet polarities by means of rotor magnetic-saturation effects.

The initial rotor position can be detected using voltagepulses, as described by Lai et al. [33]. In this paper, the dc-linkvoltage was applied to various combinations of the three star-connected phases using the six-device bridge. The current wasallowed to build up to a steady-state level in all phases, but whenthe voltage was removed, current decayed faster in the phasewith lowest inductance. There was no need for phase-currentsensors, because the current decay was evaluated by means ofthe line voltages, which underwent a sudden change in levelwhen the corresponding phase currents fell to zero.

Several methods of position sensing from inductance vari-ation have been developed for continuous rotation of salientmachines. Kulkarni and Ehsani [37] proposed a method forcalculating the effective phase inductance from the behavior ofthe hysteresis current controller for an excited phase. Ambigu-ity in the sensed position was avoided by starting the machinefrom a known location and continuously tracking changes ininductance with the assumption that the machine was always


rotating in one direction. Corley and Lorenz [38] utilized volt-age injection at a carrier frequency of 2 kHz. The correspondingfrequency component of current was modulated by the rotor-position variation of the phase inductance. Information aboutthe rotor position was extracted by making a comparison witha set of signals at the same carrier frequency and modulated byan estimated rotor position, which was derived from a simplemotion estimator. The result of the comparison was a signalmodulated by the error between the actual and estimated rotorpositions. The position-error information was decoded andused to correct the motion estimators output, which thereforetracked the actual rotor position over a wide speed range,including zero speed. A similar approach has been reported byNoguchi and Kohno [39], who used a 4-kHz carrier frequency,while Shinnaka [40] developed a new filtering algorithm,based on a phase-locked loop, which exhibited good low-speedperformance.

Sensorless operation from inductance variation has beenachieved using injected voltage sequences during breaks inthe normal voltage modulation [41], and from the pulsewidth-modulation frequency components at switching frequencies upto 5.5 kHz [42], [43]. There is a tradeoff in the choice ofmodulation frequency: a low frequency results in larger moreeasily detected current amplitudes, but can cause audible noisefrom the motor, whereas a high modulation frequency avoidsaudible noise, but the current amplitudes are much reduced.Choeisai et al. [44] were able to work with a modulationfrequency of 20 kHz by using a Walsh detector to assist in mea-suring the high-frequency current amplitudes. Hartas et al. [45]developed a novel six-phase machine and implemented sen-sorless operation from the position-dependent behavior ofthe hysteresis current controller. A detailed investigation ofhigh-frequency signal injection, using experimental and finite-element analysis techniques, by Jang et al. [46] has high-lighted the need for careful choice of signal amplitude andfrequency.

A further option for improving position sensing is to modifythe machine rotor. For example, Nondahl et al. [47] addeda short-circuited rotor winding to a surface magnet machinewith no inherent saliency. The winding current reacted withtime-varying fields acting in the direction of the main magnetfield, and therefore enhanced the position dependence of thewinding inductance. A similar effect has been obtained bycoating rotor poles of like polarity with a nonmagnetic con-ducting material [48]. Matsuse et al. [49] used a new closed-slot stator configuration to assist in rotor-position estimation.Magnetic bridges across the stator slots included a region ofconstricted cross section. These regions conducted a componentof winding leakage flux, but become saturated by the rotormagnet flux, which therefore influenced the phase-windinginductances.

V. POSITION SENSING BASED ONFLUX-LINKAGE VARIATION

A. Principles

Position sensing via flux-linkage variation has been knownfor many years, but its successful implementation has become

possible only in the last decade with the emergence of deviceswith sufficient real-time processing power. The fundamentalidea of flux-linkage position sensing is deceptively simple. Thephase-voltage equation can be written as

v = R i+ ddt

(1)

wherev phase terminal voltage;i phase current;R phase resistance; phase flux linkages;

and the phase flux linkages are a function of current and rotorposition. Equation (1) can be rearranged as

={v R i} dt. (2)

Therefore, it appears that by subtracting the resistive voltagedrop from the phase voltage and integrating, then a continuousestimate of phase flux linkage can be produced.

In most electrical machines, it is not practicable to measurethe phase terminal voltages directly, because of isolation is-sues, and instead, the applied phase voltage is estimated fromknowledge of the solid-state converter dc supply voltage anddemands being input to the voltage controller. An importantsource of error here is the conversion of voltage demands intoconverter device switching signals, which must include somedead time between switching off one device in an inverter phaseleg and switching on the other device in the same leg. The effectof dead time is to introduce an error between demanded andactual values of phase voltage, with the error being greatest atoutput voltages near zero. Several authors have highlighted thisvoltage measurement error and have developed techniques forcompensating dead-time errors [50], [51].

