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Electric Power Systems Research 108 (2014) 1– 15

Contents lists available at ScienceDirect

Electric Power Systems Research

jou rn al hom e page: www.elsev ier .com/ locate /epsr

MRAS-based stator resistance and speed estimation for sensorlessector controlled IPMSM drive

. Khlaiefa,b,∗, M. Boussaka,1, A. Châarib,2

Laboratoire des Sciences de l’Information et des Systèmes (LSIS), UMR CNRS 7296, Ecole Centrale Marseille (ECM), Technopôle de Château Gombert,3451 Marseille cedex 20, FranceUnité de Recherche en Commande, Surveillance et Sûreté de fonctionnement des Systèmes «C3S», Ecole Supérieure des Sciences et Techniques de TunisESSTT), 5 Avenue Taha Hussein, BP. 56, Bab Manara 1008, Tunis, Tunisia

r t i c l e i n f o

rticle history:eceived 21 March 2013eceived in revised form1 September 2013ccepted 27 September 2013vailable online 16 November 2013

eywords:nterior permanent magnet synchronous

otor (IPMSM) drive

a b s t r a c t

In this paper, model reference adaptive system (MRAS) technique has been used for speed estimation insensorless speed control of interior permanent magnet synchronous motor (IPMSM) with space vectorpulse width modulation (SVPWM). Most of the current researches studying the MRAS technique are basedon non-saliency PMSM model and ignore the difference between d- and q-axes inductances. This paperstudies a novel MRAS observer, considering the saliency of PMSM. However, this sensorless speed controlshows great sensitivity to stator resistance and system noise, particularly, during low-speed operation.A novel stator resistance estimator is incorporated into the sensorless drive to compensate the effectsof stator resistance variation. A stability-analysis method of this novel MRAS estimator is shown. Stableand efficient estimation of rotor speed at low region will be guaranteed by simultaneous identification of

odel reference adaptive system (MRAS)ensorless controltator resistance estimationigital signal processor (DSP)

IPMSM. The stability of proposed stator resistance estimator is checked through Popov’s hyperstabilitytheorem. The proposed observer is experimentally tested using a 1.1-kW motor drive; stable operationat very low speeds under different loading conditions is demonstrated. The real time implementationconcept on the digital signal processor (DSP) board of the VFOC design and SVPWM inverter techniqueare illustrated. Results show that the proposed MRAS technique can satisfactorily estimate the positionand speed of PMSM with saliency.

. Introduction

Recently, permanent magnet synchronous motor (PMSM) haseen widely used in high performance variable speed in many

ndustrial applications, due to its high efficiency, high ratio oforque-to-inertia ratio, high power factor, faster response andugged construction. The PMSM has increasingly been used inlectrical vehicles, aircraft, nuclear power stations, submarines,obotic applications, medical and industrial servo drives. The pres-

nce within electrical drives of rotor speed and position sensorsepresents a disadvantage under economical aspect because itetermines a cost increase, temperature sensitivity and reliability

∗ Corresponding author at: Laboratoire des Sciences de l’Information et des Sys-èmes (LSIS), UMR CNRS 7296, Ecole Centrale Marseille (ECM), Technopôle dehâteau Gombert, 13451 Marseille cedex 20, France.el.: +33 491054490; fax: +33 491054565.

E-mail addresses: khlaief.omar@yahoo.fr (A. Khlaief),ohamed.boussak@centrale-marseille.fr (M. Boussak), abdelkader.chaari@yahoo.fr

A. Châari).1 Senior Member IEEE. Tel.: +33 491054490; fax: +33 491054565.2 Tel.: +216 71461125; fax: +216 1391 166.

378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.epsr.2013.09.018

© 2013 Elsevier B.V. All rights reserved.

decrease. To overcome these problems, in recent years, there hasbeen considerable interest in sensorless vector control of PMSMdrive [1]. A number of sensorless control methods have been pro-posed in the literature for PMSM [1–21].

The first technique of sensorless control on PMSM is basedon rotor flux orientation [2,3]. The authors estimate the rotorposition by integration of back electromotive force (EMF). Thedisadvantage of this method is the DC offset which leads to mea-surement errors in flux linkages and then affects the rotor speedestimation. Moreover, this method can present good performancearound nominal speed, but it is not suitable for low and zero speedoperation.

Many researchers use the extended Kalman filter (EKF) tech-nique to estimate the speed and the rotor position of the PMSM.Some authors use the dynamic model of the PMSM in d − q axis inthe synchronous reference frame fixed to the rotor [4–6] and othersuse the PMSM model in the − axis in the stationary referenceframe fixed to the stator [7]. It is well known that EKF method is

less sensitive to the unknown measurement noise, but requires along computational time especially due to the several matrix oper-ations. The previous methods used to estimate the rotor position ofPMSM suffer from accuracy due to variation of motor parameters.

2 A. Khlaief et al. / Electric Power Syst

Nomenclature

− stationary axis reference frame quantitiesd − q synchronous axis reference frame quantitiesv˛, vˇ stator and axis voltagesi˛, iˇ stator and axis currentsid, iq stator d and q axis currentsvd, vq stator d and q axis voltages˚d, ˚q stator d and q axis flux linkagesLd, Lq stator d and q axis inductancesKe back-EMF coefficient constantˆ m peak permanent magnet fluxRs stator resistanceJ total rotor inertiaB viscous friction coefficientNp number of the pole pairs� electrical rotor positionωr electrical rotor speed˝r mechanical rotor speedı angle of the space vectorTe electromagnetic torqueTl load torquep laplace variableTs sampling periodTsw switching period*, ˆ reference value and estimated valueKi ˝ and Kp ˝ integral and proportional (IP) speed controllerKi id and Kp id integral and proportional (PI) d-axis current

controllerKi iq and Kp iq integral and proportional (PI) q-axis current

controllerKωr i est and Kωr p est integral and proportional (PI) speed

observer controllerK and K integral and proportional (PI) stator resis-

Irit

(micstvtttmualmoauu

ptp

d d d e

Rsi est Rsp est

tance observer controller

n order to overcome this problem, a robust solution to estimateotor position of PMSM based on the sliding mode observer (SMO)s proposed in [8,9]. The SMO uses the estimated speed to updatehe estimated stator currents in the sliding mode surface.

Other methods are based on high carrier-frequency injectionCFI) technique where the signal is superimposed onto the funda-

ental phase voltages [10–13]. In most cases, the injection signals a sinusoidal voltage. Thus, this may cause acoustic noise, a motorurrent distortion, torque pulsation and undesirable side effectsuch as large harmonic losses. The components of d − q axis sta-or currents are weak and they are proportional to the averagealue of the d − q axis stator inductances. These currents containhe information, which is necessary to estimate the rotor posi-ion using a proportional-integral (PI) tracking controller. The lastechniques vector control sensorless PMSM are based on MRAS

ethod [14–20]. In [14,15], an instantaneous reactive power issed for rotor speed estimation. The advantages of this methodre characterized by its independence of stator resistance and areess parameters sensitive of the PMSM. Most observers depend on

otor parameters, which vary with the temperature. In order tovercome this problem, an on-line parameter identification usingdaptive algorithm was proposed in [16]. In [17–21] the authorsse the stator currents to estimate the rotor speed and positionsing MRAS based adaptive strategy applied to non-salient PMSM.

