A1_MRAS

532 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 2, APRIL 2005

An MRAS-Based Sensorless High-PerformanceInduction Motor Drive With a Predictive

Adaptive ModelMaurizio Cirrincione, Member, IEEE, and Marcello Pucci, Member, IEEE

Abstract—This paper presents a new model reference adaptivesystem (MRAS) speed observer for high-performance field-ori-ented control induction motor drives based on adaptive linearneural networks. It is an evolution and an improvement of anMRAS observer presented in the literature. This new MRASspeed observer uses the current model as an adaptive modeldiscretized with the modified Euler integration method. A linearneural network has been then designed and trained online bymeans of an ordinary least-squares (OLS) algorithm, differentlyfrom that in the literature which employs a nonlinear backprop-agation network (BPN) algorithm. Moreover, the neural adaptivemodel is employed here in prediction mode, and not in simulationmode, as is usually the case in the literature, with a consequentquicker convergence of the speed estimation, no need of filteringthe estimated speed, higher bandwidth of the speed loop, lowerestimation errors both in transient and steady-state operation,better behavior in zero-speed operation at no load, and stablebehavior in field weakening. A theoretical analysis of some sta-bility issues of the proposed observer has also been developed. TheOLS MRAS observer has been verified in numerical simulationand experimentally, and in comparison with the BPN MRAS onepresented in the literature.

Index Terms—Artificial neural networks (ANNs), electricaldrives, field-oriented control (FOC), induction motor, leastsquares, model adaptive reference systems (MRASs), sensorlessdrives.

LIST OF SYMBOLS

Space vector of the stator voltages in the stator ref-erence frame.Direct and quadrature components of the stator volt-ages in the stator reference frame.Space vector of the stator currents in the stator ref-erence frame.Direct and quadrature components of the stator cur-rents in the stator reference frame.Direct and quadrature components of the stator cur-rents in the rotor-flux oriented reference frame.Space vector of the stator flux-linkages in the statorreference frame.Direct and quadrature component of the stator fluxlinkage in the stator reference frame.

Manuscript received May 9, 2003; revised September 9, 2004. Abstract pub-lished on the Internet January 13, 2005.

The authors are with the Section of Palermo, Istituto di Studi sui Sistemi In-telligenti per l’Automazione (I.S.S.I.A.-C.N.R.), 90128 Palermo, Italy (e-mail:[email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2005.844247

Space vector of the rotor flux-linkages in the statorreference frame.Direct and quadrature component of the rotor fluxlinkage in the stator reference frame.stator inductance.Rotor inductance.Total static magnetizing inductance.Resistance of a stator phase winding.Resistance of a rotor phase winding.

Transient time constant of the machine.Stator time constant.Rotor time constant.

Total leakage factor.Number of pole pairs.Angular rotor speed (in mechanical angles).Angular rotor speed (in electrical angles persecond).Sampling time of the control system.

I. INTRODUCTION

OVER THE LAST few years many attempts have beenmade to compute the speed signal of induction machines

for reliable high-performance vector and direct torque-con-trolled drives. In this respect, the literature is very rich anddates back from [2] through many other classical works suchas [2]–[24].

References [7] and [8] describe in detail all recent and mostwidespread solutions, most of which depend, however, on themachine parameters, which are variable because of temper-ature, saturation levels, frequency, and so on. In general, theparameter mismatch as well as the noise in the input signals ofthe flux model cause the conventional speed estimation tech-niques to fail in very-low-speed operation in a speed-sensorlesshigh-performance induction motor drive. Therefore, severalother techniques have been developed, such as open-loop esti-mators using improved schemes [4]–[6], [8], estimators usingeither saliency effects or spatial saturation stator third har-monic voltage [4]–[6], [8], model reference adaptive systems(MRASs) [1], [9], [15]–[17], adaptive observers [12]–[14] andthose estimators using artificial intelligence [18], [19], [21],[22], in particular, neural networks and fuzzy logic systems.These last two techniques seem to be among the simplest andmost powerful [1]–[3], in particular, when working together[8], [15]–[17], [20]. Remarkable works have been publishedin application both to field-oriented control (FOC) and direct

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CIRRINCIONE AND PUCCI: MRAS-BASED SENSORLESS HIGH-PERFORMANCE INDUCTION MOTOR 533

torque control (DTC) [9]–[11], [20], [23] induction motordrives.

References [4]–[6] propose an open-loop speed estimatorbased on the stator and rotor voltage equations of the induc-tion machine in the stator reference frame and apply it to astator-flux-oriented vector-controlled induction motor drive.In particular, it proposes a new methodology which eliminatesthe dc drift problem due to open-loop integration typical ofopen-loop flux estimators and a new stator resistance onlineestimation algorithm.

