04084650

150 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007

Sensorless Control of Induction Motors by ReducedOrder Observer With MCA EXIN + Based Adaptive

Speed EstimationMaurizio Cirrincione, Member, IEEE, Marcello Pucci, Member, IEEE, Giansalvo Cirrincione, Member, IEEE,

and Gérard-André Capolino, Fellow, IEEE

Abstract—This paper presents a sensorless technique for high-performance induction machine drives based on neural networks.It proposes a reduced order speed observer where the speed is es-timated with a new generalized least-squares technique based onthe minor component analysis (MCA) EXIN + neuron. With thisregard, the main original aspects of this work are the develop-ment of two original choices of the gain matrix of the observer, oneof which guarantees the poles of the observer to be fixed on onepoint of the negative real semi-axis in spite of rotor speed, and theadoption of a completely new speed estimation law based on theMCA EXIN + neuron. The methodology has been verified exper-imentally on a rotor flux oriented vector controlled drive and hasproven to work at very low operating speed at no-load and ratedload (down to 3 rad/s corresponding to 28.6 rpm), to have good es-timation accuracy both in speed transient and in steady-state andto work correctly at zero-speed, at no-load, and at medium loads. Acomparison with the classic full-order adaptive observer under thesame working conditions has proven that the proposed observer ex-hibits a better performance in terms of lowest working speed andzero-speed operation.

Index Terms—Field oriented control, induction machines, least-squares (LS), neural networks, reduced order observer, sensorlesscontrol.

NOMENCLATURE

Space vector of the stator voltages inthe stator reference frame.

, Direct and quadrature components ofthe stator voltages in the stator refer-ence frame.Space vector of the stator currents inthe stator reference frame.

Manuscript received June 15, 2005; revised October 28, 2005. Abstract pub-lished on the Internet November 30, 2006. The work of G. Cirrincione has beensupported under a grant from ISSIA-CNR, Italy in the framework of the MIURproject n. 211 entitled “Automazione della gestione intelligente della gener-azione distribuita di energia elettrica da fonti rinnovabili e non inquinanti e delladomanda di energia elettrica, anche con riferimento alle compatibilità interne eambientali, all’affidabilità e alla sicurezza.”

M. Cirrincione was with the ISSIA-CNR, Section of Palermo, Viale delleScienze snc, 90128 Palermo, Italy. He is now with the Université de Technologiede Belfort-Montbeliard (UTBM), 90010 Belfort Cedex, France (e-mail: [email protected]).

M. Pucci is with the ISSIA-CNR Section of Palermo, Institute on Intelli-gent Systems for the Automation, Viale delle Scienze snc, 90128 Palermo, Italy(e-mail: [email protected]).

G. Cirrincione and G.-A. Capolino are with the Department of Electrical En-gineering, University of Picardie-Jules Verne, 80039 Amiens, France (e-mail:[email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2006.888776

, Direct and quadrature components ofthe stator currents in the stator refer-ence frame.

, Direct and quadrature components ofthe stator currents in the rotor-fluxoriented reference frame.Space vector of the stator flux-link-ages in the stator reference frame.

, Direct and quadrature component ofthe stator flux linkage in the statorreference frame.Space vector of the rotor flux-linkagesin the stator reference frame.

, Direct and quadrature component ofthe rotor flux linkage in the stator ref-erence frame.Stator inductance.Rotor inductance.Total static magnetizing inductance.Resistance of a stator phase winding.Resistance of a rotor phase winding.Rotor time constant.Total leakage factor.Number of pole pairs.Angular rotor speed (in mechanicalangles).Angular rotor speed (in electrical an-gles per second).Sampling time of the control system.

I. INTRODUCTION

SO FAR, sensorless control of induction motors [1]–[3] hasbeen faced with two kinds of methods: those which employ

the dynamic model of the induction machine based on the funda-mental spatial harmonic of the magnetomotive force (mmf) andthose based on the saliencies of the machine. Among the first,the main ones are the open-loop speed estimators [4], MRAS(model reference adaptive system) speed observers [5], evenbased on neural networks [6], [7], full-order Luenberger adaptiveobservers [8]–[11], also with neural networks [12], and reducedorder speed observers [13]–[15]. Among the second, some arebased on continuous high-frequency signal injection [16]–[18]and some on test vectors [19], [20]. This last kind of method-ologies, even if is very promising for position sensorless controlthanksto thecapabilityof trackingsaliencies,either thesaturation

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CIRRINCIONE et al.: SENSORLESS CONTROL OF INDUCTION MOTORS BY REDUCED ORDER OBSERVER 151

of the main flux or the rotor slotting saliencies, is usually machinedependant and sometimes requires a suitable machine design(open or semi-closed rotor slots for rotor slotting tracking). Thisis not the case for the first kind of techniques, among which thefull-order Luenberger observer gives very interesting perfor-mances, even if with a significant computational requirement.In this regard, an improvement of this observer based on totalleast-squares (TLSs) speed estimation has been proposed by theauthors [12], which has shown a good performance in the speedestimation during transients, at very low-speed (down to 0.5 rad/scorresponding to 4.77 rpm) and at zero-speed. Moreover, itsstability features in regenerating mode at low-speed have beenanalyzed theoretically and tested experimentally.