Nowadays VFOC, is widely adopted to obtain high dynamicerformances in a drive system. However, the performance ofhis control method is greatly related the accuracy of the motorarameters used in the controller [22]. During operation, the stator

ems Research 108 (2014) 1– 15

resistance increases due to the motor-temperature rise. Therefore,stator resistance estimation for the VFOC is proposed in order toimplement a robust control law for industrial applications [23,24].

By comparing the methods developed previously in the liter-ature, we can notice that the MRAS technique is one of the bestmethods to be applied to estimate the rotor speed and positiondue to its performance in term of requires less computing time, toits easy implementation in DSP and to its straight forward stabil-ity approach [6]. In addition, the MRAS technique has been usedextensively for combined stator resistance and rotor speed estima-tion in PMSM. The MRAS speed estimators are the most attractiveapproaches due to their design simplicity. This is the most sig-nificant advantage of MRAS over the other speed observers andrecommended for low cost applications.

The basic speed estimation using an observer is previouslystudied in the literature. But the position and speed estimationtechnique based on MRAS observer developed in this paper isapplied to salient PMSM with more complex model. This tech-nique has been developed in the literature only for non-salientPMSM [17]-[21]. For the IPMSM, inherent saliency, i.e., the dif-ference between d- and q-axis inductance, beneficially changesboth the air-gap torque production and the field weakening char-acteristics. Application of MRAS methods to non-salient PMSM isstraightforward. However, when applying the methods to salientmachines, such as the interior PMSM (IPMSM), necessary approx-imations lead to estimation errors and decreased performance.Therefore, in our work we implemented a new technique basedon MRAS, which permits to estimate the stator resistance for sen-sorless vector control of salient PMSM drive with SVPWM. Stabilityanalysis and design of the MRAS estimators have been performedfor a IPMSM error model in a synchronous rotating reference framefixed to the estimated d − q axis stator currents. The adaptationmechanism is done by using the error between the measured andthe estimated stator currents. The rotor speed can be estimatedthrough a PI controller that controls the speed tuning signal to zero.The stability of the proposed rotor speed observer and stator resis-tance estimator is achieved through Popov’s Hyperstability theory.The convergence of the estimated rotor speed and position is guar-anteed. The sensorless control approach of IPMSM drive is appliedthrough in Matlab–Simulink environment and dSpace DS 1103 con-troller board. Finally, MRAS technique is a better alternative for lowcost applications, which have limited computation performance.

2. Dynamic model of IPMSM

A simplified schematic three phase IPMSM drive fed by volt-age source inverter (VSI) controlled by SVPWM technique is shownin Fig. 1. The power circuit of a three-phase VSI is shown inFig. 1, where va, vb and vc are the output voltages applied to thestar-connected IPMSM windings and VDC is the DC voltage inputinverter. T1 through T6 are the six IGBT components power modulethose shape the output, which are controlled by switching signalsC1 to C6.

2.1. IPMSM modeling

The state space model of the IPMSM expressed in d − q syn-chronous reference frame is presented in this section.

The d − q axis stator flux linkages in the synchronous referenceframe can be expressed as follows.{

˚ = L i + K

˚q = Lqiq(1)

where Ke =√

3/2 ˆ m

A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15 3

rce inverter fed IPMSM.

md

lmm

[

a

2

cvsTitSmTiisVe

3

amWsopbttm

d

Fig. 1. Voltage sou

Note that (1) differs from the mathematical model of the PMSotor due to saliency (Ld /= Lq /= Ls). The electromagnetic torque

eveloped by the motor may be expressed as:(2)Te = Np(Keiq + (Ld − Lq)idiq)The model of the IPMSM in the rotor reference frame is out-

ined for the development of the position and velocity estimationethod. Using the electrical equations, the d − q axis dynamicodel of the IPMSM in the synchronous reference frame becomes:

vd

vq

]=

⎡⎢⎣ Rs + d

dtLd −ωrLq

ωrLd Rs + d

dtLq

⎤⎥⎦

[id

iq

]+ Keωr

[0

1

](3)

The model Eq. (3) is used in the design of the currents regulatornd the MRAS observer.

.2. Field-oriented control structure

The IPMSM is primarily associated with high performance motorontrol and is fed by a voltage source inverter (Fig. 1) using SVPWMoltage source inverters (VSI) technique. The VFOC of IPMSM allowseparate closed loop decoupling control of both flux and torque.he SVPWM controlled VSI fed IPMSM are widely used in manyndustrial applications. The SVPWM technique control strategy ofhe inverter is based on the voltage/frequency control method. TheVPWM is more sophisticated technique for generating a funda-ental sine wave that provides a higher voltage to the IPMSM.

he main advantage of the SVPWM technique is that the switch-ng losses are low, low output harmonic distortions and offer 15%ncrease in the DC-link voltage compared with the conventionalinusoidal PWM (SPWM) [25,26]. Therefore, the SVPWM controlledSI fed IPMSM drive allows obtain a higher torque with higherfficiency.

. Structure of the proposed MRAS technique

The MRAS estimators are designed to estimate the stator d − qxis currents and the rotor speed. The main idea behind MRASethod is that there is a reference model and an adjustable model.here the first one is used to determine the required states and the

econd one as an adaptive model provides the estimated valuesf the states [27]. The output of the reference model is com-ared with an adjustable observer-based model. The error obtainedetween the reference and adjustable model is given to an adapta-ion mechanism, which adjusts the adaptive model by generatinghe estimated value of rotor speed. The block diagram of the esti-

ation technique based on MRAS method is shown in Fig. 2.

From (3) the state space d − q axis stator currents of IPMSM

esigned as reference model is given by:

d

dt[X] = [A][X] + [B][U] + [C] (4)

Fig. 2. Block diagram of the estimation technique with MRAS.

where

[X] =[

id

iq

], [A] =

⎡⎢⎢⎣

− Rs

Ld

Lq

Ldωr

− Ld

Lqωr − Rs

Lq

⎤⎥⎥⎦ ,

[B] =

⎡⎢⎣

1Ld

0

01Lq

⎤⎥⎦ , [U] =

[vd

vq

], [C] =

⎡⎢⎣

0

−Ke

Lqωr

⎤⎥⎦

The state space d − q axis stator currents of IPMSM designed asadjustable model is given by:

d

dt[X] = [A][X] + [B][U] + [C] (5)

where

[X]

=

⎡⎣ id

iq

⎤⎦ , [A] =

⎡⎢⎢⎣

− Rs

Ld

Lq

Ldωr

− Ld

Lqωr − Rs

Lq

⎤⎥⎥⎦ ,

[B] =

⎡⎢⎣

1Ld

0

01Lq

⎤⎥⎦ , [U] =

[vd

vq

],[C]

=

⎡⎢⎣

0

−Ke

Lqωr

⎤⎥⎦

where Ld, Lq, Ke are considered as constant.