The open-loop integration in (2) is prone to errors caused bydrift: Small offset signals in the measurements are summed overtime, causing the integrator output to saturate. Integrator driftcan be reduced if the pure integrator is replaced by a low-passfilter or an alternative integrator structure [53], but this modifi-cation inhibits the flux estimators low-speed operating range.Instead, the general trend of recent research on this aspect ofsensorless operation has been to concentrate on closed-loopflux-linkage estimation as part of the position-sensing process.This section examines position-sensorless operation using fluxlinkages and draws a distinction between those estimatorsthat include a mechanical system model, and therefore requireknowledge of mechanical parameters, and estimators that areindependent of a mechanical model, and are therefore moresuitable for operation with variable load conditions.

Position estimation using flux linkages may be viewed asan amalgamation of the sensing methods using motional EMF(Section III) and inductance (Section IV): Several authors havemarried the concepts by introducing the idea of an extendedEMF (EEMF) estimator, which includes motional EMF andinductive terms [54][56]. However, it should be emphasizedthat flux-linkage estimation does not access any more positioninformation than is available from the combination of motional


Fig. 10. Closed-loop observer for position estimation using flux linkages ( = estimated state).

EMF and position sensing, so there remain machine types forwhich position-sensorless operation is extremely difficult undercertain operating conditions.

B. Flux Estimation With a Mechanical Model

In the brushless PM machine, the flux linkages with eachphase arise from the permanent magnet itself and the currentsflowing in the machine windings. The magnet flux linkagesare a function of rotor position with the nature of the functiondepending on the envisaged operating mode of the machine.In a brushless dc machine, the magnet flux linkages are atrapezoidal function of position, but in the sinusoidal machine,a sinusoidal variation of magnet flux linkage with position isneeded. As noted in Section IV, the phase-inductance variation,and hence the variation of flux linkages from the phase current,depends on the machine construction. Flux-linkage approachesto position estimation in all types of machines frequently makeuse of the closed-loop observer principles shown in Fig. 10.Voltage and current supplied to a machine are input to anestimator, which first calculates values of flux linked with eachphase. Flux linkage and current can be used to calculate torque,and the torque data are input to a mechanical model

d

dt=

1J (T B TL), d

dt= (3)

(where: J = mechanical inertia,B = viscous friction constant,TL = load torque). Estimates of rotor speed and position are produced. To close the estimation loop, the estimated valuesof position and phase flux linkages are used to estimate thephase currents, which are compared with the measured currentsto generate an estimation error. This error is fed back into theinitial flux-linkage estimator, where it counteracts the tendencyto drift caused by offsets in the measurements.

Initial attempts at combined flux linkage and position ob-servation for brushless PM machines by Jones and Lang [57]and Sepe and Lang [58] were frustrated by the limits onavailable real-time processing power at that time. The subse-quent advances in DSP technology have allowed these observerprinciples to be implemented effectively. For example, an ex-tended Kalman filter estimator for a brushless dc motor has

been developed by Terzic and Jadric [51] and implementedin a DSP. Stator-resistance estimation was also included inthe algorithm to counter the effects of flux-linkage estimationerrors caused by an incorrect value of resistance as the mo-tor temperature rose during continuous operation. Sensorlessoperation at speeds down to 50 r/min was recorded for amachine with negligible saliency. An obstacle to applying theextended Kalman filter algorithm to rotor-position estimationis the need to set appropriate values for the covariance matrixparameters, which reflect the uncertainties in modeling andmeasurements. The parameter values are often chosen by trialand error, but Bolognani et al. [52] have developed selectionguidelines.

C. Flux Estimation Without a Mechanical Model

Closed-loop observers that include a model of the mechan-ical dynamics are prone to errors caused by incorrect specifi-cation or variability of the mechanical parameters. Therefore, anumber of methods for avoiding a mechanical model have beenintroduced.

Position estimation from flux-linkage variation was investi-gated by Wu and Slemon [59] for the case of a sinusoidal ma-chine without significant saliency. Analog integrators were usedfor flux-linkage calculation, because the inverter was hysteresiscontrolled, so it would have been difficult to synchronize datasampling to randomly occurring switching events. Integratordrift was counteracted by calculation of an offset signal, whichensured that the average flux linkage with each phase was zerowhen the machine operated at steady-state speed and torque.This approach was an effective low-cost solution, but did notallow the machine to self-start and was unable to deal with fastchanges in speed or torque.

