Position estimatorfor a brushless-DC machine

using core saturation and statorcurrent slopes

Juan Dixon, Lorenzo Urrutia, Matıas Rodrıguez andRodrigo Huerta

Department of Electrical Engineering,Pontificia Universidad Catolica de Chile, Santiago, Chile

Abstract

Purpose – This paper is devoted to the investigation of position estimation for a brushless DCmachine using only their stator currents. The first application is for a hybrid electric vehicle, where thegenerator will be used as a motor to start the internal combustion engine (ICE).

Design/methodology/approach – This paper describes how to estimate the rotor position of abrushless DC (BLDC). Two different strategies, both based on stator currents, will be used: one for lowspeeds to start the ICE, and one for normal speeds for future applications in a pure electric vehicle(EV). The first one uses an estimation method based on core saturation and the second one is based onthe determination of the current slopes on two of the three phases. The algorithms proposed neitherneeds to measure any machine parameters, nor the back emf. The methods use the informationcontained in the current magnitudes and slopes, and the machine mechanical speed. The system wasimplemented using a Digital Signal Processor (TMS320F241), which controls the phase currents andmakes all the calculations required for position estimation. Additionally, the PWM signals aretransmitted through a fiber optic link to minimize noise production and error on commutations.

Findings – The papers shows how an internal combustion engine can start using this approach in abrushless motor and keep it synchronized.

Research limitations/implications – This work is being applied to a hybrid electric vehicle.

Originality/value – The paper proposes a new way to start the internal combustion engine forhybrid vehicle applications through the estimation of magnets position. It also shows a way toestimate the position at other speeds for battery charging of the vehicle.

Keywords Brushless DC and synchronous machines, Position estimation,Sensorless starting torque control, Road vehicles, Electric cells

Paper type Research paper

1. IntroductionAhybrid electric vehicles (HEVs) of the series type can utilize the same generator to starthe engine. The DC machine fulfils these requirements, but this machine needs periodicmaintenance. The AC machines, particularly brushless permanent magnet motors donot have brushes and their rotors are robust because commutator and/or rings do notexist. Thatmeans very lowmaintenance. The brushless characteristic also increases thepower-to-weight ratio and the efficiency. The development of brushless permanent

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The authors want to thank Conicyt through Project Fondecyt 1100175, for the support given tothis work and ICM through NEIM Project P-07-087-F.

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COMPEL: The International Journalfor Computation and Mathematics inElectrical and Electronic EngineeringVol. 31 No. 1, 2012pp. 170-181q Emerald Group Publishing Limited0332-1649DOI 10.1108/03321641211184896

magnet machines (Millner, 1994; Pillay and Krishnan, 1991; Low and Jabbar, 1990) haspermitted an important simplification in the hardware for electric machines because it isfed with quasi-square-wave currents, and virtually eliminate the rotor losses, givingvery high peak efficiency comparedwith other electric machines (around 95 percent andmore in Nd-Fe-B machines in the 10-100 kW range). Besides, the power-to-weight ratiois higher than in other machines. The aforementioned characteristics and a highreliability control make this type of machine a powerful alternative for electric vehicles(EVs) and HEVs applications (Chan and Chau, 1997). However, sensing the rotorposition is one of the drawbacks that has a machine of this type. In this paper, a controlsystem for brushless-DC (BLDC) motors, based on current magnitude and slopeevaluation to estimate the rotor position at starting, at low speeds and a normal speeds,is presented. Furthermore, it is added a position estimator dynamic analysis, which willpermit to find a solution for each one the dynamic possible changes.

The most popular way to control BLDC motors is through the use of voltage sourcecurrent-controlled inverters. The inverter must supply a quasi-square currentwaveform, whose magnitude is proportional to the machine shaft torque (Murphy andTurnbull, 1988). To control it, the phase currents, instantaneous rotor position andspeed are measured.