After developing adjustable and reference models, the adapta-

tion mechanism will be built for MRAS method. The adaptationmechanism is designed in a way to generate the value of estimatedspeed used so as to minimize the error between the estimated and

4 er Systems Research 108 (2014) 1– 15

rtdta

ε

�

ta

f

f

mf⎧⎪⎨⎪⎩⎡⎢⎣

d

wma

[

wb

bftls

c

itrh

t

Fig. 3. Equivalent representation of nonlinear and time varying feedback system.

Real Axis

Imag

inar

y Ax

is

-25 0 -20 0 -15 0 -100 -50 0-40 0

-30 0

-20 0

-10 0

0

100

200

300

4000.050.1 10.180.250.340.48

0.64

0.86

0.050.110.180.250.340.48

0.64

0.86

50100150200250300350

50100150200250300350

A. Khlaief et al. / Electric Pow

eference d − q axis stator currents. By adjusting the estimated rota-ional speed, the error between the reference and the estimated

− q axis stator currents from (5) is reduced. The error betweenhe estimated and reference d − q axis stator currents are defineds:

d = id − id, εq = iq − iq (6)

The value of the rotor speed error is given as:

ωr = ωr − ωr (7)

The difference between the state model given by Eq. (6) andhe adjustable model given by Eq. (7), is used to drive a suitabledaptation mechanism.

The state stator currents error can be described by theollowing dynamic equations in the synchronous reference

rame.(8)

⎧⎨⎩

dεd

dt= −Rs

Ldεd + Lq

Ldωriq − Lq

Ldωr iq

dεq

dt= −Rs

Lqεq + Ld

Lqωrid − Ld

Lqωr id + Ke

Lqωr − Ke

Lqωr

Adding and subtracting of the term (Lq/Ld) ωr iq, the state errorodel of the IPMSM expressed in the d − q synchronous reference

rame is given as follow:

dεd

dt= −Rs

Ldεd + Lq

Ldωrεq + Lq

Ld(ωr − ωr)iq

dεq

dt= −Rs

Lqεq − Ld

Lqωrεd − Ke

Lq(ωr − ωr) − Ld

Lq(ωr − ωr)id

(9)

Eq. (9) can be written in state error model representation as:

dεd

dt

dεq

dt

⎤⎥⎦ =

⎡⎢⎣

−l

�dωr

Lq

Ld

− ωrLq

Ld

−l

�q

⎤⎥⎦

[εd

εq

]+

⎡⎢⎣

Lq

Ldiq

Ld

Lqid − Ke

Lq

⎤⎥⎦ (ωr − ωr)(10)

Therefore, the state error model of the IPMSM expressed in the − q synchronous reference frame is given as follow:

d

dt[ε] = [A1] [ε] + [W1] (11)

here [ε] =[

εd εq

]Tis the error state vector, [A1] is the state

atrix and [W1] is the output vector of the feedback block defineds follow:

A1] =

⎡⎢⎢⎣

− Rs

Ld

Lq

Ldωr

− Ld

Lqωr − Rs

Lq

⎤⎥⎥⎦ , [W1] =

⎡⎢⎣

Lq

Ldiq

− Ld

Lqid − Ke

Lq

⎤⎥⎦(

ωr − ωr

)

The design of MRAS relies on the hyperstability concept [20],hich mainly concerns the stability proprieties of a class of feed-

ack systems as shown in Fig. 3.To ensure the hyperstability of the system, two criterions should

e established. Firstly, the linear time-invariant forward path trans-er matrix, H1(p) = (p [I] − [A1])−1 must be strictly positive real (allhe poles of a H1(p) have negative real parts). Secondly, the non-inear feedback (which includes the adaptation mechanism) mustatisfies the following Popov’s criterion for stability [20,21].

(12)∫ t0

0[ε]T [W1]dt ≥ −�2

0 where t0 ≥ 0, �0 is a finite positive realonstant, which is independent of t0

In this case of a single-input/single-output nonlinear time-nvariant feedforward block, the hyperstability conditions arehat the transfer function of the feedforward block be positive

eal for hyperstability and strictly positive real for asymptoticyperstability.

The first condition is validated by the root locus study of theransfer function H1(p).

Fig. 4. Poles loci for the transfer matrix H1(p) · ωr = 0 → ±314 elec.rad/s.

The Fig. 4 shows the pole-zero loci for the transfer matrix H1(p)for a range of speed starting at 0.1 up to ±314 elect.rad/s. In Fig. 4,we can see that the poles have negative real parts. So the conditionis confirmed on H1(p).

H1(p) must be a strictly positive real transfer matrix.Let

ωr = A2([ε]) +∫ t0

0

A1([ε])dt (13)

where A1, A2 are non-linear function of εd, εq.We search solutions to A1 and A2 such that the equivalent feed-

back block verifies Popov’s criterion (13).Using the expression [W1], the inequality (12) becomes:∫ t0

0

{[εd

(Lq

Ldiq

)]+

[εq

(− Ld

Lqid − Ke

Lq

)]}[ωr − ωr

]dt ≥ −�2

0

(14)

Using ωr, Popov’s criterion for the present system becomes:∫ t0

0

{[εd

(Lq

Ldiq

)]+

[εq

(− Ld

Lqid − Ke

Lq

)]}

×∫ t0

0

{[ωr − A2([ε]) −

∫ t0

0

A1([ε])dt

]}dt ≥ −�2

0 (15)

r Systems Research 108 (2014) 1– 15 5

w∫

t

A

A

w

o

ω

0ttaTitt

emfm

ω

wωp

srllt

w

r

W

fh

-r + ˆ ˆ_ _r rp est i estK p K

p+

PI Controller

ˆr ˆrˆ_ rpG

ˆr

( )1W p

Fig. 5. Rotor speed estimator block diagram.

Pole-Zero Map

Real Axis

Imag

inar

y A

xis

-500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0-250

-200

-150

-100

-50

0

50

100

150

200

2500.160.340.50.640.760.86

0.94

0.985

0.160.340.50.640.760.86

0.94

0.985

100200300400

poles are located in the left-hand side of the p-plane. Consequently,the locus of closed-loop poles shows stable operation for the wholespeed range.

Table 1Interior permanent magnet synchronous motor parameters.