The main goal of this work is the design of an adaptive speedobserver, with a performance comparable to that obtainable withthe full-order Luenberger observer. This is achieved by a re-duced-order rotor flux observer, which results in lower com-plexity and computational burden. In fact, the reduced order ob-server has to solve a problem of order two, while the full-orderobserver of order four. Particularly, this paper presents a newsensorless technique based on the reduced order observer, wherethe speed is estimated on the basis of a new generalized least-squares technique, the MCA EXIN + neuron. Moreover, thiswork also deals with the development of two original choicesof the gain matrix of the observer, one of which ensures thatthe poles of the observer be fixed on one point of the negativereal semi-axis, in spite of the variation of the speed of the motor,with a consequent dynamic behavior of the flux estimation inde-pendent of the rotor speed. The adoption of the completely newspeed estimation law, based on the MCA EXIN + neuron, en-sures very low operating speed at no-load and rated load (downto 3 rad/s corresponding to 28.6 rpm), good estimation accuracyalso in speed transient and correct zero-speed operation. Dif-ferent from [13], which employs a combination of the reducedorder observer, used as reference model, and the simple currentmodel, used as adaptive model, to estimate the rotor speed, hereonly the reduced order observer is employed, while the rotorspeed is estimated by the MCA EXIN + algorithm, just on thebasis of the stator voltage and current measurements and the es-timated flux. It should be remarked that the MCA EXIN + sched-uling is more powerful than the other existing techniques, evenleast-squares based, in terms of smoother convergence transient,shorter settling time, and better accuracy [21]. In addition, thechoice of MCA EXIN + neuron allows to take into considerationthe measurement flux modeling errors, which influence the ac-curacy of the speed estimation, since it is inherently robust to thethis source of errors. This speed observer has been tested exper-imentally in a rotor-flux-oriented field oriented control (FOC)drive and compared with the classic full-order adaptive observerof [8]. Also, this paper shows a complexity analysis of the pro-posed methodology with respect to other observers, both classicand based on neural networks.

II. LIMITS OF MODEL-BASED SENSORLESS TECHNIQUES

A. Open-Loop Integration

One of the main problems of some speed observers, whenadopted in high-performance drives, is the open-loop integration

in presence of DC biases. The speed observers suffering fromthis problem are those which employ open-loop flux estimators,e.g., open-loop speed estimators and those MRAS systems wherethe reference model is an open-loop flux estimator [5]–[7], whilespeed estimators employing closed-loop flux integration, like theclassic full-order adaptive observer [8], do not have this problem.In particular, DC drifts are always present in the signal before it isintegrated, which causes the integrator to saturate with a resultinginadmissible estimation error, and also after the integrationbecause of the initial conditions [22]. In general, low-pass (LP)filters with very low cutoff frequency are used instead of pureintegrators; however, since they fail in low-frequency ranges,close to their cutoff frequency, some alternative solutions havebeen devised to overcome this problem, e.g., the integrator withsaturation feedback [22], the integrator based on cascaded LPfilters [23], [24], the integrator based on the offset vector estima-tion and compensation of residual estimation error [4] and theadaptive neural integrator [25]. With regard to the reduced orderadaptive observer, the problem of the DC drift in the integrandsignal exists only for those choices of the observer gain matrixwhich transform, at certain working speeds of the machine, thereduced order observer in an open-loop flux estimator, like thecurrent voltage model (CVM) in [26] which gives rise to a smoothtransition from the “current” to the “voltage” model accordingto the increase of the rotor speed (see Section III). With such achoice, below a certain speed and above another one, the observerbehaves like a simple open-loop estimator, and therefore suffersfrom the mentioned problem. It is not the case of the proposedgain matrix choice, which is described in Section III.

B. Inverter Nonlinearity

The power devices of an inverter present a finite voltage dropin “on-state,” due to their forward nonlinear characteristics.This voltage drop has to be taken into consideration at low-fre-quency (low-voltage amplitude) where it becomes comparablewith the stator voltage itself, giving rise to distortion and dis-continuities in the voltage waveform. Here, the compensationmethod proposed by [4] has been employed. This technique isbased on modeling the forward characteristics of each powerdevice with a piecewise linear characteristics, with an averagethreshold voltage and with an average differential resistance.

C. Machine Parameter Mismatch

A further source of error in flux estimation is the mismatchof the stator and rotor resistances of the observer with their realvalues because of the heating/cooling of the machine. The loaddependent variations of the winding temperature may lead up to50% error in the modeled resistance. Stator and rotor resistancesshould be, therefore, estimated online and tracked during theoperation of the drive. A great deal of online parameter estima-tion algorithms have been devised [4], [8], requiring low com-plexity and reduced computational burden when used in controlsystems. In any case, it should be emphasized that steady-stateestimation of the rotor resistance cannot be performed in sen-sorless drives, thus rotor resistance variations must be deducedfrom stator resistance estimation. In the case under study, dif-ferently from [13] where the allocation of the poles of the ob-server has been chosen to minimize the sensitivity of the ob-


Fig. 1. Block diagram of the MCA EXIN + reduced order observer.

server to the rotor resistance variations, the gain matrix choicehas been chosen (see Section III) to make the dynamic of theflux estimation constant, by fixing the position of the poles ofthe observer in a precise point of the negative real semi-axis, inspite of the variation of the speed of the motor, and therefore thesensitivity to the rotor resistance variations has not been consid-ered as a design criterion of the observer. No stator resistanceestimation algorithm [4] has been used, since the goal is to de-velop one observer which is not too complex and computation-ally cumbersome.