The purpose of this paper is to eliminate the rotor position sensor and find a newway to estimate the position, without using machine parameters or other complicatedmethods suggested in previous works ( Jonesand and Lang, 1989; Furuhashi et al., 1992;Dhaouadi et al., 1991). The knowledge of machine parameters requires very preciseinformation, which has to be verified periodically. On the other hand, voltage sensorsnormally measures the voltage in the open phase of the machine, and for this reasontwo drawbacks appear: the instantaneous knowledge of the open phase, and a neutralpoint connection, which is necessary. The most important characteristic of theestimation method proposed in this work over other methods are:

. motor parameters are not required; and

. emf voltage measurement (voltage sensors) is neither required.

For a BLDC motor, a precise determination of rotor angle is not required. It only needsto know the position of commutation points, because the objective is to achievequasi-square current waveforms, with dead time periods of 608.

There are several sensorless methods to know the rotor initial position in a BLDCmachine, such as stator inductance variation (Schroedl, 1988; Matsui, 1996), applicationof an external DC voltage pattern (Tursini et al., 2003), or using an injection of highfrequency signal (Chung et al., 1999).

This paper shows two different strategies to estimate the rotor position, whichdepends on speed and dynamic operation. The first one proposes a solution to get theposition of the rotor at standstill, based on inductance variation method. The secondconsists on a method to estimate the rotor position using current slopes when the rotoris running at normal speeds (300-3,000 rpm for traction applications).

2. Current control systemThe circuit of Figure 1 shows the basic topology of the system implemented (Dixon andLeal, 2002). It senses the current in the motor phases and rectify them to get only onecurrent, which is commutated periodically, each 608 electrical degrees. The control uses

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a digital signal processor (DSP) that calculates the currents from two of the threephases, takes their absolute values and makes a process similar to a rectification. Lateron, this “rectified” current, called IMAX, is compared with a reference IMAX

REF coming fromthe control system (acelerator or brake), and the error signal is processed through aproportional integral (PI) controller. The output of the PI controller is compared with asaw-teeth carrier signal, to generate a common and unique pulse width modulation(PWM) pattern for all the power transistors. At the same time, this PWM pattern isapplied to the corresponding couple of transistors in the inverter according with theinformation given for a rotor position estimator. This information will be obtainedfrom the phase currents of the machine.

The phase currents of Figure 1 are sensed using current sensors, whose outputsignals are filtered by two independent analog, second order, lowpass filters: one forcurrent control and the other for position estimation. Then, this independent signalsare passed through analog-to-digital converters. The digital information of these twosignals (current through IMAX and position estimation through dIMAX/dt) are thenprocessed on the DSP. It is important to mention that all the operations shown inFigure 1, with exception of some conditioning hardware, are executed inside the DSP.Figure 2 shows the block diagram of the overall control system.

3. Rotor position estimation at standstill and at very slow speedsTo reach a full torque for engine starting, the knowledge of rotor position at standstillmust be achieved. Some interesting methods are explained in Ying and Zaiping (2010)

Figure 1.System topology

+

Digital Selector

PICOMP

PWM

IMAX

|ia|, |ib|

_+

i

t

errore(t)

VDC

ReferenceCommand

Accelerator

Brake

DEAD TIMEGENERATOR

PROTECTIONSYSTEM

Brakecontrol

(The Brake Controlreverses the position

estimator signals)

Saw-teethCarrier

Modulator Control Circuit

iaib

IMAX

IMAX

OPTO DRIVERS

TbL Tc

LTaL

TaU Tb

U TcU

PositionEstimator

IMAX

BLDCMOTOR

IMAX REF

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and Champa et al. (2009). In this work the iron saturation produced in one of the poles(Nort or South depending on the current direction) is applied. The saturation methodproduces a different value of inductance for the North and South pole, which permits todiscriminate between them.