Reference [23] applies an MRAS closed-loop flux observer(CLFO) based on a proportional–integral (PI)-controller-basedminimization of the cross product between the rotor fluxes, esti-mated, respectively, by the voltage model and the current model.In this observer, which is an evolution of [24], the closed-looptopology provides the necessary feedback for the voltage modelintegration, so that in the voltage model a low-pass (LP) filter isnot required to cancel the dc drift, differently from [1]. However,this causes a bad behavior of the observer at low speeds: in fact,as clearly written in [23], on the one hand the current model hasno dc constant output and, therefore, the flux-coupling PI con-troller ensures zero dc level at the output. On the other hand, asfrequency approaches zero, the cross product also approacheszero and speed estimate forcing is lost. A mechanical model ofthe machine for compensating this aspect is then to be used atthe expense, however, of an increase in the complexity of theobserver. Moreover, this observer requires two coordinate trans-formations and the flux estimation is dependant on the speed es-timation, differently from [1]. In the end, the lowest limit of thisobserver is not shown explicitly.

Reference [9] applies an MRAS speed estimator both to aclassical DTC and to a DTC space-vector modulation (SVM).In particular, the MRAS speed estimator structure is the same asin [1] which is based on the PI-based minimization of the crossproduct between the rotor fluxes estimated, respectively, by thereference and the adaptive models. However, differently from[1], the reference model is not a simple voltage model estimator,but a full-order stator and rotor flux observer, containing boththe voltage and the current models, while the adaptive model issimply the current model. Thus, this speed estimator employsthe current model twice, firstly in the reference model (in therotor flux oriented reference frame) and secondly in the adaptivemodel (in the stator reference frame). Also here the referencemodel requires two coordinate transformations. The limit of thisspeed estimator, as presented in those papers, is 30 r/min butonly the estimated speed is shown at that reference speed, whileno corresponding measured speed, no speed estimation error,and no zero-speed operation are shown.

References [10] and [11] apply an open-loop speed estimatorrespectively to a classical DTC and a DTC-SVM and to a DTCsliding mode (SM). In both articles the speed is open-loop esti-mated on the basis of the difference between the angular speedof the rotor flux linkage and the angular slip speed. In partic-ular, [10] presents a full-order stator and rotor flux observer,which contains both the voltage and the current models andis practically an evolution of [9]: the lowest presented speedlimit of this estimator is 30 r/min by correctly showing boththe estimated and measured speed at that speed reference; how-

ever, zero-speed operation is not shown. Also, [11] presents afull-order stator and rotor flux observer, which contains both thevoltage and the current models and is also an evolution of [9]but which is based on the sliding-mode techniques: the lowestspeed limit of this estimator is not explicitly shown, while onlyzero-speed operation at rated load is shown; zero-speed opera-tion at no load is not shown.

In particular, [15]–[17] present an MRAS speed observerwhich is an evolution of [1] and minimizes the error betweenrotor fluxes estimated respectively with a reference and anadaptive flux model, and then they apply it to an FOC. Like in[1] it employs, as a reference model, the voltage model of theinduction machine and the open-loop integration is performedby an LP filter. However, it uses the adaptive model, by rear-ranging the rotor equations of the machine so that a multilayerperceptron can be employed. On this basis, these articles ex-ploit the classical backpropagation network (BPN) algorithmfor the online training of the neural network to estimate therotor speed. In [17] the observer is verified also experimentally,even if neither the lowest speed limit of the observer nor thezero-speed operation, at no load and at load, are presented.

This paper proposes an improvement of the MRAS artifi-cial-neural-network (ANN)-based speed observer presented in[17], for basically two reasons. First it does not use the BPNneural network but an ADaptive LInear neural NEtwork (ADA-LINE), since the problem to be solved is linear: it is in factquestionable to use a nonlinear method like the BPN algorithmwhich causes local minima, paralysis of the neural network,need of two heuristically chosen parameters, initialization prob-lems, and convergence problems. In [17] this linearity problemhas been recognized, but the minimization has been performedwith a gradient-descent dependent also from the momentum,which is not necessary.

Second, the adaptive model in [17] is used in simulationmode, which means that its outputs are fed back recursively.In this paper, in contrast to this, a modified adaptive modelis used as a predictor, without feedbacks, no need of filteringthe estimated signal, and resulting in higher accuracy both intransient and steady-state operation. Moreover, differently from[17], a stable behavior in field weakening is achieved, which isnot the case of the adaptive model used in simulation mode, asdemonstrated also theoretically in the paper. In this paper theBPN algorithm presented in [17] is compared experimentallyto the presented speed observer and the improvements achievedwith the MRAS OLS observer are emphasized.

II. SENSORLESS FOC DRIVE

The MRAS ANN-based speed observer has been imple-mented experimentally in an FOC induction motor drive.