Parameters Specification

R = 7.1 Rated power = 1.1 kW

A. Khlaief et al. / Electric Powe

A solution of this inequality can be found through the followingell-known relation (Landau [28,29]):t0

0

k [pf (t)] f (t)dt ≥ −12

kf (0)2, k > 0 (16)

Then the observed rotor resistance satisfies the following adap-ation laws:

1 = K1

[Lq

Ldiqεd − Ld

Lqidεq − Ke

Lqεq

](17)

2 = K2

[Lq

Ldiqεd − Ld

Lqidεq − Ke

Lqεq

](18)

here K1 and K2 are the positive adaptation gains.Substituting A1 and A2 in (13), it can be easily shown that the

bserved rotor speed satisfies the following adaptation laws:

ˆ r = A2([ε]) + 1p

A1([ε]) (19)

Finally, by using the Popov’s theory, we obtain: limt→∞

= [ε(∞)]T = and therefore, the adaptive law on (13) of the MRAS speed estima-ion is asymptotically stable. Therefore, a PI controller is sufficiento satisfy Popov’s integral inequality. The other criterion for glob-lly stable MRAS is to make the feedforward path gain real positive.o do this an error manipulation block “adaptation mechanism” isncorporated in Fig. 2, which achieves the same by properly settinghe sign of [ε]. These satisfy both the Popov’s criterion and confirmhe stability of the system.

The speed tuning signal is minimized by PI controller which gen-rates the estimated rotor speed and is fed back to the adaptiveodel as shown in Fig. 2. The rotor estimated speed is generated

rom the adaptation mechanism using the error between the esti-ated and reference currents obtained by the model as follows:

ˆ r = Kiωr est

∫ t

0

(Lq

Ldiqεd − Ld

Lqidεq − Ke

Lqεq

)

· dt + Kpωr est ·(

Lq

Ldiqεd − Ld

Lqidεq − Ke

Lqεq

)+ ωr(0) (20)

here Kiωr est and Kpωr est are the PI speed observer controller andˆ r(0) is the initial estimated speed. Finally the estimated rotorosition is obtained by integrating the estimated rotor speed.

The parameters ωr and ωr both vary with time and each may beeen as an input to the stator Eq. (5). To investigate the dynamicesponse of the MRAS rotor speed estimation, it is necessary toinearize the stator equation for small deviation around the equi-ibrium point [30]. Therefore, substituting (17) and (18) into (11),he transfer function relating εωr to � ωr is:

�εωr

� ωr

∣∣∣�ωr=0

= Gp ωr= K2

L (p + Td) + KLiqωr[(p + Td)(p + Tq) + ω2

r

] (21)

here KL = Ke/Lq ; Td = Rs/Ld and Tq = Rs/Lq.The closed loop block diagram of the dynamic response of MRAS

otor speed identification as shown in Fig. 5.The forward transfer function of the speed estimator is:( )

1(p) = ωr

� ωr= Gp ωr

Kp ωr estp + Ki ωr est

p(22)

From (21) and Fig. 5, since the poles and the zeros of transferunctions Gp ωr

of the rotor speed estimator are located in the left-and side of the p-plane, the estimator PI controller gains can be

Fig. 6. Pole placement of the transfer function of the MRAS speed estimation.ωr = 0.1 → ±314 elec.rad/s.

selected as high as possible to provide quick tracking of the esti-mated rotor speed. Before proceeding to determine the rotor speedestimator PI controller gains, it can be noted that the existence of aGp ωr

pole at the origin of the p-plane guarantees the convergenceof � ωr to zero. Indeed, the locations of the closed-loop transferfunction poles characterize the control-system dynamics. Thus, thevalue of the integral and proportional speed observer controller canbe selected to give close tracking of the actual rotor speed. It can beseen that the design of Kpωr est and Kiωr est is selected to ensure thatall of the poles and zeros are located in the left hand side of the p-plane. This allows for the required fast response. The implementeddesign of the speed observer PI controller leads to Kiωr est = 4100and Kpωr est = 160.

The stability study of the speed loop is based on pole-placementfor the closed loop transfer function ωr/� ωr of the speed estimator.Fig. 6 shows the loci of the closed-loop poles for a range of speedstarting at 0.1 up to ±314 elect.rad/s and fixed controller gain forthe motor parameters given in Table 1. It can be seen that the all

s

Ld = 25.025 mH Rated voltage = 400 VLq = 40.17 mH Rated current = 2.53 Amd (rms) = 0.305 Wb Number of pole pairs = 3Ke = 0.5283 V s rad−1 Rated speed = 3000 r/minJ = 0.0036 Kg m2 Rated torque = 4 N mB = 0.0011 Nm s rad−1 DC link voltage = 540 V

6 A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15

4

sdtr

dwTmetrwr

at

ε

⎡⎢⎣

p

m

fafa

∫ t0

0

[ε]T [W2]dt ≥ −�21 /= for allt0 ≥ 0 (26)

Pole-Zero Map

Imag

inar

y A

xis

-400

-300

-200

-100

0

100

200

300

4000.070.150.240.340.460.6

0.76

0.92

0.070.150.240.340.460.6

0.76

0.92

50

100

150

200

250

300

350

50

100

150

200

250

300

350

400

-50% Rs+50% Rs

Fig. 7. Block diagram of MRAS for stator resistance estimation.

. Stator resistance estimation

The basic configuration of the MRAS is described by a classicalcheme often presented in specialized literature [28]. This blockiagram is called parallel model reference adaptive system usinghe output error method. The basic scheme of MRAS for statoresistance estimation is shown in Fig. 7.

In general, the stator resistance is variable and the modeleduced from vector spatial equations in d − q coordinates, rotatingith electrical angular velocity ωr is non-linear and time varying.

he main idea of the MRAS is to compare the outputs of the twoodels and to adjust the value of Rs in order to minimize the result

rror. The adjustment value is the stator resistance generated fromhe error between measured and estimated stator currents. Statoresistance plays an important role and its value has to be knownith good precision in order to obtain an accurate estimation of the

otor speed in the low speed region.The error between the states of the two models is used to drive

suitable adaptation mechanism that generates the estimate Rs forhe adjustable model.