The effects of rotor position over the stator phase inductance can be described bythe following relationship (Boussak, 2005):

½L� ¼

LS þ L0 þ Lu · cosð2uÞ 2 L0

2 þ Lu · cos 2u2 2 ·p3

� �2 L0

2 þ Lu · cos 2uþ 2 ·p3

� �

2 L0

2 þ Lu · cos 2u2 2 ·p3

� �LS þ L0 þ Lu · cos 2uþ 2 ·p

3

� �2 L0

2 þ Lu · cosð2uÞ

2 L0

2 þ Lu · cos 2uþ 2 ·p3

� �2 L0

2 þ Lu · cosð2uÞ LS þ L0 þ Lu · cos 2u2 2 ·p3

� �

26664

37775 ð1Þ

where, LS is the leakage inductance, L0 the mutual inductance and Lu is the componentof the mutual inductance that changes with the position of the rotor. The angle u is therotor electrical angle. The phase inductance reaches two maximum values when ucovers one electrical turn (3608). Then, the magnets polarity cannot be obtained and themachine initial rotation is unknown:

LðuÞ < LC þ L1 · cosð2uþ KÞ ð2Þ

Then an additional information is required to discriminate the polarity of magnets.Otherwise the control will not be able to get the initial position of the rotor. In thisimplementation, a simplified method that takes advantage of the stator saturation,given by the polarity of permanent magnets in the rotor is used. The saturation effect isdifferent for the South and North poles as shown in Figure 3 and this characteristicpermits to differentiate them.

The saturation depends on the relative position of magnets with respect of statorcurrent direction. In “I”, the field direction are opposed and then the total magnetic fluxis reduced. In “II”, the field direction is the same and then the core saturates. Underthese conditions, the stator inductance becomes smaller and poles North and South arediscriminated.

Figure 2.Control scheme based

on DSP

PositionEstimator

I_max DSP TMS320F241

A/DConv.

Position Estimator Signal Position Sensor Signal

Signal to Optodrivers

Digital Selector

PIController

PWMGenerator Fiber Optic

Transducer

AnalogLowPass filter

Fc = 5 kHz

Inverter-MotorSystem

MaxABS (Ia, Ib)

IrefError

PWMSignal

Ia

Ib

6

AnalogLowPass filterFc = 50 kHz

+

–

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4. Position estimation when machine rotates at medium and high speedsThe position estimator for a BLDC machine needs to identify six positions, whichdetermine the commutation points. The diagram of Figure 8 shows an idealcommutation sequence for the trapezoidal emf of the machine, centered with the phasecurrents for optimal commutation.

As can be shown in Figure 4, the slopes of both, phase-to-phase and phase-to-neutralvoltages change during commutation. Then, either of these voltages could be used forposition detection.

Since the neutral point of the machine is floating and not accessible, the only way touse this information is through the phase-to-phase induced voltages. The problem isthat the change in slope of these voltages and the voltages themselves are notmeasurable and then information must be obtained from the phase currents. As in thiskind of machine only two of the three phases transfer current at the same time, thecircuit to be considered uses the two phases in conduction. The model for a BLDCmotor being measured is shown in Figure 5(a).

When a couple of phases of the motor are conducting, i.e. the current IMAX flowingfrom phase a to phase b, the differential equation to be solved is:

VDC ¼ 2R · IMAX þ 2L ·dIMAX

dtþ ðEga2 EgbÞ ð3Þ

Figure 3.Rotor and stator magneticfield aligned

Stator Iyon Flux

CurrentComponent

MagnetComponent

I)

I

II

B

H

LI>LHII)

N

N

N

S

S

N

N

N

S

S

S

S

Notes: I – normal; II – saturated stator iron

Figure 4.Ideal currents and inducedvoltages, and thecommutation pointsfor a BLDC motor

a)

b)

c)

IMAXIa

Ega

Egb-Egc

Notes: (a) phase currents; (b) phase-to-neutral voltages; (c) phase-to-phase-voltages

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where VDC is the DC supply voltage of the inverter, R and L are the stator windingresistance and inductance, respectively, IMAX the phase currents being controlled bythe PWM, dIMAX/dt the slope of IMAX, and Ega-Egb, the phase-to-phase back emf.Similar equations can be written for the other two voltages.