III. MCA EXIN + REDUCED ORDER OBSERVER

A. Reduced Order Observer Equations

The matrix equations of the reduced order flux observer, witha voltage error used for corrective feedback are [13], [26], [27]

(1)

where

(2a)

(2b)

(2c)

(2d)

(2e)

where all space vectors are in the stator reference frame:stator current vector,

stator voltage vector, rotor flux vector,

, , is the rotor speed, and

is the observer gain matrix. For the list of parameters, see theNomenclature.

The proposed MCA EXIN + reduced order observer is basedon the classical reduced order flux observer structure, while anew speed estimation law is proposed, which is based on theMCA EXIN + technique. Fig. 1 shows the block diagram of theproposed reduced order observer, whose equations are describedin Section III-A. The rotor speed is estimated by a MCA EXIN+ algorithm, on the basis of the estimated rotor flux linkage ,as well as the measured stator voltage and current space vec-tors . Moreover, since the gain matrix is time dependant, thecorrection term which takes into consideration the time deriva-tive of the gain matrix is also included in the scheme.

B. Proposed Choice of the Gain Matrix of the Observer

The choice of a suitable gain matrix of the observer hasbeen a problem largely faced in literature [13] and [26]–[34].It is well-known [13] that the poles of the reduced orderobserver are the couple of eigenvalues of the matrix

where

and .This paper develops two new choices of the gain matrix and

proposes one of them as the most suitable for sensorless control.The first, called choice 1, makes the observer poles amplitude


Fig. 2. Pole locus, amplitude versus speed, � versus speed and gain locus with the proposed gain matrix choice.

constant, the second, called fixed pole position (FPP) choice,fixes the position of the poles, in spite of the rotor speed. TheFPP choice is proposed as the best for sensorless control for thereasons explained beneath.

The FPP gain matrix choice permits the position of the polesof the observer to be fixed on the negative part of the real semi-axis at distance from the origin, according to the variationof the rotor speed, to ensure the stability of the observer itself.The proposed gain choice is obtained by imposing and

and gives

(3)Correspondingly, the time derivative of the gain matrix to beused in the observer scheme is

(4)

Fig. 2 shows the observer pole locus, the amplitude of polesversus rotor speed, the damping factor versus rotor speed, andgain locus ( versus ) as obtained with the FPP gainmatrix choice. It shows that this solution permits to keep thedynamic of the flux estimation constant, because the amplitudeof the poles is the constant and the damping factor is alwaysequal to 1. This last feature is particularly important for sensor-less control in high-speed range: in fact, most of the choices ofthe matrix gain cause a low damping factor at high rotor speed,which can easily cause instability phenomena. Actually, highervalues of the damping factor result in low sensitivity to esti-mated speed perturbations or parameter variations.

C. Other Gain Matrix Choices

Fig. 3 shows the observer pole locus, the amplitude of polesversus the rotor speed, and the damping factor versus the rotorspeed, obtained with five different gain choices of the matrixgain; the first has been developed by the authors and the otherfour have been proposed in literature.

1) Choice 1: A criterion for choosing the locus of the ob-server poles is to make their amplitude constant with respect forthe rotor speed. This criterion leads either to the above proposedsolution if or, if , to a semicircle polelocus with centre in the origin, with radius and lying in thecomplex semiplane with negative real part. In this last case, theposition of the poles varies with the rotor speed and therefore toavoid instability, a maximum rotor speed must be properlychosen, in correspondence to which the poles of the observer lieon the imaginary axis. The matrix gain choice which guaranteesthis condition is the following:

(5)

This matrix gain is dependant on the rotor speed, and thereforethe observer requires the correction term . With such amatrix gain choice, the poles are complex with a constant ampli-tude , but with a damping factor which drastically decreases,from 1 at zero-speed to about 0 at rated speed and above.

2) Choice 2: Proposes the following matrix gain choice [30]:

(6)


Fig. 3. Pole locus, amplitude versus speed, and � versus speed with five matrix gain choices.

With such a matrix gain choice, the poles of the observer areimaginary with magnitude increasing with the rotor speed andthe damping factor drastically reducing at increasing speed,from 1 at zero-speed to about 0 at rated speed and above. Thischoice cancels the contribution of the stator current from theobserver (1). It has the advantage that the gain matrix is notdependent on the rotor speed, and therefore is simpler than boththe FPP choice and the others; for the same reason, it does noteven require the correction term .