Let us compute the state error components from:

d = id − id and εq = iq − iq (23)

The error state equation becomes:

dεd

dt

dεq

dt

⎤⎥⎦ =

⎡⎢⎢⎣

−Rs

Ldωr

Lq

Ld

− ωrLd

Lq

−Rs

Lq

⎤⎥⎥⎦

[εd

εq

]−

⎡⎢⎣

1Ld

id

1Lq

iq

⎤⎥⎦ (Rs − Rs) (24)

Eq. (24) can be written in state error model representation as:

[ε] = [A2][ε] − [W2] (25)

where [ε] =[

εd εq

]Tis the error state vector, [A2] is the state

atrix and [W2] is the feedback block defined as follow:

[A2] =

⎡⎢⎢⎣

−Rs

Ldωr

Lq

Ld

− ωrLd

Lq

−Rs

Lq

⎤⎥⎥⎦ , [W2] =

⎡⎢⎣

1Ld

id

1Lq

iq

⎤⎥⎦ (Rs − Rs)

The term of [W2] is the input and [ε] is the output of the linear

eedforward block and it can be easily shown that the linear equiv-lent system will be completely observable and controllable. Theormer state Eq. (25) describe the equivalent MRAS in a linear ways it was previously specified and [ε] is the main information upon

Fig. 8. MRAS representation as a nonlinear feedback system.

which differences existing between the adjustable model and thereference model. The asymptotic behavior of the adaptation mech-anism is achieved by the simplified condition [ε(∞)]H = 0 for anyinitialization.

Since Rs is a function of the state error, these equations describea nonlinear-feedback system as illustrated in Fig. 8. FollowingLandau, hyperstability is assured, provided that the linear time-invariant forward-path transfer matrix is strictly positive real andthat the nonlinear feedback (which includes the adaptation mech-anism) satisfies Popov’s criterion for hyperstability [28–30]. Toensure the hyperstability of the system, two criterions should beestablished. Firstly, the linear time-invariant forward path trans-fer matrix, H2(p) = (p[I] − [A2])−1 must be strictly positive real (allthe poles of a H2(p) have negative real parts). Secondly, the non-linear feedback (which includes the adaptation mechanism) mustsatisfies the following Popov’s criterion for stability.

The Fig. 9 shows the pole placement of the transfer matrixH2(p) depending on stator resistance changes from −50% to +50%of their nominal value for a range of speed starting at 0.1 up to±314 elect.rad/s. In the figure above, we can see that the poles havenegative real parts. So the condition is confirmed on H2(p).

The feedback system will be hyperstable for any feedback blockof the class satisfying the inequality:

Real Axis-350 -300 -250 -200 -150 -100 -50 0

Fig. 9. Pole placement of the transfer matrix H2(p) depending on stator resistancechanges from −50% to +50% of their nominal value. ωr = 0 → ±314 elec.rad/s.

A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15 7

-+

PI Controller

( )2W p

sR ˆsR

ˆsR

ˆsR

ˆ_ sp RG _ _ssR p est R i estK p Kp+sR

Fs

wt

br

R

w

A

A

ttpiueel

R

wt

srlat

w

i

b

W

tF

-250 -200 -150 -100 -50 0-5

-4

-3

-2

-1

0

1

2

3

4

50.9750.9940.9980.9990.9991

1

1

0.9750.9940.9980.9990.9991

1

1

501001502000

Pole-Zero Map

Real Axis

Imag

inar

y A

xis

Fig. 11. Pole placement of the transfer function of the MRAS stator resistance esti-

ig. 10. Simplified block scheme of the MRAS stator resistance estimator used fortability analysis.

here �1 is a finite positive real constant, which is independent of0

From the previous Eq. (26) and the Popov’s inequality, it cane easily show that the observed stator resistance satisfies thiselationship:

ˆ s = A3([ε]) + 1p

A4([ε]) (27)

ith:

3([ε]) = K3

(1Ld

idεd + 1Lq

iqεq

)(28)

4([ε]) = K4

(1Ld

idεd + 1Lq

iqεq

)(29)

In Eq. (27), A3 and A4 are the positive adaptation gains by meanshe stator resistance which can be adjusted. Based on adaptive con-rol theory, the state error [ε] can be tending to zero by means ofarameters adjustable model using adaptive laws when the system

s stable. The error between the states of the two models is thensed to drive a suitable adaptation mechanism that generates thestimate stator resistance for the adjustable model. Therefore, tostimate stator resistance, we used a PI controller. So, the adaptiveaw of stator resistance is written as:

ˆ s = KRsi est

∫ t0

0

(1Ld

idεd + 1Lq

iq.εq

)dt

+ KRsp est

(1Ld

idεd + 1Lq

iqεq

)+ Rs(0) (30)

here KRsi est and KRsp est are the PI stator resistance observer con-roller and Rs(0) is the initial value of Rs.

Both parameters Rs and Rs vary with time and each may beeen as an input to the rotor Eq. (26). To investigate the dynamicesponse of the MRAS rotor resistor estimation, it is necessary toinearize the stator and rotor equations for small deviation around

working point. Therefore, substituting (17) and (18) into (11), theransfer function relating εRs to �Rs is:

�εRs

�Rs

∣∣∣∣�Rs=0

= Gp Rs= pari2q + i2qRsbr[

(p + Td)(p + Tq) + ω2r

] (31)

here ar = (1/Lq)2 and br = 1/LdLq2.

The transfer function of the open loop MRAS estimator (Fig. 7)s described by the Eq. (31).

Finally, the transfer function of the closed-loop system is giveny (32), which is shown at this relationship:

2(p) = Rs = Gp Rs

(KRsp estp + KRsi est

p

)(32)

�Rs

The closed loop diagram of the dynamic response of MRAS sta-or resistance estimation can be drawn as in Fig. 10. From (31) andig. 10, since the poles and the zeros of transfer functions Gp ωr

mation depending on stator resistance changes from −50% to +50% of their nominalvalue. ωr = 0.1 → ±314 elec.rad/s.

of the stator resistance estimator are located in the left-hand sideof the p-plane, the estimator PI controller gains can be selected ashigh as possible to provide quick tracking of the estimated statorresistance. Before proceeding to determine the rotor speed estima-tor PI controller gains, it can be noted that the existence of a Gp Rs

pole at the origin of the p-plane guarantees the convergence of �Rs

to zero. Indeed, the locations of the closed-loop transfer functionpoles characterize the control-system dynamics. Thus, the valueof the integral and proportional speed observer controller can beselected to give close tracking of the actual rotor speed. It can beseen that the design of KRsi est and KRsp est is selected to ensure thatall of the poles and zeros are located in the left hand side of the p-plane. This allows for the required fast response. The implementeddesign of the speed observer PI controller leads to KRsi est = 180 andKRsp est = 1. The stability study of the speed loop is based on pole-placement for the closed loop transfer function Rs/�Rs of the speedestimator [33,34]. Fig. 11 shows the pole placement of the trans-fer function of the MRAS stator resistance estimation for a rangeof speed starting at 0.1 up to ±314 elect.rad/s depending on statorresistance changes from −50% to +50% of their nominal value. Itcan be seen that the all poles are located in the left-hand side of thep-plane. Consequently, the locus of closed-loop poles shows sta-ble operation for the whole speed range and the stator resistancechanges from −50% to +50% of their nominal value.

