First International Power and Energy Coference PECon 2006November 28-29, 2006, Putrajaya, Malaysia

Simulation of MRAS-based Speed SensorlessEstimation of Induction Motor Drives using

MATLAB/SIMULINK

Ahmad Razani Haron, Nik Rumzi Nik Idris, IEEE Member

Abstract - Model Reference Adaptive System (MRAS) basedtechniques are one of the best methods to estimate the rotorspeed due to its performance and straightforward stabilityapproach. These techniques use two different models (thereference model and the adjustable model) which have madethe speed estimation a reliable scheme especially when themotor parameters are poorly known or having largevariations. The scheme uses the error vector from thecomparison of both models as the feedback for speedestimation. Depending on the type of tuning signal driving theadaptation mechanism, there could be a number of schemesavailable such as rotor flux based MRAS, back e.m.f basedMRAS, reactive power based MRAS and artificial neuralnetwork based MRAS. All these schemes have their own trendsand tradeoffs. In this paper, the performance of the rotor fluxbased MRAS (RF-MRAS) and back e.m.f based MRAS(BEMF-MRAS) for estimating the rotor speed was studied.Both schemes use the stator equation and rotor equation as thereference model and the adjustable model respectively. Theoutput error from both models is tuned using a PI controlleryielding the estimated rotor speed. The dynamic response ofthe RF-MRAS and BEMF-MRAS sensorless speed estimationis examined in order to evaluate the performance of eachscheme.

Index terms - BEMF-MRAS, MRAS, parameter variations, RF-MRAS, sensorless speed, tracking capability.

I. NOMENCLATURE

d- and q-axis stator and rotor currents in

the stationary reference frame.Stationary reference frame d- and q-axisstator voltages.Stator-, rotor- and magnetizing selfinductance.Stator resistance.Rotor time constant.Actual and estimated rotor speed.

ds 2s s

dr' YVsr d- and q-axis stator and rotor fluxlinkage in the stationary referenceframe.Total leakage reactance.Actual and estimated induced back

e.m.f in d- and q-axis.

II. INTRODUCTIONThe study of speed sensorless control of the IM has

undergone through maturing years when new techniquescame into introduction to improve the previous techniques.The motivation is to find one method that can cater theentire problem related to speed sensorless IM. Among them,

1-4244-0273-5/06/$20.00 (©2006 IEEE

MRAS based techniques have been proven to be one of thebest methods being proposed by the researchers due to itsgood high performance ability and straight-forward stabilityapproach [1].

The method was first proposed in [2] followed by [3]which consists of a reference model (RM), an adjustablemodel (AM) and an adaptation mechanism. RM isindependent of the rotor speed whereas AM requires therotor speed information. Through Landau' s idea ofcomparing the outputs ofRM and of AM, the error betweenthe two models can be minimized using the adaptationmechanism [4], as depicted in Fig. 1.

Various structures of MRAS can be realized dependingon the quantities that form the error vector. They are rotor-flux based MRAS, back e.m.f based MRAS, reactive powerbased MRAS and artificial intelligence based MRAS [5].Each of these schemes has their own trends and tradeoffs.

Fig. 1. Basic configuration of MRAS-based speed sensorless estimationscheme.

This paper studied the performance of the rotor-fluxbased MRAS (RF-MRAS) and back e.m.f based MRAS(BEMF-MRAS) for estimating the rotor speed. Thebehavior of the estimators prior to the IM parametervariations also has been studied.

II. MRAS ESTIMATORSThe study in this paper compares the performance of two

MRAS techniques, the RF-MRAS and BEMF-MRASestimator. Both schemes use the stator equation and rotorequation as the reference model and adjustable modelrespectively. The RF-MRAS estimator is constructed fromequations (la) - (Id) and the structure for this estimator isdepicted in Fig. 2. The tuning signal for RF-MRASestimator is the rotor-flux error vector which is fed to theadaptation mechanism to ensure that the system will bestable and the estimated quantity will converge to the ideal(actual) value.

411

lds , lqs, idr , lqr

Vds, Vqs

Ls Lr Lm

RsTrC4 )(r

e e

emd,emq,emd,emq

where dimd IdI

d+I s

Tr Tr(a) Reference Model:

qi=r (Vqs-Rsiqs )t-tLsJiqsJLM

Vdr = LM k(vd-R js dt- LsJds]

(la)

(lb)

where = ILs Lr

(b) Adjustable Model:

d qr

dt T- VQr + WOrVdr+ s

Tr Tr~.s

dt T Vdr LrVqr + dsdt Tr Tr

(Ic)

(Id)

dimqI . I i I i

dt rrmdT mq +Tr"dt T~r Tr

Vd,

Fig. 2. Block diagram of RF-MRAS scheme.