The principles of flux linkage and position estimation witha closed-loop observer but without the need for a mechanicalmodel are represented schematically in Fig. 11. Flux linkage iscalculated by integration of the input voltage and current, andthe stored flux linkage/position/current characteristic is used toestimate current and rotor position. The estimated current is fedback for use in the lookup block, as well as being comparedto the measured currents to generate an estimation error. Thisclosed-loop feature counteracts integrator drift.


Fig. 11. Position estimation using flux linkages without a mechanical model( = estimated state).

Batzel and Lee [60] used a Luenberger observer for flux link-age and position estimation in a sinusoidal PM machine, whichwas both slotless and had surface-mounted rotor magnets. Theflux linkage/position/current characteristic was represented bya sinusoidal characteristic for the magnet flux linkages. In theabsence of saliency, position estimation was not possible atthe lowest speeds, so Hall sensors were used to provide anauxiliary position measurement with a resolution of 30 foroperation below 100 r/min. A later work by the same authors[61] has involved a neural network for the real-time correctionof position-estimation errors arising from uncertainty in themachine parameters.

An alternative to a mechanical model in a flux linkageand position estimator is to obtain an initial estimate of rotorposition, by extrapolation from previous position estimates, andthen correct the position in response to measured voltage andcurrent information. An example of this approach [62], [63]used a combined phase flux linkage and rotor-position estima-tor, in which integrator drift was counteracted by reconcilingthe estimates with measured values of current according to thestored flux-linkage/current/rotor-position characteristics of themachine. The same algorithm has been used successfully byOstlund and Brokemper [26], who reported the need for anauxiliary starting method when using a surface-mounted mag-net machine. Sensorless operation with flux-linkage estimationhas been developed for the control of a PM motor with amatrix power converter [64]. The problems of flux integratordrift have been avoided [65] by considering the relationshipbetween incremental changes in flux linkage and rotor positionto establish a tracking algorithm requiring only integration ofposition increments.

VI. CONCLUSION

Sensorless technology for PM machines has been researchedextensively with a surge of recent interest being prompted bythe availability of more powerful digital signal processing de-vices. Solutions have been found to the more difficult problemsof sensorless operation, such as starting from rest and positionsensing for surface-mounted magnet machines. Despite thisextensive development, only in the very specific areas of low-cost [7], [23] or safety-critical applications [66] for brushless

dc PM machines is there an established commercial interest,with the major manufacturers producing integrated circuits forsensorless operation using motional EMF. However, furtherreductions in the cost of processing power will improve theeconomic viability of many of the more sophisticated sensorlesstechniques described here.

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Paul P. Acarnley received the B.Sc. and Ph.D. de-grees in electrical engineering from Leeds Univer-sity, Leeds, U.K., in 1974 and 1977, respectively,and the M.A. degree from Cambridge University,Cambridge, U.K., in 1978.

After seven years in the Department of Engineer-ing at Cambridge University, he joined the PowerElectronics, Drives, and Machines Group at the Uni-versity of Newcastle upon Tyne, U.K., in 1986. Heauthored Stepping Motors: A Guide to Theory andPractice, which was first published by the Institution

of Electrical Engineers, London, U. K., in 1982 with the fourth edition appear-ing in 2002. In 2003, he founded Research Engineering Education Services(RESEEDS) based in Stonehaven, U.K. He is also a Research Professor inthe School of Engineering at Robert Gordon University (RGU), Aberdeen,U.K., and Emeritus Professor at the University of Newcastle upon Tyne, U.K.His principal research interest is in the control of electric drives, includingwork on state and parameter estimation applied to torque, current, temperature,speed, and position estimation in motors, and temperature estimation in powerelectronic devices. In addition, he has made contributions in the areas ofstepping motors, permanent-magnet (PM) generators, flywheel energy storage,and brushless dc drives.

Prof. Acarnley is a Fellow of the Institution of Electrical Engineers, U.K.

John F. Watson (SM94) was born in Kirkcaldy,U.K., in 1955. He received the degree in elec-tronic and electrical engineering (with honors) fromHeriot Watt University, Edinburgh, U.K., in 1973,and the Ph.D. degree in electrical engineering fromthe Council for National Academic Awards (CNAA)in 1981.

He was a Development Engineer with GE (U.K.)for two years before joining the Robert GordonUniversity (RGU), Aberdeen, U.K., in 1982. He iscurrently a Professor and the Head of the School of

Engineering at RGU. His main research interests are in the fields of conditionmonitoring and electrical drives.

Prof. Watson is a Chartered Engineer in the U.K. and a Fellow of theInstitution of Electrical Engineers, U.K.

1_review of position-sensorless operation of brushless permanent-magnet machines

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