The estimating performance of rotor speed is designed onlyby the PI coefficients. The proposed sensorless control of IPMSMwith online estimation of stator resistance is presented in Fig. 12.The field oriented control (FOC) allows separating the closed loopdecoupling control of both flux and torque.

From the IPMSM described below, we carried out usingMatlab–Simulink to simulate VFOC sensorless speed control withonline estimation of stator resistance taking into account thedecoupling stator vector components.

5. Simulation results

This section presents simulation results obtained from sensor-

less speed control of IPMSM drives. The simulation was performedwith the Matlab–Simulink software environments using the motorparameters listed in Table 1. The speed loop is realized by anintegral-proportional (IP) controller instead of PI controller. For

8 A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15

with s

ctrtcamiisTbm

rcosemTvtsoscsltscar

rsa

Fig. 12. Block scheme representation of VFOC IPMSM drive

urrent regulation, this paper proposes a conventional PI con-roller with feedforward compensation terms in the synchronouseference. Owing to its advantages, an integral-proportional IP con-roller is used for rotor speed regulation. The advantage of the IPontroller is to obtain a closed loop transfer function without zerosnd its parameters are easier to design. The IP speed controller isore suitable to overcome the problems of overshoot and instabil-

ty. The choice of the parameters of speed and currents controllerss done according to the desired performances for the closed loopystem by imposing the natural frequency and the damping ratio.his kind of control loops is very appreciated, and used abundantlyy the control system because its structure is simple. Another, theeasured rotor speed is used for comparison purpose only.Fig. 13(a) shows the estimated and actual rotor speed with speed

eference from stand-still to 800 rpm and then to −800 rpm. Wean see that the estimated rotor speed is very close to the measuredne. The average value of the rotor speed error converges to zero, ashown in Fig. 13(b). Fig. 13(c) shows the estimated and measuredlectrical rotor position with a step change command while theotor is running from 800 rpm to stand-still and then to −800 rpm.

he estimated error position during the whole speed profile isery small as shown in Fig. 13(d). From Fig. 13(a), we can see thathe estimated rotor speed accurately follows the reference even attand-still speed operation. The results show a high performancef the proposed sensorless speed control IPMSM drive. Fig. 13(e)hows the electromagnetic torque of the proposed sensorless speedontrol with load torque equal to 4 Nm applied at t = 4.2 s. The sen-orless speed control is robust under the electromagnetic torqueoad. We can observe that the estimated and measured q-axis sta-or currents are directly proportional to the electromagnetic torquehown in Fig. 13(g). The estimated and measured d-axis statorurrents are kept constant at zero (Fig. 13(f)). The estimated d − qxis stator currents are close to the measured ones both in high andeversal speed range.

Fig. 14 shows the performance of the parallel speed and statoresistance estimation by simulation. Fig. 14(b) shows the referencepeed equal to 50 rpm and stator resistance estimator is tuned ont t = 4.1 s. Fig. 14(c) shows the performance of the estimator due

peed and stator resistance observer using MRAS technique.

to 41% increase in stator resistance when the machine is running at800 rpm. In both case, the difference between the real and observedspeeds remains very small even beginning of the transient when thestator resistance increased by 41%. The stator resistance estimatoris very effective at both low speeds and transient step load torqueas it is able to identify the actual stator resistance value within ashort time frame.

Fig. 15 shows the performance of stator resistance estimationusing MRAS technique under temperature effect. In Fig. 15 the realstator resistance is changed exponentially to 10.1 in referencemodel intended to cover the temperature variations, and after 0.3 sthe rotor resistance is stepped up to 3 (increased by 41% fromits initial value). In Fig. 15(b) the real stator resistance is changedexponentially to 4.1 in reference model intended to cover thetemperature effect. The behavior of the system is analyzed assum-ing a negative step of the stator resistance.

It is very clear that, the estimated stator resistance in adjustablemodel follows.

It is observed that the variation in rotor resistance has no effecton stator resistance estimation process and the estimated statorresistance follows its reference value in very good shape (Fig. 15(c)and (d). One can see that stator resistance identification is satisfac-tory.

Consequently, the simulation results show the efficiency and thefeasibility of the proposed simultaneous estimation of rotor speedand stator resistance in sensorless IPMSM drive based on MRASscheme.

6. Real-time implementation

The effectiveness of the proposed sensorless drive scheme wastested experimentally. A DSP is a type of microprocessor that hasbeen specially designed to implement the algorithms required to

process signals digitally. These algorithms are characterized byrepetitive mathematical computation at high-speed, similar to thisapplication where the mathematically intensive VFOC and SVMalgorithms must be run within every 150 �s sampling period Ts.

A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15 9

erence

svg

Fig. 13. Simulation results with speed ref

In our laboratory, we developed a nonlinear observer for theame motor (salient PMSM) using the flux linkage as new stateariable without speed dependence [31]. The nonlinear observerives estimation of the rotor position using a trigonometric

profile under 100% rated load condition.

function and the speed estimation is obtained from estimated posi-tion using proportional-integral (PI) tracking controller. In thiswork, the sampling period Ts of the system is 150 �s. The exper-imental results show that the program execution time is equal

10 A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

Time (sec)

Sta

tor

resi

stan

ce (

Ohm

)

Rs

Rs-est

Rs Stepped -up (41 %)

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

Time (sec)

Sta

tor

resi

stan

ce (

Ohm

)

Rs

Rs-est

Rs Stepped -up (41 %)

a) Esti mated and mea sured spee d. b) Esti mated and mea sured spee d.

0 1 2 3 4 5 6 7 8 9 10 11-10 0

0

100

200

300

400

500

600

700

800

900

Time (sec)

Rot

or s

peed

(rp

m)

W-est

W-mes

W-r ef

Rs Stepped -up (41 %)

0 1 2 3 4 5 6 7 8 9 10 11-10

0

10

20

30

40

50

60

Time (sec)

Rot

or s

peed

(rp

m)

W-est

W-mesW-r ef

Rs Stepped -up (41 %)

due t

tsteTcfioo(mtctsfaMM

iwTpaic

m

c) Real and esti mated stator resistance .

Fig. 14. Simulation results with stator resistance estimation

o 65 �s (43.33% of sampling period). Contrariwise, the proposedensorless control of IPMSM with online estimation of stator resis-ance, in our paper, the experimental results show that the programxecution time is less than 35 �s (23.33% of sampling period).his is possible since the MRAS observer doesnot require a largeomputing time. We can see that the sensorless indirect-rotor-eld-orientation speed control algorithm of IPMSM using nonlinearbserver requires more computation time compared to the MRASbserver (an increase of 30 �s). Another, Extended Kalman filtersEKF) have also been proposed for rotor speed and position esti-

ation [7]. The main difficulty in developing an EKF for IPMSM ishe complexity of the dynamic model expressed in the stationaryoordinate system. The EKF algorithm predicts the state in tk withhe sampling period Ts fixed at 500 �s. The experimental resultshow that the program execution time is equal to 200 �s. There-ore, the sensorless speed control algorithm of IPMSM using EKFlgorithm requires many more computation time compared to theRAS observer (an increase of 165 �s). Consequently, with theRAS method the computing time is reduced.On the other hand, it is shown in [6] that the algorithm of MRAS

s much simpler than the extended Kalman filter (EKF) technique,hich needs more than 60% of overall program execution time.

herefore, the MRAS technique is simple and it requires less com-utation time. The MRAS speed estimators are the most attractivepproaches due to their design simplicity. Finally, MRAS technique

s a better alternative for low cost applications, which have limitedomputation performance.