For the BEMF-MRAS estimator, it is constructed usinginduced back e.m.f as given by equations (2a) - (2d). Thestructure is realized in Fig. 3. The distinct feature of BEMF-MRAS from RF-MRAS estimator is the elimination of pureintegration both in the RM and AM.

(a) Reference Model:

emd = Vds s ids sdis

dt )

(2a)

(2b)emq =qs - jiqs +s dtj

Fig. 3. Block diagram of BEMF-MRAS scheme.

III. ADAPTATION MECHANISMThe most important part of the estimation process is the

designs of the adaptation mechanism which at the end willdetermine whether the system is stable or not. Therefore, theestimated quantity will converge to the actual value withsuitable dynamics characteristics.

As described by Landau [4], the practical synthesistechnique for MRAS structures which is based on theconcept of hyper-stability can be used to design theadaptation mechanism. These rules will ensure that the stateerror equations of the MRAS structures are globallyasymptotically stable. However, this method does notestablish the dynamics of the convergence process which inturn, analysis of the system equations, linearized about a

selected operating point is required.In this paper, the detail of the adaptation mechanism

design is not elaborated since it has been clearly discussedin [3] and [6]. Therefore, the design of the adaptationmechanism for RF-MRAS and BEMF-MRAS estimatorshas yielded the estimated rotor speed as given by equations(3) and (4) respectively.

I) K +K

(r p )I dndi

Or = (Kp + s)em (S em )

(3)

(4)

(b) Adjustable Model:

emd = L (_r mc- i + iI s )

Tr

(2c)

(2d)mq L irinmd +qT qs )L r

IV. SIMULATION RESULTSThe simulations have been carried out using

MATLAB/Simulink platform and the estimators were

implemented in the direct torque control IM drive. Theparameters of the IM are given in Table 1.

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TABLE 1

INDUCTION MOTOR'S PARAMETERS FOR SIMULATION

Parameter ValueStator Resistance (Q) 5.5Rotor Resistance (Q) 4.51Stator Self Inductance (H) 0.3065Rotor Self Inductance (H) 0.3065Mutual Inductance (H) 0.2919Moment of Inertia (kgm2) 0.03Load Torque (Nm) 1No. of Poles 4Rated Speed (rpm) 1410

The performance of the estimators has been studied interms of its ability to converge to the actual speed and theresponse of the estimators towards parameters changes.Thus, to fit that purpose, the values of parameter in the IMare kept unchanged while the values of the estimators arevaried from its rated value.

Fig. 4 shows the speed response of the RF-MRAS speedestimator when the IM is operated at different referencespeeds. It shows that the estimated speed tracks the actualspeed reasonably well at high speed and even at low speed.But, as the speed decreased, the steady state values of theestimated speed tend to deviate from actual speed. Thisdeviation is caused mostly by the error in the statorresistance Rs [2].

As a result, the speed estimation below reference speedof 20rad/s is not applicable and generalization of the resultsapplied only for this range of speeds.

Weeid Response

(a)

0 m Om FIS D -32 3 am 0 a4D Us

(b)

(c)

X agD S a I 11 a 2 D:M .3 a 3 S a 45 D

(d)

Fig. 4. RF-MRAS estimator's tracking performance at reference speed(a) 100rad/s, (b) 70rad/s and (c) 50rad/s (d) 30rad/s.

In addition to its well tracking performance, the effectof parameter variations at high speed is quite negligible butas the frequency decrease, for stator resistance, the termRsi/p becomes relatively large and therefore the values ofstator resistance will seriously affect the estimated speed.This situation is depicted in Fig. 5.

The effect of rotor resistance and moment of inertiavariations also being studied but the changes is notsignificant since no direct relationships establish betweenthese parameters with rotor speed as given in equations (la)

(2d).In the case of BEMF-MRAS estimator, it shows an

improvement in terms of speed tracking performance andeffect of parameter variations as compared to the RF-MRAS. The good tracking capability as depicted in Fig. 6 isdue to the elimination of the pure integration process in thereference model as shown in the equation (2a) - (2d).

This estimator also has less parameter dependentcompared to its predecessor. In Fig. 6, prior to four differentreference speeds, it shows that the estimator has better speedtracking response at high and even at low speed.

BEMF-MRAS estimator shows an outstandingperformance over incorrect setting of parameter values(especially stator resistance value, Rs) even as large as 100%deviations from the rated value.

The BEMF-MRAS estimator's response at different R,values is depicted in Fig. 7. In this figure, it shows that thisscheme is completely robust to parameters variations sinceno significant changes in estimated speed can be noted priorto the variations.