In particular, a “voltage” direct rotor-flux-oriented vectorcontrol has been implemented in which current control isperformed at the field reference frame level [8]. Fig. 1 showsthe block diagram of the FOC sensorless induction motordrive, as implemented for the experimental verification. Thecontrol system has five control loops, three on the direct axisand two on the quadrature axis. All the loops of the controlsystem (current, flux, voltage, and speed) are performed at the


Fig. 1. Block diagram of the FOC algorithm.

sampling frequency kHz. The rotor flux linkage andthe rotor speed are controlled by closed loops. Speed control isachieved by employing a PI controller for processing the speederror resulting from the comparison between the reference andthe speed estimated by the “MRAS ANN Speed Observer”block (described in detail in Section III). The feedback on

determines the secondary loop in which in which a PIcontroller processes the current error. On the direct axis thevoltage is controlled at a constant value to make the driveautomatically work in the field weakening region. Inside the

loop are respectively the rotor flux-linkage loop and theloop. The rotor flux linkage is controlled by employing aPI controller, processing the flux error between the referenceflux and that estimated by the above mentioned block. Theblock “vector modulation” performs the modulation of thevoltage-source inverter (VSI). In particular, the VSI is drivenby an asynchronous SVM algorithm with a switching frequency

kHz. This frequency has been selected as much ashalf the sampling frequency of all acquired signals to limit theripple on the stator current. The implemented SVM algorithmpermits the generation of any voltage vector inside the “inverterhexagon” and, therefore, the full exploitation of the dc-linkvoltage capability.

In particular, in a modulation period , each commandsignal to the upper devices of the three legs of the inverter musthave the following time length:

(1)

with

(2)

where is the duration of the signal command to the upperdevice of the inverter connected to the phase in a modulationperiod is the reference voltage onthe phase , and is the dc-link voltage of the inverter. Inthe experimental application, a protection time of 2 s has beenset and an algorithm which compensates the protection time hasbeen adopted.

III. MRAS ANN-BASED SPEED OBSERVER

In the MRAS speed observation scheme proposed here thereference model is based on the well-known stator equations ofthe induction motor [8], while the adaptive model is a linearANN.

In particular, the reference model is described by the fol-lowing voltage stator equations (voltage model) of the inductionmotor in the stator reference frame:

(3)

For explanation of the symbols, see the List of Symbols at thebeginning of the paper. The voltage model employs, to performopen-loop integration, LP filters with a low cutoff frequencyinstead of pure integrators.

The adaptive model is based on the well-known voltage rotorequations (current model) in the stator reference frame

(4)

Equation (4) can also be written in the following manner:

(5)where


(a)

(b)

Fig. 2. (a) Block diagram of the ANN MRAS BPN observer (adaptive model in simulation mode). (b) Block diagram of the ANN MRAS observer (adaptivemodel in prediction mode).

Its corresponding discrete model is, therefore, given by

(6)

is generally computed by truncating its power series ex-pansion, i.e.,

(7)

if , the simple forward Euler method is obtained, whichgives the following finite-difference equation:

(8)

where marks the variables estimated with the adaptive modeland is the current time sample. A neural network can repro-duce these equations, where are the weights of theneural networks defined as:

is the sampling time of the control system,


Fig. 2. (Continued.) (c) Block diagram of the ANN MRAS observer with modified Euler adaptive model (adaptive model in prediction mode).

is the three-phase magnetizing inductance of the motor, isrotor time constant, and is the rotor speed in electrical an-gles. The ANN has, thus, four inputs and two outputs [15]–[17].In the ANN, the weights and are kept constant to theirvalues computed offline while only is adopted online. Theseequations are the same as those obtained in [17], and the corre-sponding MRAS-based speed estimation scheme is representedin Fig. 2(a).

It is clear from Fig. 2(a) that the adaptive model is character-ized by the feedback of delayed estimated rotor flux com-ponents to the input of the neural network, which means thatthe adaptive model employed in [17] is in simulation mode [25].Moreover, in [17] the adaptive model is tuned online (training)by means of a BPN algorithm, which is, however, nonlinear in itsnature with the consequent drawbacks (local minima, heuristicsin the choice of the network parameters, paralysis, convergenceproblems, and so on).

On the contrary, in this paper the adaptive model employsan ADALINE and, differently from [17], the values of the rotorflux-linkage components at the input of the ANN come from thereference model, and not from the adaptive one; this means thatthe ANN is employed in prediction and not in simulation mode[25].

The reasons why a linear least-square algorithm is moresuitable than a nonlinear one, such as the BPN, have beenalready highlighted. Furthermore, the employment of the adap-tive model as a “predictor” instead of a “simulator” leads toa quicker convergence of the algorithm, a higher bandwidthof the speed control loop, a better behavior at zero speed,lower speed estimation errors both in transient and steady-stateconditions and to a far more stable behavior of the estimator,

in particular, in the field-weakening region, as it will be clearlyexplained in Sections IV and V. In this respect, two schemescan be proposed. The first is derived from (4) by simply Eulerintegration, and the second by modified Euler integration.These are shown in the following.

A. Euler Integration

Equation (8) can be written in the following matrix form,taking into consideration the employment of the adaptive modelas a predictor:

(9)

This is a classical matrix equation of the type ,where is called a “data matrix,” is called an“observation vector,” and is the scalar unknown,solvable by means of any least-squares techniqueordinary least squares OLS data ordinary least squares

DLS total ordinary least squares . In this application aclassical OLS algorithm in a recursive form has been employed;see [26] for a detailed description of the adopted algorithm.Fig. 2(b) shows the block diagram of the corresponding MRASOLS speed observer.