The experimental setup (Fig. 16) is composed by a com-ercial 20 KVA 3-phase VSI based on IGBT power components

d) Real and esti mated stator resistance .

o 41% increase in stator resistance at (c) 800 and (d) 50 rpm.

from SEMIKRON with current limitation of about 30 A, aMatlab–Simulink software, a dSpace DS1103 laboratory controlboard and a 3-phase IPMSM. We used the IR2130 driver in order toamplify the PWM signals generated by dSpace card and to guar-antee a reliable isolation between the high voltage and controlpanel. The dSpace DS1103 board is a very flexible and powerfulsystem both for high computational capability and comprehensiveI/O periphery.

The IPMSM under test is 3-phase 400 V, 1.1 kW, with 4 Nm nom-inal load torque with the characteristics are given in Appendix.In order to have a comparison between real and estimated rotorposition, an incremental encoder with 4096 pulses is coupled withthe motor, and the magnetic powder brake is used as load torque.Also, an incremental encoder was used to obtain the measuredrotor speed, which was solely used for comparison and not for con-trol purposes. It should be noted, the estimated speed is used asfeedback in a vector speed control system for SVPWM inverter-fedIPMSM.

The system is based on Motorola Power PC604, the DSP subsys-tem, based on the Texas Instruments TMS320F240 DSP fixed-pointprocessor. The DSP provides 3-phase SVPWM generation makingthe subsystem useful for drive applications. Two LEMs current sen-sors (LEM LA 100P) are used to measure the phase current. In orderto avoid noise switching transistors, the analog digital converters(ADC) inputs are synchronized with the PWM signals. We used

the DS1103SL-DSP-PWMINT block from RTI library of dSpace. Thisblock is configured to generate a trigger signal to ADC inputs inthe OFF-period of PWM signal. Using this technique, the measuredphase currents are well filtered. Indeed, we donot use additional

A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15 11

a) St ator res istance es timati on un der temperature effect. b) Stat or resistance esti mati on under t emp erat ure effec t.

0 1 2 3 4 5 6 7 80

2

4

6

8

10

12

Time (sec)

Sta

tor r

esis

tanc

e (O

hm)

RsRs-est

0 1 2 3 4 5 6 7 81

2

3

4

5

6

7

8

Time (sec)

Sta

tor r

esis

tanc

e (O

hm)

RsRs-est

0 1 2 3 4 5 6 7 8-1

0

1

2

3

4

5

6

Time (sec)

Sta

tor r

esis

tanc

e er

ror (

Ohm

)

0 1 2 3 4 5 6 7 8-1

0

1

2

3

4

5

6

Time ( sec)

Sta

tor r

esis

tanc

e er

ror (

Ohm

)

tion u

fiiid

c) Stator res ista nce esti mation error.

Fig. 15. Performance of stator resistance estima

lters on the sampled current. Another, in order to compensate the

nverter nonlinearities to the ideal reference voltage componentsn stationary reference frame, a compensation signal is added. Theead time equal to 3 �s was compensated, and voltage command

Fig. 16. The block diagram of VFOC IPMSM drive system

d) Stat or resistance esti mati on err or.

sing MRAS technique under temperature effect.

values were used for v in the MRAS observer. An experimen-

dq

tal setup developed in our laboratory used for sensorless vectorcontrol of IPMSM drive based on MRAS technique is displayed inFig. 17.

with stator resistance and rotor speed observer.

12 A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15

the ex

7

iresrhsp

attspsTatnfoIoascraolrr

cu

Fig. 17. Picture of

. Experimental results

The model used for SVPWM sensorless VFOC for an IPMSM drives implemented using dSpace DS1103 and Matlab–Simulink envi-onment. The carrier frequency of SVPWM waveform used in thexperimentation is 14 KHz. In many industrial applications, thepeed overshoot response cannot be permitted (for example theolling mill drive), therefore the IP speed control is designed toave a critical damping (� = 1) [30,32]. For comparison betweenimulation and experimental results, we have used the same speedrofile.

In order to verify the effectiveness and the dynamic perform-nces of the proposed sensorless algorithm, many experimentalests have been carried out (Fig. 18). The result in Fig. 18 showshe performance of the MRAS observer tracking the rotationalpeed in all speed range. In Fig. 18(a), the performance of the pro-osed sensorless speed algorithm is again assessed by changing thepeed reference from 800 rpm to stand-still and then to −800 rpm.he motor accelerates to 800 rpm and the nominal load torque ispplied at time t = 4 s, after it is decelerated to zero speed. At time

= 12 s, the reference speed is changed from −800 rpm. Finally, theominal load torque is applied at time t = 14 s. The estimated speed

ollows the actual speed during the reversal and at zero speedperations showing the effectiveness of the proposed sensorlessPMSM drive. Error between the measured and estimated speedscillates around zero (Fig. 18(b)). Therefore, the performance of

sensorless control algorithm during speed transients and zeropeed is verified. These results confirm the choice of the IP speedontroller and confirm that there is no overshoot in the step speedesponse. Fig. 18(c) shows a good agreement between the measurednd estimated electrical rotor position and proves the agreementf the proposed method. These results show that MRAS sensor-ess vector control of IPMSM can accurately estimate the speed andotor position during the speed reversal and can meet the precision

equirements of the system.

In Fig. 18(d), the results show the position error under speedhanges with nominal load torque condition. The position errorsing the MRAS method with load condition is not bigger than

perimental setup.

0.5 elect.rad, during transients and about 0.08 elect.rad at steadystate. Position estimation using MRAS sensorless control is robustunder the transient step load torque change and reversal speed.