As the current is kept at the reference value IREF by the controller, the term 2R· IMAX

does not change significantly, and then:

2L ·dIMAX

dtþ ðEga2 EgbÞ ¼ VDC 2 2R · IMAX < K ¼ constant ð4Þ

Despite IMAX is kept around a constant reference value, the differential terms of IMAX

does not disappear, because of the slopes. These slopes balance the instantaneousmagnitude of the induced voltage (Ega-Egb). Then, the information about thecommutation points for position estimation can be obtained from the slopes of IMAX,avoiding the calculation of (Ega-Egb).

Figure 5.(a) Motor circuit modeland (b) the two possible

topologies during positiveconduction of phase “a”

RL

Ega

Egb

L EgcR

RL

(a)

(b)

+ VDC

+

BLDC MOTOR

VDC

Positive slope

Negative slope

IMAX

IMAX

+

-VDC+

VDC

R

R

RL

2L

2L

2R

2R

BLDC MOTORINVERTER

INVERTER

Equivalentcircuit

Equivalentcircuit

R

Ega

Ega

Egb

EgbEga-Egb

Ega-Egb

L

L

L

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Now, because the current controller implemented here uses the same PWM for allthe transistors, when two phases are in operation during their corresponding 608, boththe transistors commutate at the same time and the slopes during commutation remainconstant. When the current slope changes, the term (Ega-Egb) changes. Then, equation(4) allows determining the commutation points through the information given byslopes change of the current IMAX. The negative slopes can also be utilized for thecalculations when the duty cycle of the PWM is smaller than 0.5. Figure 5(b) shows thetwo topologies during the conduction period of 608. During this period, the PWM ischanging the operation of insulated gate bipolar transistors from “on” state to “off”state. When transistors are “on” the slope of currents is positive and when they are“off” the slopes are negative. After commutation is produced, a new couple of phaseswill be conducting, and they will give information for the next commutation. Figure 6shows how dIMAX/dt variation is obtained from the positive slopes of the phase current.The current controller of the machine maintains the phase currents and the positiveslope of IMAX is being computed. When the slope of the current begins to change, thecorresponding phase is commutated as shown in Figure 6. The algorithm is appliedsequentially to commutate the phases a, b, c and so on.

At this point, it is quite important to mention that the strategy proposed in this work,does not depend on the values of R and L, because is based on current slope variations(dIMAX/dt) regardless of its magnitude (IMAX), which is kept at the value of the reference.Even more, R and L can change in time because of many factors, but the slope variationsused in this method will be produced always at the same places. The system neither usesthe value of the slope. It just uses the change of the slopes todetect the commutation points.

5. Dynamic state considerationsThe method used to obtain the rotor position described in the previous chapter, isbased on the current slopes variation. However, these slope variations can also begenerated by changes in the system dynamic, which can generate a wrong informationand hence a wrong commutation.

Figure 6.Calculation of dIMAX/dt, toget commutation instantsin a BLDCM

Ia is switched-off Ib is switched-on

d/dt(IMAX+)

d/dt(IMAX–)

IMAXREF

IMAXREF

Ia

Ib

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For dynamic analysis, as mechanical speed cannot change as fast as electric variablesdo, the electric and mechanic transients can be separated. As mechanical speed doesnot change abruptly, it allows predict, with reasonable accuracy, where the nextcommutation will take place. To take advantage of the slow mechanical dynamics, it isproposed to save information about the last machine commutations.

The dynamic analysis will be described for each of the following cases:. current reference increases;. current reference decreases;. load torque increases; and. load torque decreases.