B. Modified Euler Integration

A more efficient integration method is given by the so-calledmodified Euler integration, which also takes into consid-eration the values of the variables in two previous timesteps [26]. From (4) discrete-time equations (10) can be


obtained, as shown at the bottom of the page. Also in thiscase, a neural network can reproduce these equations, where

are the weights of the neuralnetworks defined as:

.From (10), matrix equation (11) is obtained in prediction

mode, as shown at the bottom of the page. Fig. 2(c) shows theblock diagram of the corresponding MRAS speed observer.Because of its better numerical efficiency (see Section IV),this scheme will be adopted for the experimental phase in thefollowing.

IV. SIMULATION MODE AND PREDICTION MODE: MODIFIED

EULER AGAINST SIMPLE EULER

Some considerations should be made, however, on the use ofthe simulation mode to fully justify the use of the adaptive modelin prediction mode. This section will also show that, even in sim-ulation mode, the modified Euler integration tuned with the OLSmethod gives better performance in comparison with the resultsobtainable by using the simple Euler integration method trainedeither by the OLS or by the BPN. First, it will be shown that, byusing the simple Euler method in prediction mode, better resultsare obtainable as far as stability is concerned than by using thesame Euler integration trained by a BPN in simulation mode.Then, the improvement achieved by using the modified Eulerintegration is shown.

The adaptive model can be used either as a simulator or asa predictor. When used as a simulator, the process output, thatis, the rotor flux linkage, is delayed and then used as an input.In case the simple Euler integration method is used, the corre-sponding simulator model is described as follows:

(12)

where is the rotor linkage flux estimated by the adaptivemodel.

This means that the transfer function in the domainis

(13)

where stands for transform which has one pole, and one zero at the origin of the domain. For stability

reasons, the poles of the transfer function must lie within the unitcircle in the domain. However, it should be noted that, whilethe real part of the pole is constant and less than one, because

, its imaginary part depends on the rotor speed .This means that there is a critical value of the rotor speed whichcauses instability of the system. More precisely, the followingrelationship must be satisfied:

(14)

By solving for this inequality and recalling the meaning of ,it results that

(15)

This relationship shows that the drive goes into instability forincreasing values of the rotor speed. From (14), it also resultsthat

that is, the sampling time has an upper limit for stability if themotor runs at a defined angular speed.

For instance, for the motor at hand whose rated speed is 314electrical rad/s and s, this upper limit for the sam-pling time is 0.15 ms. Conversely, (15) shows that if a samplingtime of 0.1 ms is employed, which is the case under study, thehighest limit of the speed is 385 electrical rad/s (Fig. 3(a) upperfigure), which implies that the speed can be increased to as muchas 18% of the rated speed and not over this limit, with resultingdifficulties in using the drive in the field-weakening region.

To overcome this difficulty the adaptive model should be usedas a predictor, that is, the delayed outputs of the reference modelare used as inputs to the adaptive model. In this case, no feed-back exists and no stability problems occur. The predictor modelis then described as follows:

where is the delayed output of the reference model,that is, the rotor flux linkage estimated by the reference flux.

The simple Euler method was obtained by using in (7).Better stability results can be obtained if is chosen in (7).

(10)

(11)


(a)

(b)

Fig. 3. (a) Amplitude of the poles in simple Euler integration with theapproximated exponential function with n = 1 and n = 2. (b) Amplitude ofthe poles with the modified Euler integration.

Then, the speed stability limit increases as shown in Fig. 3(a),bottom figure. This approximation has been at least used in [17]to avoid the stability problems in simulation mode. It shouldbe emphasized that this last method implies at least the onlinecomputation of the square of the matrix, which makes thismethod too cumbersome for online applications.

Better results, at the expense of a slight increase of com-putation in comparison with the simple Euler method, can beobtained with the modified Euler method [26]. In this case, asimilar analysis of stability shows that two poles of the transferfunction vary with speed, but the resulting speed stability limitis much higher than that obtained with the simple Euler method,thus allowing the exploitment of the field-weakening region[Fig. 3(b)].

Moreover, the use of the modified Euler integration causes astrong increase in the accuracy of the computation of the rotorflux magnitude at rotor speeds different from zero. Fig. 4 showsthe amplitude of the real rotor flux as well as the rotor flux es-timated with the simple Euler integration and with the modi-fied Euler integration when the machine is first magnetized andthen is given a speed reference of 100 rad/s. In this numerical

Fig. 4. Rotor flux amplitude estimation with the current model integrated withthe Euler and modified Euler methods (simulation test with current model usedin simulation mode).

simulation, the actual speed has been used in the flux model,so the mismatch between the estimation with the two methodsis caused only by the discretization methods. The simple Eulercauses a substantial error at steady state (as much as 40%). Thisproblem can be avoided either by using a simple Euler integra-tion in prediction mode or by using a modified Euler integrationeither in simulation or in prediction mode. In this last case, how-ever, the use of the prediction mode results in better accuracy inrotor flux estimation, and higher speed-loop bandwidth and abetter performance at zero speed as shown in the experimentalresults in Section VI.