3) Choice 3: Proposes the following matrix gain choice [13]

(7)

This matrix gain is dependant on the rotor speed, and thereforethe observer requires the correction term . With such amatrix gain choice, the poles of the observer are complex withmagnitude increasing with the speed and the damping factorreducing at increasing speed, from 1 at zero-speed to about 0.7at rated speed and above. However, in [13], it is claimed thatthis matrix gain choice reduces the sensitivity of the observer torotor resistance variations.

4) Choice 4: Proposes also the following matrix gain choice[30]:

(8)

This matrix gain is dependant on the rotor speed, and thereforethe observer requires the correction term . With such amatrix gain choice, the poles of the observer are real and lieon the negative real semi-axis with magnitude increasing withthe speed and a damping factor constant with rotor speed andalways equal to 1.

5) Choice 5: Proposes the following matrix gain choice [26]:

forfor

for(9)

Assigned two threshold values and to the rotor speed,the gain matrix has three different values. Below , no cor-rection feedback is given to the observer and it behaves as thesimple “current” model of the induction machine, based on itsrotor equations. Above , the correction feedback given to theobserver is a constant multiplied with the identity matrix, andit behaves as the simple “voltage” model of the induction ma-chine, based on its stator equations. Between and , thegain matrix linearly varies from the two limit conditions. Forthis reason, it has been called current voltage model (CVM),since it gives rise to a smooth transition from the “current”to the “voltage” model according to the increase of the rotorspeed. With such a choice, the poles of the observer are com-plex with magnitude first increasing and then decreasing withthe rotor speed, and a damping factor drastically reducing atincreasing speed, from 1 at zero-speed to about 0 at rated speedand above. As mentioned above, however, this solution makesthe observer work as a simple open-loop estimator both at lowand high speeds, with the consequent dc drift integration prob-lems. This is not the case neither of the FPP choice nor the otherfour ones. See [26] for the choice of and .


TABLE IISSUES OF ALL MATRIX GAIN CHOICES

A slightly different approach is presented in [35], whichproposes an observer where the rotor flux is estimated as thesum of a high-pass filtered and a LP filtered flux, estimated,respectively, by the “voltage” and the “current” models. Thisleads to a correction term which depends, differently fromthe other choices above, on the difference between the twoestimated fluxes, which are subsequently processed by a PIcontroller. The resulting observer presents a smooth transi-tion between “current” and “voltage” model flux estimationwhich is ruled by the closed-loop eigenvalues of the observer,determined by the parameters of the PI controller. At rotorspeeds below the bandwidth of the observer, its sensitivity tothe parameters correspond to that of the “current” model, whileat high speeds its sensitivity corresponds to that of the “voltagemodel.” In this sense, it behaves like choice 5.

Table I summarizes the features of all six choices, mainly fo-cusing on the variation of the observer pole amplitude with therotor speed, the variation of the damping factor with the rotorspeed, the dependance on the matrix gain by the rotor speed,and the DC drift integration problems. From the standpoint ofthe pole amplitude variation, the FPP choice and choice 1 arethe best, since they permit the amplitude to be constant; choices2, 4, and 5 permit a low variation of the pole amplitudes, whilechoice 3 causes a high variation. As for the damping factor vari-ation, the FPP choice and choice 4 are the best since they keep

always equal to 1; choice 3 permits a low decrease of at in-creasing rotor speeds, while choices 1, 2, and 5 cause a strongreduction of . As for the dependance of on the rotor speed,all the choices except choice 2 suffer from this variation. As forthe DC drift integration problems, only choice 5 presents thisnegative issue, especially at low and high rotor speeds.

For the above reasons, FPP choice for the gain matrix is thebest among the six presented here for sensorless control, and hasbeen therefore adopted in the following experimental tests.

IV. MCA EXIN + BASED SPEED ESTIMATION

The MCA EXIN + based speed estimation derives from amodification of the complete state equations of the inductionmotor [8], [12] so that it exploits the two first scalar equationsto estimate the rotor speed, as shown below in discrete form fordigital implementation, as shown in (10) at the bottom of thepage, is the sampling time of the control algorithm and is

Fig. 4. Schematics of the LSs techniques in the monodimensional case.

the current time sample. Note that the is applied on the statorvoltage space vector to mean that it is computed from the DClink voltage considering the blanking time of the inverter and thevoltage drop on the power devices of the inverter on the basis ofthe method proposed in [4]. The same symbol on the rotor fluxindicates the estimated flux.

This matrix equation, which can be written more generallyas , can be solved for by using LS techniques. Inparticular, in literature there exist three LS techniques, i.e., theordinary least-squares (OLSs), the total least-squares (TLSs),and the data least-squares (DLSs) which arise when errors are,respectively, present only in or both in and in or only in

.In classical OLSs, each element of is considered without

any error: therefore, all errors are confined to . However, thishypothesis does not always correspond to the reality: modelingerrors, measurement errors, etc., can cause errors also in .Therefore, in real-world applications, the employment of TLSswould be very often better, as it takes also into consideration theerrors in the data matrix.