5.1 Current reference increasesEquation (3) showed that when the reference current is increased, the induced voltage,which depends only on mechanical speed, will not change as fast as current does.Besides, as the DC source VDC is constant, the only thing that compensates thereference current increase is a reduction in current slopes.

As was already shown, the position estimator waits for an increase in the currentslopes for commutation. However, when current reference IMAX is increased its slopeswill decrease, so this information will not be computed by the position estimator, whichis expecting for larger slopes. A situation in which the current slope increases due tocommutation instant and, at the same time, reference current is increased, a slopechange cancelation can be produced. This problem is solved by commuting at aninstant predicted by the previous commutation recorded.

5.2 Current reference decreasesIn a similar way, when current reference is decreased, the current slopes increase. Theproblem here is that the slope also increases at commutation moments. This situationcan produce a wrong commutation and to solve this problem, two cases should beconsidered:

(1) The reference change takes place earlier than predicted for next commutationand in this case, the commutation is not executed. The controller actualizes theslope information and at the same time commutates in a predictive way.

(2) The reference change is close to the next commutation and in this case thecommutation moment is predicted using previous information. Predictions canbe used because the machine speed changes slower than electrical signals do.

5.3 Load torque increaseWhen the load torque increases, the machine speed and induced voltage will decrease.This situation will produce an increase in the current slopes that could generate awrong commutation. However, the change in current slope should be slow and then thecontrol system can ignore this information and wait for the expected fast slope change.

5.4 Load torque decreasesIf the load torque decreases, the mechanical speed and induced voltages will increase,but again the slope change will be slow and then it can be ignored by the controlsystem.

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6. Experimental resultsThe experiments were done using a machine with sinusoidal emf which was fed withtrapezoidal (quasi-square) currents. This implementation has the difficulty of a naturaltorque ripple generation because of the constant current compared to a non-uniformemf, which is overcomed when using a trapezoidal back emf motor. The proposedmethod can be implemented in this machine too, but with an increase in computationtime and complexity. Characteristics of the machine used are:

Motor model : Solectria BRLS-16

INOM (A) : 140

VNOM (Vdc) : 120

Max speed (rpm) : 5,000

Magnets : Nd-Fe-B

Weight (kg) : 29

The first case consists of showing the rotor position estimator at standstill and verylow speeds, where the induced voltages are negligible and then not measurable. Theposition to discriminate between North and South poles of the magnets is found usingthe saturation method explained in Section 2.

Figure 7 shows an experiment for standtill in which the inductance is evaluated as afunction of rotor posicion. Two situations are shown. The firts one without saturationand the second one with iron saturated. In the first case the inductance reaches twominimum values of similar magnitude and in the second case, when the core issaturated, the inductance reaches two minimum values quite different, which permitsto discriminate between North and South poles of the Nd-Fe-B magnets.

Figure 8 uses the second method for medium and high speeds, which is based oncurrent slopes explained in Section 3. The most difficult task here is to obtain a cleancurrent waveform. Since the inverter tested was operated at a switching frequency of15 kHz, in order to obtain phase current measurements that can give information aboutdIMAX/dt, the sampling frequency must be faster than the 15 kHz. The DSP used has aminimum conversion time of 2ms which is equivalent to 500 kHz sampling rate.In order to allow time for calculations, samples are taken only for a period of around30ms, either on the positive slope (conducting semi-period of the PWM) or on the

Figure 7.Experimentalphase-to-phase statorinductance with respectto rotor position fornon-saturated stator iron(normal inductance) andsaturated stator iron(at 50 percent of nominalcurrent)

270

250

230

210

190

170

1500 60 120 180 240 300 360

Electrical Degrees (°)

Non-satured Stator Iron Satured Stator Iron

Indu

ctan

ce (

µH)

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negative slope (non-conducting semi-period). This situation will depend on the dutycycle (bigger or smaller than 0.5, respectively). Special care has to be taken in order toavoid sampling currents on noisy transient instants, like the ones produced just after acommutation has occurred. For this reason, a delay of 4ms is implemented beforeacquisitions are done. The experimental oscillogram in Figure 8 shows the instantswhere the samples are taken for the positive slope case. This oscillogram is a realcurrent taken from the machine.