V. DESCRIPTION OF THE TEST SETUP

The OLS MRAS ANN-based speed observer has been testedin simulation and experimentally on a suitable test setup. Thetest setup consists of the following [35]:

• three-phase induction motor with rated values shown inTable I;

• dc machine for loading the induction machine with ratedvalues shown in Table II;

• electronic power converter: three-phase diode rectifierand VSI composed of three IGBT modules without anycontrol system, of rated power 7.5 kVA;

• electronic ac–dc converter for supplying the dc machine;• electronic card with voltage sensors (model LEM LV

25-P) and current sensors (model LEM LA 55-P) formonitoring the instantaneous values of the stator phasevoltages and currents;

• voltage sensor (model LEM CV3-1000) for monitoringthe instantaneous value of the dc-link voltage;

• incremental encoder (model RS 256-499, 2500 pulses perround), only for comparison measurements;

• dSPACE card (model DS1103) with a PowerPC 604e at400 MHz and a floating-point digital signal processor(DSP) TMS320F240.

Fig. 5 shows the schematics of the test bench.


TABLE IPARAMETERS OF THE INDUCTION MOTOR

Fig. 5. Block diagram of the test setup.

TABLE IIPARAMETERS OF THE DC MACHINE

VI. EXPERIMENTAL RESULTS

The MRAS ANN-based observer has been verified numeri-cally in simulation and applied experimentally to the test benchdescribed in Section V. Simulations have been performed in theMatlab-Simulink environment. With regard to the experimentaltests the speed observer as well as the whole control algorithmhave been implemented by software on the DSP of the dSPACEboard by employing the Matlab-Simulink Real Time Workshop-Real Time Interface environment. A suitable virtual instrumenthas also been properly developed to manage the drive and mon-itor all the electrical and mechanical signals of the motor online,e.g., the rotor speed, the dc-link voltage and the stator voltagesand currents. In particular, the speed observer has been testedin both the FOC schemes described in Fig. 2(a) and (c) to makecomparisons with the algorithm in [17]. For control purposes,the estimated speed has been fed back and instantaneously com-pared with the measured one to compute the speed error at each

instant and in each working condition. The phase voltages havebeen computed on the basis of the instantaneous measurementof the dc-link voltage and the switching state of the inverter [8].An algorithm which compensates the dead time of the inverterhas been adopted. Finally, the sampling frequency of the signalshas been set to 10 kHz.

Tests have been performed to verify the goodness of theproposed OLS MRAS speed observer and each test has beencompared with the BPN MRAS observer of [17]; then, theimprovements achieved with the OLS MRAS speed observer inthe different working conditions are presented and discussed.

1) Experimental Test 1: Stability Behavior in Field-Weak-ening: As explained in Section V, if the adaptive model issimply discretized with the forward simple Euler method andused in simulation mode, that is, (8) is used; the MRAS BPNobserver has an unstable behavior above a certain thresholdspeed which depends on the sampling time of the controlsystem. In the system under study, with a sampling time of10 s, this threshold speed is 192 rad/s in mechanical angles.In [17], to overcome this problem, an approximated adaptivemodel is used with (see Sections III and IV), which,however, increases the maximum speed at which the observerhas a stable behavior at the expense of higher computationalburden. Fig. 6 shows the reference, the real, and the estimatedspeeds, obtained in numerical simulation, with the MRASBPN observer where the adaptive model is the current modediscretized with the simple forward Euler method and used in


Fig. 6. Estimated and measured speed in field weakening, BPN MRASobserver with the discrete Euler current model (simulation).

(a)

(b)

Fig. 7. (a) Estimated and measured speed in field weakening, BPN MRASobserver with the approximate current model and � = 0:003 (simulation).(b) Estimated and measured speed in field weakening, BPN MRAS observerwith the approximate current model and � = 0:0008 (simulation).

simulation mode, during two speed step references, respec-tively, at 100 and 200 rad/s. It clearly shows that, when the

Fig. 8. Estimated and measured speed and speed error during a speed reversalin field weakening, OLS MRAS observer (experiment).

Fig. 9. Rotor flux and i during the speed reversal in field weakening, OLSMRAS observer (experiment).

Fig. 10. Measured and estimated speed before and after filtering during a stepreference of 100 rad/s, BPN MRAS observer (experiment).

speed reaches about 200 rad/s, the drive becomes unstable,as expected. The same test has also been done in numericalsimulation by employing the MRAS BPN observer, with the


(a)

(b)

Fig. 11. (a) Estimated and measured speed and speed error during a speed reversal from 100 to �100 rad/s, OLS MRAS observer (experiment). (b) Estimatedand measured speed and speed error during a speed reversal from 100 to �100 rad/s, BPN MRAS observer (experiment).

approximated adaptive model ( ) of [17] in simulationmode. Fig. 7(a) and (b) shows the reference, the real and theestimated speeds during two speed step references, respectively,at 100 and 200 rad/s, obtained with two different values of the

learning rate of the BPN neural network. These graphs clearlyshow that with higher values of , the drive at 200 rad/s tendsto approach instability with a large estimation error and withenormous oscillations of the estimated speed. On the contrary,