In the monodimensional case ( ), which is the caseunder study, the resolution of the LS problem consists in deter-mining the angular coefficient of the straight line of equation

. The LS technique solves this problem by calculatingthe value of which minimizes the sum of squares of the dis-tances among the elements , with , and theline itself. Fig. 4 shows the difference among the OLS, TLS,and DLS. OLS minimizes the sum of squares of the distancesin the direction (error only in the observation vector). TLSminimizes the sum of squares in the direction orthogonal to theline (for this reason, TLS is also called orthogonal regression),

(10)


while DLS minimizes the sum of squares in the direction (er-rors only in the data matrix). In particular, it must be expectedthat, in absence of noise, the results obtained with TLS are equalto those obtained with OLS; however, in presence of increasingnoise, the performance of TLS remains higher than that of OLS,as TLS is less sensitive to noise. For these reasons, the TLS algo-rithm is particularly suitable for estimation processes in whichdata are affected by noise or modeling errors; this is certainly thecase of speed estimation, where the estimated rotor flux, presentin , is affected both by modeling errors and noise. Therefore,a TLS technique should be used instead of the OLSs technique.The TLS EXIN neuron, which is the only neural network ca-pable to solve a TLS problems recursively online, has been suc-cessfully adopted in MRAS speed observers [6]. In this work, anew generalized LS technique, the MCA EXIN + (minor com-ponent analysis) neuron, is used for the first time to compute therotor speed. This technique is a further improvement of the TLSEXIN neuron [36], [37] and is explained below.

A. The MCA EXIN + Neuron

is the linear regression problem under hand. In [38],all LS problems have been generalized by using a parameter-ized formulation (generalized TLS, GeTLS EXIN) of an errorfunction whose minimization yields the corresponding solution.This error is given by

(11)

where represents the transpose and is equal to 0 for OLS, 0.5for TLS, and 1 for DLS. The corresponding iterative algorithm(GeTLS EXIN learning law), which computes the minimizer byusing an exact gradient technique, is given by

(12)where

(13)

where is the learning rate, is the row of fed at in-stant , and is the corresponding observation. The GeTLSEXIN learning law becomes the TLS EXIN learning law forequal to 0.5 [38]. The TLS EXIN problem can also be solved byscheduling the value of the parameter in GeTLS EXIN, e.g., itcan vary linearly from 0 to 0.5, and then remains constant. Thisscheduling improves the transient, the speed, and the accuracyof the iterative technique [38]. [21] shows that a TLS problemcorresponds to a MCA problem and is equivalent to a particularDLS problem. Indeed, define as the augmented ma-trix built by appending the observation vector to the right of thedata matrix. In this case, the linear regression problem can be

reformulated as and can be solved as a homo-

geneous system ; the solution is given by the eigen-vector associated to the smallest eigenvalue of (MCA).

This eigenvector can be found by minimizing the following errorfunction:

(14)

which is the Rayleigh quotient of . Hence, the TLS solu-tion is found by normalizing in order to have the last com-ponent equal to . Resuming, TLS can be solved by applyingMCA to the augmented matrix . [21] also proves the equiv-alence between MCA and DLS in a very specific case. Indeed,setting and (DLS) in (11) yields (14) with .Hence, the MCA for the matrix is equivalent to the DLS ofthe system composed of as the data matrix and of a null obser-vation vector. In particular, TLS by using MCA can be solvedby using (12) and (13) with and with . Theadvantage of this approach is the possibility of using the sched-uling. This technique is the learning law of the MCA EXIN+ neuron [21], which is an iterative algorithm from a numer-ical point of view. It yields better results than other MCA iter-ative techniques because of its smoother dynamics, faster con-vergence, and better accuracy, which are the consequence of thefact that the varying parameter drives toward the solutionin a smooth way. These features allow higher learning rates foraccelerating the convergence and smaller initial conditions (in[21], it is proven that very low initial conditions speed up thealgorithm).

V. IMPLEMENTATION ISSUES

A. Control System

The MCA EXIN + reduced order observer has been testedon a “voltage” rotor flux oriented vector control scheme [6], [7](Fig. 5). For control purposes, the estimated speed has been fed-back to a PI speed controller and instantaneously compared withthe measured one to compute the speed error at each instant andin each working condition. Inside the speed loop there is theloop. On the direct axis, the voltage is controlledat a constant value to make the drive automatically work in thefield-weakening region. Inside the loop are, respectively, therotor flux-linkage loop and the loop. The voltage source in-verter (VSI) is driven by an asynchronous space vector modula-tion algorithm with a switching frequency . Thephase voltages have been computed on the basis of the instan-taneous measurement of the DC link voltage and the switchingstate of the inverter. Moreover, the method proposed in [4] forthe compensation of the on-state voltage drops of the inverter de-vices has been employed. In the case under study, the employedIGBT modules, which are the Semikron SMK 50 GB 123, havebeen modeled with a threshold voltage and with anaverage differential resistance . Finally, the sam-pling frequency of the acquired signals has been set to 10 kHz, atwhich also all control loops work. For reproducibility reasons,Table II shows all the parameters of the control system adoptedfor the experimental implementation.