To get a reliable information about the dIMAXþ /dt, a linear statisticalmodel was used to

calculate the desired slope Graybill, 1961. As shown in Figure 8, each sample is obtainedaveraging two points of the current slope taken every 2ms. A total of six pairs of samplesare taken to calculate the slope at each “on-off” operation of power transistors.

With both the metods explained above, it becomes possible to estimate the positionof the rotor. Special care have to be taken to avoid false and erroneous measurement,by using good filtering of the current signals, which is the most difficult part of thisstrategy.

7. ConclusionsA different way to estimate the rotor position of a BLDC motor for EVs, based onphase-currents information only has been presented. Two strrategies were developed:one for standstill and very low speeds, and one for normal and high speeds. The first oneuses a core saturation methods to identify the North and South polarity of magnets andthe second one uses the information contained in the current slopes generated by the“on-off” operation of transistors. This operation allows to find the six commutationpoints required for this kind of machine, without the need of parameters information.The system was implemented using a DSP, which is programmed to control the phase

Figure 8.Current sensing points toevaluate positive slopes

IMAXREF

dIMAX+/dt

1.5000000

1.3000000

1.1000000

0.9000000

0.7000000

0.5000000

0.3000000

0.1000000

–0.1000000

–20.0 µs 10 µs/Div

66 ms

24 ms

4 ms

Acquisition Memory A

V

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currents and to estimate the rotor position. Experimental results show that it is possibleto implement this strategy, but the currents sensed have to be carefully filtered to getaccurate measurements. The strategy has proven to be feasible by results obtainedexperimentaly.

References

Boussak, M. (2005), “Implementation and experimental investigation of sensorless speed controlwith initial rotor position estimation for interior permanent magnet synchronous motordrive”, IEEE Transactions on Power Electronics, Vol. 20, pp. 1413-22.

Champa, P., Somsiri, P., Wipasuramonton, P. and Nakmahachalasint, P. (2009), “Initial rotorposition estimation for sensorless brushless DC drives”, IEEE Transactions on IndustryApplications, Vol. 45, pp. 1318-24.

Chan, C.C. and Chau, K.T. (1997), “An overview of power electronics in electric vehicles”, IEEETransactions on Industrial Electronics, Vol. 44 No. 1, pp. 3-13.

Chung, D.-W., Kang, J.-K. and Sul, S.-K. (1999), “Initial rotor position detection of PMSM atstandstill without rotational transducer”, Electric Machines and Drives, InternationalConference IEMD ’99, Seattle, WA, pp. 785-7.

Dhaouadi, R., Mohan, N. and Norum, L. (1991), “Design and implementation of an extendedkalman filter for the state estimation of a permanent magnet synchronous motor”, IEEETransactions on Power Electronics, Vol. 6 No. 3, pp. 491-7.

Dixon, J. and Leal, I. (2002), “Current control strategy for brushless DC motors, based on acommon DC signal”, IEEE Transactions on Industrial Electronics, Vol. 17 No. 2, pp. 232-40.

Furuhashi, T., Sangwongwanich, S. and Okuma, S. (1992), “A position-and-velocity sensorlesscontrol for brushless DC motors using an adaptive sliding mode observer”, IEEETransactions on Industrial Electronics, Vol. 39 No. 2, pp. 89-95.

Jonesand, L.A. and Lang, J.H. (1989), “A state observer for the permanent magnet synchronousmotor”, IEEE Transactions on Industrial Electronics, Vol. 36 No. 3, pp. 374-82.

Low, T. and Jabbar, M.A. (1990), “Permanent-magnet motors for brushless operation”, IEEETransactions on Industry Applications, Vol. IA-26 No. 1, pp. 124-9.