(a)

(b)

Fig. 12. (a) Estimated and measured speed and speed error during a speed reversal from 50 to�50 rad/s, OLS MRAS observer (experiment). (b) Estimated andmeasured speed and speed error during a speed reversal from 50 to �50 rad/s, BPN MRAS observer (experiment).

with lower values of , the estimation is almost correct downto 200 rad/s, while the estimated speed is far from the real onebelow the rated speed (at 100 rad/s), because of the slow con-vergence of the algorithm. It should be noted again, however,

that this better stability behavior in field weakening, obtainedwith the approximated adaptive model, is traded off with ahigher computation burden required by the adaptive modelitself, because of the need of transcendent sin/cos functions.


(a)

(b)

Fig. 13. (a) Estimated and measured speed and speed error during a speed reversal from 10 to�10 rad/s, OLS MRAS observer (experiment). (b) Estimated andmeasured speed and speed error during a speed reversal from 10 to �10 rad/s, BPN MRAS observer (experiment).

On the contrary, by adopting the MRAS OLS observer withthe adaptive model employed in prediction mode with themodified Euler integration, no instability phenomena occur infield weakening, as shown in the following experimental tests.

In these tests, the drive has been given a speed reference of200 rad/s, then a speed reversal from 200 to 200 rad/s in thefield-weakening region, and, finally, a step reference of 0 rad/sat no load. Fig. 8 shows the estimated and measured speeds and


TABLE IIIDYNAMIC PERFORMANCE: OLS MRAS VERSUS BPN MRAS

the speed error while Fig. 9 shows the rotor flux linkage and thecurrent during this test. They show that the speed reversal

in the field-weakening region is accomplished in 1 s, that themaximum instantaneous speed estimation error is 25 rad/s, andthat the torque response is practically instantaneous. Moreover,these figures show that the MRAS OLS observer with modifiedEuler in prediction mode works correctly in field weakening,without any instability phenomena, differently from the MRASBPN observer, no matter whether the approximated adaptivemodel with or is adopted in simulation mode.

2) Experimental Test 2: Dynamic Performance: For com-parison purposes, a set of speed reversals has been performedboth with the OLS MRAS and with the BPN MRAS observer.In this respect, it should be remarked that, since in the BPNMRAS observer (as in [17]) the adaptive model is employedin simulation mode, the speed estimation convergence is slowerthan that obtained with the OLS MRAS observer in predictionmode. In addition, the estimated speed is highly affected byripple and cannot be directly fed to the control system withoutany filtering. This is not the case for the OLS MRAS observerin which, thanks to the employment of the adaptive model as apredictor, the estimated speed is directly fed back to the controlsystem without any filtering.

Fig. 10 shows the speed transient obtained with the BPNMRAS observer when a step speed reference of 100 rad/s isgiven. It shows, in particular, the measured speed as well as thespeed estimated by the BPN MRAS observer, respectively, be-fore and after filtering. It can be clearly seen that the estimatedspeed before filtering is noisy and affected by high ripple whilethe estimated speed after filtering is clean and without ripple.This is paid off with the resulting time delay of the filtering,which brings about a reduction of the proportional and integralgains of the PI as shown below.

In fact, the improvements in terms of dynamic performanceachieved with the OLS MRAS observer have been verified bycomparing the speed responses of both MRAS observers duringthree speed reversals, respectively, from 100 to 100 rad/s, from50 to 50 rad/s, and from 10 to 10 rad/s. Fig. 11(a) and (b)shows the measured speed, the estimated speed, the speed es-timation error, and the current component during the speedreversal from 100 to 100 rad/s obtained, respectively, with theOLS MRAS observer and the BPN MRAS observer. Fig. 12(a)and (b) shows the measured speed, the estimated speed, thespeed estimation error, and the current component duringthe speed reversal from 50 to 50 rad/s obtained, respectively,with the OLS MRAS observer and the BPN MRAS observer.Fig. 13(a) and (b) shows the measured speed, the estimatedspeed, the speed estimation error, and the current compo-nent during the speed reversal from 10 to 10 rad/s obtained,

(a)

(b)

Fig. 14. (a) Estimated and measured speed and speed error during a series ofspeed steps with rated load, OLS MRAS observer (experiment). (b) Estimatedand measured speed and speed error during a series of speed steps with no load,OLS MRAS observer (experiment).

respectively, with the OLS MRAS observer and the BPN MRASobserver. All these figures reveal that the OLS MRAS observerpermits a faster speed response: the time during which the speedreversal is performed is lower in all tests and this time reductionis in percentage more significant during a reversal at low speed,e.g., 0.1490 s with the OLS MRAS against 0.1780 s with theBPN MRAS during the speed reversal from 10 to 10 rad/s.Moreover, in all tests the speed estimation error obtained withthe OLS MRAS observer is lower than the corresponding oneobtained with the BPN MRAS, even if the estimated speed is


(a)

(b)

Fig. 15. (a) Estimated and measured speed and speed error during a constant speed reference of 10 rad/s at no load and at rated load, OLS MRAS observer(experiment). (b) Estimated and measured speed and speed error during a constant speed reference of 10 rad/s at no load and at rated load, BPN MRAS observer(experiment).

filtered with the latter method. Finally, the torque response ob-tained with the OLS MRAS observer is very smooth, while the

corresponding one obtained with the BPN MRAS observer ismuch affected by ripple (see, in particular, Fig. 11).