As for the integration of state (1) of the reduced order ob-server in the discrete domain, the pure integrator in the con-tinuous domain has been replaced by the following discrete


Fig. 5. Implemented FOC scheme.

TABLE IIPARAMETERS OF THE CONTROL SYSTEM

filter in the -domain . This is ob-tained by the transform of the following discrete equation:

where is the integrator input at the current time sampleand is the corresponding integrator output. This formulais the sum of a simple Euler integrator and an additional termtaking into consideration the values of the integrand variablesin two previous time steps; it guarantees a correct integration ofthe state equations, and thus a correct flux estimation with theadopted value of differently from the simple forward Eulerintegrator .

With reference to the MCA EXIN + reduced order observer,the only two parameters set by the user have been given thefollowing values: and (kept constant).With reference to the parameter , the following scheduling hasbeen adopted: at each speed transient commanded by the con-trol system, a linear variation of from 0 to 1 in 0.3 s has beengiven. This scheduling has been implemented in software by adiscrete integrator with the constant value 1/0.3 in input, whichpermits the output to get the value 1 in 0.3 s with linear law, andwhose output is reset to zero at each change of the referencespeed of the drive. With the above scheduling, the flatness ofthe OLS error surface around its minimum, which prevents thealgorithm from being fast, is smoothly replaced by a ravine inthe corresponding DLS error surface, which speeds up the con-vergence to the solution [minimum of (14)] as well as its finalaccuracy. Fig. 6 shows the error surfaces obtained with(OLS) and (DLS) and the MCA EXIN + error trajec-tory versus the two components of with regard to the DLSerror surface, obtained when a speed step reference from 0 to150 rad/s has been given to the drive without load. It should beremarked that the proposed speed observer does not need anyLP filtering of the estimated speed to be fed back to the controlsystem, with consequent higher bandwidth of the speed loop.

Fig. 6. Error surfaces with � = 0 and � = 1 and the MCA EXIN + errortrajectory versus x.

TABLE IIIPARAMETERS OF THE INDUCTION MOTOR

B. Experimental Setup

The employed test setup consists of the following [6], [7].• A three-phase induction motor with parameters shown in

Table III.• A frequency converter which consists of a three-phase

diode rectifier and a 7.5 kVA, three-phase VSI.• A DC machine for loading the induction machine with pa-

rameters shown in Table IV.• An electronic AC-DC converter (three-phase diode recti-

fier and a full-bridge DC-DC converter) for supplying theDC machine of rated power 4 kVA.

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


TABLE IVPARAMETERS OF THE DC MACHINE

C. Hardware Choice

With regard to the hardware implementation of the pro-posed sensorless control technique, a floating point DSP(TMS320F240) has been employed, since its programmingneeds a lower development time than a fixed point DSP. Ingeneral, the choice between floating or fixed point DSPs ishighly dependent on the application at hand, its complexity, andits cost reduction needs. For industry products, the productionvolumes play a relevant role in this choice: for high volumes,the lower cost of a fixed point DSP justifies the amount ofany nonrecurring engineering (NRE) cost [39], like controlsoftware development, while for low volumes, the NRE costdominates and thereby floating point choice seems to be thebest, as it reduces the development costs. In the industrialdrives market, where high production volumes dominate, thecost issue is important, and thus the potential implementationof each technique on fixed point DSP is a real advantage.

The big difference between floating and fixed point DSPs isthe coding of the numbers. Fixed point chips, differently fromfloating point ones, need a scaling factor to be managed by theuser. If all variables of the program are normalized betweenand 1, not even the scaling factor is needed. Moreover, fixedpoint DSPs are also capable of a finer resolution than fixedpoint ones (of the same word length) because of the extra bitsin the mantissa. In drive control, the development of the en-tire control system, including the observer, can be performedby working in per-unit (p.u.), i.e., by dividing each values bythe corresponding base value: this assumption highly simpli-fies the transport of the software from floating point to fixedpoint format, exploiting also its better resolution. In additionto this, many development tools have been recently proposedto convert control software from floating point to fixed pointrepresentation [39].

Some specific suggestions for the implementation on fixedpoint DSPs of an MRAC speed controller for a FOC inductionmotor drive with a LSs-based parameter estimator are given in[40]. [40] explicitly addresses the difficulties associated with thelarge dynamic range of the covariance matrix (used by the LSsalgorithm) with respect to the finite length of the DSP word. Theproposed solution is the adoption of a double-word fixed pointrepresentation, which increases the dynamic range of the pro-cessed data, and consequently reduces the rounding/truncationerrors, at the expense of higher execution time.

With regard to the proposed technique, the state equations ofthe reduced order observer can be implemented in software bysimple operations (sums and multiplications/divisions) betweenquantities in p.u. With specific regard to the MCA EXIN + algo-rithm, any quantization error, which is larger in fixed point thanin floating point DSPs, can degradate its solution (typical of allof gradient-based algorithms), with respect to the performance

achievable in infinite precision (see [36] for more details). Thiskind of error accumulates in time without bound, leading in thelong run (ten of million of iterations) to an eventual overflow(the so called numerical divergence). The source of this di-vergence is both the analog-to-digital (A/D) conversion and thefinite word length used to store all internal algorithmic quanti-ties. The degradation of the solution is proportional to the condi-tioning of the input, i.e., to the eigenvalue spectrum of the inputautocorrelation matrix [36]. Decreasing the learning rate inthe infinite precision algorithm leads to improved performance.Neverthless, this decrease increases the deviation from infiniteprecision performance, while its increase magnifies numericalerrors, so a tradeoff is required [41]. A technique for avoidingoverflows caused by this kind of divergence, at the expense ofsome increase of complexity and small degradation of the solu-tion, is the technique called leakage (see [36] for its details).