Matsui, N. (1996), “Sensorless PM brushless DC motor drives”, IEEE Transactions on IndustrialElectronics, Vol. 43, pp. 300-8.

Millner, A.R. (1994), “Multi-hundred horsepower permanent magnet brushless disc motors”, IEEEApplied Power Electronics Conference, APEC’94, Orlando, FL, February 13-17, pp. 351-5.

Murphy, J.M.D. and Turnbull, F.G. (1988), Power Electronic Control of ACMotors, Wheaton & Co,Exeter, pp. 424-8.

Pillay, P. and Krishnan, R. (1991), “Application characteristics of permanent magnetsynchronous and brushless DC motors for servo drives”, IEEE Transactions onIndustry Applications, Vol. 27 No. 5, pp. 986-96.

Schroedl, M. (1988), “Detection of the rotor position of a permanent magnet synchronous machineat standstill”, International Conference on Electrical Machines, ICEM, Pisa, pp. 195-7.

Tursini, M., Petrella, R. and Parasiliti, F. (2003), “Initial rotor position estimation method for PMmotors”, IEEE Transactions on Industry Applications, Vol. 39, pp. 1630-40.

Ying, M. and Zaiping, P. (2010), “A novel starting method of sensorless BLDC motors for electricvehicles”, International Conference on Electrical and Control Engineering (ICECE), Wuhan,pp. 3212-5.

Graybill, F.A. (1961), An Introduction to Linear Statistical Models. Volume I, McGraw-Hill,New York, NY, pp. 106-48.

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About the authors

Juan Dixon (Senior Member IEEE) was born in Santiago, Chile. He received theMs. Eng. degree and a PhD from McGill University, Montreal, Canada in 1986,and 1988, respectively. Since 1979, he has been with the Electrical EngineeringDepartment, Pontificia Universidad Catolica de Chile, where he is presentlyProfessor. He has presented more than 70 works in International Conferences andhas published more than 40 papers related to Power Electronics in IEEETransactions and IEE Proceedings. His main areas of interest are in electric

traction, PWM rectifiers, active filters, power factor compensators and multilevel converters.He has created an Electric Vehicle Laboratory, where state-of-the-art vehicles are developed andinvestigated. Juan Dixon is the corresponding author and can be contacted at: jdixon@ing.puc.cl

Lorenzo Urrutia was born in Chillan, Chile, in 1984. He received the B.S. degree inElectrical Engineering from the Pontificia Universidad Catolica de Chile, where heis currently working toward the M.S. degree. His research interests includeinverter/converter control and circuit design for electric vehicles.

Matıas Rodrıguez received the Degree in Electrical Engineering and Master ofScience from the Universidad Catolica de Chile in 2002. Later on, he got theMaster of Business Administration (MBA) at UCLA in the USA. He also had anactive participation in the implementation of the first state-of-the-art electricvehicle using BLDC in 1998, which was constructed in the Electric TractionLaboratory at the Department of Electrical Engineering. At present, he works inCompass Group RS Latin America, where he is one of the managers of thecompany.

Rodrigo Huerta was born in Chuquicamata, Chile, in 1976. He received hisElectronics Engineer degree in 2000 from Universidad Tecnica Federico SantaMaria, Valparaiso, Chile. The same year he joined the Electronics Department ofUniversidad Tecnica Federico Santa Maria as Research Fellow (2000-2004) andLecturer of Digital Signal Processing Laboratory (2001-2003). His researchinterests deal with power electronics and digital signal processing, participating inseveral publications. In 2004 he joined the European Southern Observatory, ESO,

where he works in the Electronics group acting as the main person responsible for the amplifiersand servo systems. His duties include, among others, evaluation of new systems, to carry outobsolete equipment upgrades, and to develop improvements aimed to achieve better performancein the existing systems.

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