(a)

(b)



(a)

(b)



All the above results are summarized in Table III whichdisplays, for both observers, the proportional and integral gainsof the speed controller, the 3-dB bandwidth, the speed reversaltimes during the three above-mentioned tests, and the maximumpercent overshoot during the most critical speed reversal (from100 to 100 rad/s). It can be seen that, because of filtering, theproportional and integral gains of the speed controller with theOLS MRAS observer are almost 1.6 times as much as thoseobtained with the BPN MRAS. In the same way, the 3-dBbandwidth with the OLS MRAS observer is almost 16% higherthan the corresponding one with the BPN MRAS. Finally, evenif during speed transients the dynamic performance is betterand the maximum instantaneous estimation error is lower, themaximum overshoot obtained with the OLS MRAS is lowerthan the corresponding one with the BPN MRAS, respectively,9.5% against 16%, because of the absence of filtering of theestimated speed in the OLS MRAS observer.

3) Experimental Test 3: Medium/Low-Speed Accuracy: Inthe third test the accuracy of the speed estimation has beenverified in the medium/low-speed ranges, by giving a set ofsteps of speed references ranging from 140 to 30 rad/s. Thistest has been performed twice, at rated load and at no load.Fig. 14(a) shows the estimated speed, the measured speed, andthe speed error at rated load while Fig. 14(b) shows the samewaveforms at no load, obtained with the OLS MRAS observer.These figures clearly show that the estimation accuracy in themedium/low-speed range is very good, with negligible estima-tion errors during steady state and very low instantaneous esti-mation errors during the speed transients. Similar results havebeen obtained with the BPN MRAS observer: they presented,as a difference, only a slightly higher instantaneous estimationerror, as explained in Test 2.

4) Experimental Test 4: Low-Speed Accuracy: In the fourthtest the accuracy of the speed estimation has been verified in thelow-speed ranges, by giving a set of constant-speed referencesranging from 10 to 5 rad/s. This test has been performed twiceboth with the OLS MRAS and the BPN MRAS observer, re-spectively, at no load and at rated load torque. Fig. 15(a) and (b)shows the measured speed , the estimated speed, and the speedestimation error obtained at the constant reference speed of 10rad/s at no load and at rated load, respectively, with the OLSMRAS and the BPN MRAS observer. Figs. 16(a) and (b) and17(a) and (b) show the same waveforms obtained at the constantreference speeds of 8 and 5 rad/s at no load and at rated load,respectively, with the OLS MRAS and with the BPN MRASobserver. These figures show that, with both speed observers,the estimation accuracy reduces with increasing load torquesand that the steady-state percent speed estimation error obtainedwith the OLS MRAS observer is slightly lower than that with theBPN MRAS, especially at rated load: 6% against 13.4% at ratedload with 10 rad/s reference, 6.72% against 18.5% at rated loadwith 8 rad/s reference, and, finally, 34.6% against 39% at ratedload with 10 rad/s reference.

Finally, Fig. 18 shows the variation of the steady-state per-cent estimation error against the percent load torque obtainedwith the OLS MRAS observer and it reveals an increase of theestimation error with load, as expected; in particular, the percent

Fig. 18. Percent speed estimation error versus percent rated load torque duringa constant speed reference of 6 rad/s, OLS MRAS observer (experiment).

Fig. 19. Real and LP estimated rotor flux linkage d-axis component ata constant speed reference of 5 rad/s at no load, OLS MRAS observer(simulation).

speed error varies from almost 2% at 20% rated torque to 15%at rated load. Similar results have been obtained with the BPNMRAS observer, with slightly higher steady-state estimation er-rors at each load.

It is noteworthy, however, that the accuracy in the very-low-speed region is mainly limited by factors almost independentfrom the estimation algorithm, the main of which are the sensi-tivity of the reference model to the stator resistance variation dueto heating/cooling [28], the sensitivity of the adaptive model tothe rotor time constant variation due to heating/cooling or mag-netic saturation [28], and the problems due to open-loop inte-gration of the flux signal and to the inverter nonlinearity effects([4]–[6]).