0 0.2 0.4 0.6 O.S 1 1.2 1.4 1.6 1.8 2

time (s)

(a)

Effect of Stator Resistance Variation

_ pffAfS ~~~~~-a4tual4 i ~~~~~~~~~-eslimated

.7/ \2 ~~~~~~~~~~-speeci error_-

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2time (s)

(b)

Effect of Stator Resistance Variation

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2time (s)

(c)

Effect of Stator Resistance Variation

estimated

10 spe errIorI,.

0 0. 0. 0. 0. 1 1. 1. 1. 1. 2

time (s)

(d)

Fig. 5. Effect of incorrect setting of RS values to the RF-MRAS estimator'sspeed response. (a) Rs (b) Rsnew = 1.1 Rs (C) Rsnew = 1.5 Rs (d) Rsnew = 2 RS.

Effect of Rotor Resistance Variation

- actual"If - estimated4 'b ~~~~~~~~~-speed error_

414

Speed Responser r l r r r ~ ~

-a4ual

=- eastimrated

0 0.05 0.1 0.1 5 0.2 0.25 0.3 0.35 0.4 0.45 0.5time (s)

(a)

Sopeed Response

0.05 0.1 0.1 5 0.2 0.25 0.3 0.35 0.4 0.45 0

time (s)

(b)

Sopeed Response

- eslimated

40

-1 00 0.05 0.1 0.1 5 0.2 0.25 0.3 0.35 0.4 0.45 O.E

time (s)

(C)

Speed Response35

-a4ual- eslimated I. f

25 ,, _

10 _

,Y-5 _

I1

f/2 -~~~~~~~~~~~~~esftimated_ fff \ - ~~~~~~~~~~~~~speed error__ ,r i~~~~~~~~~~~

KJ zuv1X\

0 0.05 0.1 0.1 5 0.2 0.25 0.3

time (s)

(d)

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Fig. 6. BEMF-MRAS estimator's tracking performance at reference speed(a) 100rad/s, (b) 70rad/s and (c) 50rad/s (d) 30rad/s.

415

Speed Response

< X ~~~~~~~~- actual_

0 0.2 0.4 0.6 08 1.2 1.4 1.6 1.8 2timne (s)

(a)

Effect of Stator Resistance Variation

- actual _~~~~ / =~~~~~~~~ esrtimated_o 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2

timne (s)

(b)

Effect of Stator Resistance Variation8~~~~~~~~~~~~~ actual/ ~~~~~~~~~-estimated

_~~~~~~~~~~~~-error

0 0. 0. .6 12 14

8~~~~~~~~~tm (s

I ;~~~~~c

o 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2

time (s)

(d)

V. CONCLUSIONPerformance of RF-MRAS and BEMF-MRAS

estimators based on the tracking capability and parametersensitivity was presented. The result shows that the BEMF-MRAS estimator is more superior to the RF-MRASestimator at that particular defined range of referencespeeds. This is prior to the elimination of pure integratorsused in the RF-MRAS scheme. However, the BEMF-MRASestimator is more difficult to design due to the non-lineareffect of the adaptation gain constants.

Therefore, as a whole, considering all the key criteria ofcomparison, it can be concluded that the BEMF-MRASscheme embrace the requirement as a versatile estimator. Itdemonstrate good tracking capability and superb ininsensitivity to parameter variations.

VI. REFERENCES[1] M. Ta-Cao, Y. Hori and T. Uchida, "MRAS-based speed sensorless

control for induction motor drives using instantaneous reactivepower", IEEE-IES Conference Record, pp. 1717-1422. 2001.

[2] S. Tamai, H. Sugimoto, M. Yano, "Speed-sensorless vector control ofinduction motor with model reference adaptive system", Conf. Recordof the 1985 IEEE-IAS Annual Meeting, pp. 613-620, 1985.

[3] C. Shauder, "Adaptive speed identification for vector control ofinduction motor without rotational transducers", IEEE Trans. Ind.Application, Vol. 28, No. 5, pp. 1054-1061, Sept./Oct. 1992.

[4] Y.P. Landau, "Adaptive Control: The model reference approach",Marcel Dekker, New York, 1979.

[5] M.N. Marwali, A. Kehyani, "A comparative study of rotor flux basedMRAS and back e.m.f based MRAS speed estimators for speedsensorless vector control of induction machine", IEEE-IAS AnnualMeeting, New Orleans, Louisiana, pp. 160-166, 1997.

Fig. 7. Effect of incorrect setting of Rs values to the BEMF-MRASestimator's speed response. (a) Rs (b) Rs,ew = 1.1 Rs (c) Rs,ew = 1.5 Rs(d) Rs,ew = 2 Rs.

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