Finally, the MCA EXIN + algorithm does not need partic-ularly critical operations (the most complex operation is a dotproduct between vectors of dimension two) and explicitly em-ploys neither the covariance matrix [40] nor its inverse compu-tation, as needed in some versions of the recursive least-squares(RLSs). In any case, it should be remarked that, independentlyof the DSP choice, the elements of data matrix and the obser-vation vector (both bidimensional vectors) processed by theMCA EXIN + algorithm must be properly scaled before pro-cessing, so that the estimated will result in a quantity rangingbetween and 1, otherwise, the effect of the parameter in(11) is null. This intrinsic algorithm demand further facilitatesthe potential conversion of the software into fixed point format.

D. Computational Complexity

From the computational point of view, the MCA EXIN + re-duced order observer has been compared here with some neuralnetwork-based observers, in particular, the TLS EXIN full-orderobserver [12] and the TLS EXIN MRAS observer with adap-tive neural integrator [6], and with the classic full-order ob-server [8]. This comparison has been done on the basis of thenumber of floating operations (flops) needed by each algorithmfor every iteration. The comparison is shown in Table V. If thecorrection term is not adopted in the proposed observer,the most demanding observer is the TLS EXIN full-order ob-server which requires 126 flops + 3 IF-THEN instructions andthen there is the MCA EXIN + reduced order speed observerwith 120 flops + 4 IF-THEN instructions. If the correction term

is adopted, the proposed observer is the most complex,with 147 flops + 4 IF-THEN instructions. However, a series ofexperimental tests performed with and without this term haveshown that the MCA EXIN + reduced order observer can be im-plemented either without the without a significant wors-ening of the performance of the flux and speed estimation. Then,there is the TLS EXIN MRAS observer with the adaptive neuralintegrator which requires 87 flops + 3 IF-THEN instructions,and finally the classic full-order observer requiring 76 flops.

However, it should be remarked that both the TLS EXINfull-order observer in [12] and the classic full-order observer in[8] are implemented with a matrix gain correction term whichis null, i.e., without any feedback term. The adoption of such aterm would require the product of a (2 4) matrix for a (4 1)


TABLE VCOMPLEXITY OF THE PROPOSED OBSERVER COMPARED WITH OTHERS IN LITERATURE

Fig. 7. Reference, estimated, and measured speed during a 50–0–50 rad/s test at no-load (experimental).

vector, where the gain matrix could be either constant or variablewith the speed of the machine in dependence on the desired ob-server dynamics, and thus would highly increase the complexityof both observers. It can be concluded that with in allcases the reduced order observer requires fewer flops than thefull-order ones. In any case, the total flops of the different ob-servers is of the same order.

VI. EXPERIMENTAL RESULTS

The proposed MCA EXIN + reduced order observer has beenverified in simulation and experimentally on a test setup (see

appendix). Moreover the results obtained experimentally havebeen compared with those obtained with the full-order classicadaptive observer proposed in [8]. The parameters of the full-order classic observer are exactly the same as those suggestedin [8]. Note also that in the full-order classic observer no com-pensation of the inverter nonlinearity has been considered. Onthe other hand, the parameter estimation method of [8] has beenadopted in the full-order classic observer only. Simulations havebeen performed in Matlab®–Simulink®. With regard to the ex-perimental tests the speed observer as well as the whole controlalgorithm have been implemented by software on the DSP ofthe dSPACE 1103.


Fig. 8. Reference, estimated, and measured speed during a set of speed step references (experimental).

A. Dynamic Performances

As a first test, the drive has been operated at the constantspeed of 50 rad/s at no-load, then a zero step reference has beengiven and the drive has been operated at zero-speed for almost2 s, and then a step speed reference of 50 rad/s at no-load hasbeen given. Fig. 7 shows the waveforms of the reference, esti-mated (used in the feedback loop), and measured speed duringthis test. It shows that the measured speed and the estimated oneboth follow correctly the reference, even at zero-speed.