It should also be remarked that at very low speeds incorrespondence of the cutoff frequency of the LP filter, the LPintegrator (employed here with both speed observers) does notwork properly since its frequency response highly differs both


Fig. 20. Estimated and measured speed in zero-speed operation at no load, OLS and BPN MRAS observers (experiment).

in magnitude and in phase from that of an ideal integrator.Therefore, below the cutoff frequency of the LP integrator, thedetuning of the flux models due to the not perfect integrationis also to be considered. In this respect Fig. 19 shows the realrotor flux direct-axis component in the stator reference frameand the estimated one at the speed reference of 5 rad/s when anLP integrator is used and the parameters of the flux estimatorare correctly tuned, as obtained by numerical simulations (in anexperiment, the real flux would be unknown). It shows that, evenif the flux model is correctly tuned, the incorrect integrationbrings about a wrong estimation of both the magnitude and thephase of the estimated flux: the amplitude of the real flux is2.24 times as much as the estimated one and the angle error isabout 64 . This requires proper modified integrators ([29]–[34]).In any case, better results in the estimation accuracy at lowspeeds are to be expected with both OLS MRAS and BPNMRAS observers, if proper integrators are used ([29]–[34]).These integrators, however, increase the overall complexity andcomputational burden of the control algorithm and, therefore,are to be recommended only if very-low-speed operation isrequired. In the latter case, because of the high sensitivity of thereference model (open-loop estimator) to the stator resistancevariation at low speed, an online estimation algorithm of thestator resistance is necessary (see [4]–[6]).

5) Experimental Test 5: Zero-Speed Operation: In the fifthtest the drive has been operated at the rated rotor flux linkageat zero speed. The test has been performed at no load bothwith the OLS MRAS observer and with the BPN MRAS one.

Fig. 20 shows the waveforms of the reference, measured, andestimated speeds for a time interval of about 60 s obtainedboth with the OLS MRAS and BPN MRAS observers. Withreference to the results of the OLS MRAS observer, it showsthat, after the magnetization of the machine, the drive canwork properly at zero speed and at no load, even without anysignal injection: this is mainly due to the fact that the adaptivemodel is used in prediction mode and is, thus, more stablethan when used in simulation mode, that is, with feedbackloops of the estimated rotor flux linkage. In particular, theestimated speed has small oscillations around 0 rad/s while themeasured speed is always zero, except for some spikes causedby the not perfect filtering of the speed signal coming from theincremental encoder: in any case the rotor does not move. Withreference to the results of the BPN MRAS observer, this figureshows that the estimated speed hardly follows the measured oneand its instantaneous speed estimation error is higher than thatobtained with the OLS MRAS observer. Moreover, with theBPN MRAS observer the estimated speed does not correctlyfollow its reference of 0 rad/s with a resulting worse behaviorof the drive, which rotates around zero speed, even reachinga speed of 15 rad/s during transients.

VII. CONCLUSION

This paper has presented a new MRAS speed observer forhigh-performance FOC induction motor drives based on adap-tive neural networks. It is an evolution and an improvement of


the MRAS observer shown in [17]. In particular, the new MRASspeed observer uses the current model as an adaptive model dis-cretized with the modified Euler integration method. Then, alinear neural network is obtained and trained online by means ofan OLS algorithm, and not a nonlinear BPN algorithm, whichis heavier from the computation point of view and can causesome drawbacks because of its inherent nonlinearity. Moreover,the neural adaptive model is employed here in prediction mode,and not in simulation mode as in [17]. The use of the predictionmode ensures better accuracy and stability than the simulationmode. In detail, the proposed OLS MRAS observer outperformsthe one presented in [17] in the following aspects, as proven the-oretically, in numerical simulation, and experimentally:

• quicker convergence in speed estimation;• absence of filtering in the estimated speed;• higher bandwidth of the speed loop, that is, better dynamic

performances;• lower estimation errors both in transient and steady-state

operation;• better behavior in zero-speed operation at no load;• lower complexity and computational burden of the adap-

tive model;• stable behavior in field weakening.

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Maurizio Cirrincione (M’03) received the “Laurea”degree from the Politecnico di Turino, Turin, Italy, in1991, and the Ph.D. degree from the University ofPalermo, Palermo, Italy, in 1996, both in electricalengineering.

Since 1996, he has been a Researcher with theSection of Palermo, Istituto di Studi sui SistemiIntelligenti per l’Automazione (I.S.S.I.A.-C.N.R.),Palermo, Italy. His current research interests areneural networks for modeling and control, systemidentification, intelligent control, electrical ma-

chines, and drives.Dr. Cirrincione was awarded the “E. R. Caianiello Prize” for the best Italian

Ph.D. dissertation on neural networks in 1997.

Marcello Pucci (M’03) received the “Laurea” andPh.D. degrees in electrical engineering from the Uni-versity of Palermo, Palermo, Italy, in 1997 and 2002,respectively.

In 2000, he was a Host Student at the Instituteof Automatic Control, Technical University ofBraunschweig, Braunschweig, Germany, workingin the field of control of ac machines, with a grantfrom the Deutscher Akademischer Austauscdi-enst-German Academic Exchange Service (DAAD).Since 2001, he has been a Researcher with the

Section of Palermo, Istituto di Studi sui Sistemi Intelligenti per l’Automazione(I.S.S.I.A.-C.N.R.), Palermo, Italy. His current research interests are electricalmachines, control, diagnosis and identification techniques of electrical drives,intelligent control, and power converters.

Dr. Pucci is a Member of the Editorial Board of the Journal of ElectricalSystems.

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