The experimental results presented in Fig. 18(e) shows themeasured electromagnetic torque. The bandwidth of the speedcontroller is usually below the bandwidth of the d − q axis statorcurrents controllers. Fig. 18(f) shows the experimental waveformsof estimated d-axis stator current and measured current stepresponse. We can observe that these currents show a low noisebut they are maintained to zero during all the experimental time.Fig. 18(g) shows that the estimated q-axis stator current is track-ing the measured one in both directions and varies proportionallywith the load torque. The switching ripple is not clearly seen inthe stator currents because we have used a low pass filter in thed − q axis currents. For the experimental results shown in Fig. 19,at 50 rpm (1.6% rated speed) and a load torque, Rs was chosento be equal to 7.1 , the torque is applied with 4 Nm at t = 7.5 s(Fig. 19(b)). The obtained experimental result at very low speeddemonstrates that even if we apply a load torque, the proposedobserver procedure still gives a good estimate of this parameter.The estimated stator resistance, as shown in Fig. 19(d), matchesthe actual stator resistance of the motor with a low error and sowe obtain a robust control performance. In Fig. 19(a), we can seethat the rotor speeds converge to the actual value (800 rpm). Therobustness of the adaptation algorithm to resistance change is con-sidered in Fig. 19. At t = 1.2 s the reference speed is set equal to 50and 800 rpm (Fig. 19(b) and Fig. 19(a)), Rs was chosen to be equal to7.1 and increased by 41% from its initial value at t = 4 s. To achievestator resistance variation, we have used in series with each phaseof the machine motor a resistance of value 3 . We start the drivesystems without adaptation of the stator resistance and then we usethe estimator at t = 2 s to adjust the stator resistance. It should benoted that we have considered the stator resistance to be constant.However, like stator resistance, also depends on temperature. It is

clear that an improvement of high performance sensorless speedcontrol requires tracking changes in stator resistance.

The increasing of the stator resistance agrees with an eventualheating of the stator winding (Fig. 19(c) and (d)). This experimental

A. Khlaief et al. / Electric Power Systems Research 108 (2014) 1– 15 13

Fig. 18. Experimental results with speed reference profile under 100% rated load torque.

1 er Syst

rpllc

rrstral

ts

4 A. Khlaief et al. / Electric Pow

esult shows that even if the stator resistance changes, the pro-osed method still gives a good estimate of this parameter. The full

oad current is used to study the robustness of the proposed sensor-ess control of IPMSM against stator resistance variation at nominalondition.

In Fig. 19(a) and (b) the two trajectories of estimated and realotor speed coincide fairly well and a very good coincidence iseached. As expected from Fig. 19(a) and (b), the operation of theystem is stable, although small oscillations appear due to the exci-ation of the lightly damped poles by the change in estimatedesistance. We can see that when a load step is applied (Fig. 19(c)nd (d)), the quadrature current iq is increased to compensate this

oad torque but the current id is maintained at zero.

Fig. 19(f) shows the experimental results and confirms that, dueo the accurate stator resistance estimation, the drive does not loosetability during temporary operation at very low speed.

Fig. 19. Stator resistance estimation scheme due to 41% increase in stator r

ems Research 108 (2014) 1– 15

These last experimental results show clearly the robustness ofthe proposed method even for an increasing stator resistance and inpresence of load torque. In both cases, the machine is operated withrated load condition, and it can be observed that the resistance esti-mator is satisfactory. Furthermore, the stator resistance Rs can beidentified within a short interval. In the analyzed sensorless-drivesystem with stator resistance estimation both speed, estimated andmeasured, are close to each other. Not only for the steady-stateoperation but also under speed reference and load torque changes,the speed estimation error tends to zero very fast. However, wenotice that the experimental results show an improved and robust-ness performance in the sensorless control of IPMSM with online

estimation of stator resistance. The comparison between the sim-ulations and experimental results shows a good agreement andconfirms the effectiveness of the proposed stator resistance esti-mation method for speed-sensorless IPMSM drive.

esistance at (c) 50 and (d) 800 rpm under 100% rated load condition.

r Syst

8

upsctcMrauwTishptttThutorfia

A

f

K

t

K

o

K

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

A. Khlaief et al. / Electric Powe

. Conclusion

The new speed estimator based on the MRAS technique, whichses the current-based model and stator-current estimator, haserformed very well in the wide range of the speed reference in theensorless VFOC drive system. The performance sensorless speedontrol of IMPSM drive based on MRAS observer with stator resis-ance estimation has been investigated in this paper. A sensorlessontrol for SVPWM inverter fed IPMSM drive is implemented usingRAS based adaptive speed estimation. A novel and simple online

esistance estimator has been proposed to compensate for the vari-tions in the stator resistance. The MRAS technique is simple and itses simplified expressions in the reference and adjustable modelsith a capability to reduce the mathematical computation time.

he sensorless control method with stator resistance estimations based on the error between measured and observed d − q axistator currents of IPMSM. The proposed sensorless speed controlas been experimentally validated using a dSpace DS1103 with aowerful processor. The experimental results are obtained both inransient step load torque and reversal speed conditions. Moreover,he measured and estimated rotor speeds are accurately trackingheir reference during speed transients and stand-still operation.he results clearly demonstrate the good performances and theigh dynamic behavior of the proposed IP speed controller. Sim-lation and experimental results has proved the effectiveness ofhe proposed sensorless control of IPMSM with online estimationf stator resistance. The drive system works well for very low speedeference with the nominal load torque. The stability analysis con-rms very good dynamics and robustness of the MRAS rotor speednd stator resistance estimator.

ppendix

The PI controllers of d and q-axis current are made up by theollowing parameters:

p id = 106.67[p.u.], Ki id = 2315.1[s], Kp iq = 127.83[p.u.]

and Ki iq = 2315.1[s].

The parameters of the integral and proportional (IP) speed con-roller are set as:

p W = 0.0541[p.u.] and Ki ˝ = 2.3868[s].

The PI controllers of stator resistance estimator and speedbserver are made up by the following parameters:

Rsi est = 180[s], KRsp est1[p.u.], Kiωr est10[s]

and Kpωr est = 60[p.u.].

eferences

[1] B. Singh, B.P. Singh, S. Dwivedi, A review of sensor reduction techniques inpermanent magnet synchronous motor drives, International Jornal of Powerand Energy Systems 29 (1) (2009) 10–18.

[2] F. Genduso, R. Miceli, C. Rando, G.R. Galluzzo, Back EMF sensorless-control algo-rithm for high-dynamic performance PMSM, IEEE Transactions on IndustrialElectronics 57 (6) (2010) 2092–2100.

[3] S. Morimoto, K. Kawamoto, M. Sanada, Y. Takeda, Sensorless control strategyfor salient-pole PMSM based on extended EMF in rotating reference frame, IEEETransactions on Industrial Applications 38 (4) (2002) 764–771.

[4] Y.H. Kim, Y.S. Kook, High performance IPMSM drives without rotational posi-

tion sensors using reduced-order EKF, IEEE Transactions on Energy Conversion14 (4) (1999) 868–873.

[5] S. Bolognani, M. Zigliotto, M. Zordan, Extended-range PMSM sensorless speeddrive based on stochastic filtering, IEEE Transactions on Power Electronics 26(1) (2001) 110–117.

[

[

ems Research 108 (2014) 1– 15 15

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