Subsequently, the transient behavior of the observer at verylow speeds has been tested. First, the drive has been given a setof speed step references at very low speed, ranging from 3 rad/s(28.65 rpm) to 6 rad/s (57.29 rpm). Fig. 8 shows the wave-forms of the reference, estimated and measured speed duringthis test, and Table VI shows the 3 dB bandwidth of the speedloop versus the reference speed of the drive. Both Fig. 8 andTable VI show a very good dynamic behavior of the drive witha bandwidth which, however, decreases from 69.3 rad/s at thereference speed of 6 rad/s to 12.3 rad/s at 3 rad/s. This con-sideration is confirmed by Fig. 9 which shows the reference,

TABLE VIBANDWIDTH OF THE SPEED LOOP VERSUS THE REFERENCE

SPEED (EXPERIMENTAL)

estimated, and measured speed during a set of speed reversal,respectively, from 3 to , from 4 to , from 5to , and from 6 to . These last figures showthat the drive is able to perform a speed reversal also at very lowspeeds, i.e., in very challenging conditions. However, it shouldbe noted that the lower the speed reference, the higher the timeneeded for the speed reversal, as expected, because of the reduc-tion of the speed bandwidth of the observer at decreasing speedreferences, which is typical of all observers.

B. Low-Speed Limits

In this test, the drive has been operated at a constant verylow-speed (3 rad/s corresponding to 28.65 rpm), at no-load andrated load. Fig. 10 shows the reference, estimated, and measuredspeed during these tests. It shows that the steady-state speed


Fig. 9. Reference, estimated, and measured speed during a set of speed reversal (experimental).

Fig. 10. Reference, estimated, and measured speed during a constant speed of 3 rad/s at no-load and rated load with the MCA EXIN + reduced order observer(experimental).


Fig. 11. Reference, estimated and measured speed during a constant speed of 4 rad/s at no-load and rated load with the classic full-order observer (experimental).

Fig. 12. Reference, measured , estimated speed, and load torque at the constant speed reference of 30 rad/s with two consecutive load torque steps of �5 Nm(experimental).

estimation error is very low, equal to 2.45% at no-load and to7.67% with rated load. For comparison reasons, the test has beenalso performed with the full-order classic observer [8]: Fig. 11shows the reference, estimated, and measured speed, obtained

when giving a constant reference speed of 4 rad/s (38.19 rpm),at no-load and at rated load for the classic full-order observer. It,therefore, shows that the mean estimation error is about 30% atno-load and 30.5% at rated load. The comparison shows a better


Fig. 13. (a) Reference, estimated, measured speed, and position at zero-speed at no-load (experimental). (b) Reference, estimated, measured speed, and positionat zero-speed with 5 Nm load torque (experimental).

accuracy in the speed estimation of the MCA EXIN + reducedorder observer than the one the classic full-order adaptive ob-server, even at a higher reference speed (4 rad/s against 3 rad/s).Below 2 rad/s, however, the speed accuracy estimation of theMCA EXIN + reduced order observer drastically reduces.

C. Rejection to Load Perturbations

In this test, to verify the robustness of the speed response ofthe proposed observer to a sudden torque perturbation, the drive

has been operated at the constant speed of 30 rad/s and twosubsequent load torque square waveforms of amplitudehave been applied. Fig. 12 shows the reference, measured, andestimated speed during this test, as well as the applied loadtorque, created by the torque of a controlled DC machine. Thesefigures show that the drive response occurs immediately whenthe torque steps are given. Moreover, even during the speed tran-sient caused by the torque step, the estimated speed follows thereal one very well.


Fig. 14. Reference, estimated, measured speed, and speed estimation error during zero-speed operation at no-load with the classic full-order observer (experiment).

D. Zero-Speed Operation

Finally, to test the zero-speed operation capability of the ob-server, the drive has been operated for 60 s fully magnetized atzero-speed with no-load. Fig. 13(a), which shows the reference,estimated, measured speed and position during this test showsthe zero-speed capability of this observer, and highlights a notperceptible movement of the rotor during this test, which is con-firmed from the graph of the measured position. The same kindof test has been performed at the constant load torque of 5 Nm.Fig. 13(b) shows the reference, estimated, measured speed andposition during this test, and highlights that the measured speedis in average close to zero and the rotor has an undesired angularmovement of 2 rad, achieved in 60 s with a constant appliedload torque of 5 Nm. This is the ultimate working condition atzero-speed. Above 5 Nm load torque, the rotor begins to moveand instability occurs. For comparison reasons, Fig. 14 showsthe reference, estimated, measured speed, and the instantaneousspeed estimation error obtained with the classic full-order ob-server [8] at zero-speed with no-load. The classic observer atalmost 15 s after the magnetization of the machine, has an un-stable behavior and the machine eventually runs at 45 rad/swith a mean speed estimation error of 13.74 rad/s. The com-parison shows a better accuracy in the speed estimation of theMCA EXIN + reduced order observer than the classic full-orderadaptive observer, which has an unstable behavior after a fewseconds.

VII. CONCLUSION

This paper presents a new sensorless technique which is basedon a reduced order observer where the speed is estimated bya new neural LSs-based technique, the MCA EXIN + neuron.

This work deals with those sensorless techniques of inductionmachine drives based on the fundamental harmonic of the mmf.In particular, it is in the framework of previous LSs based sen-sorless techniques developed by the authors. However, the targetof this work is the design of an observer with performances com-parable to those obtainable with the full-order Luenberger ob-server, but with lower computational burden. The main originalaspects of this work are the following: 1) the development of twooriginal choices of a gain matrix of the observer, one of which(the FPP choice) ensures the poles of the observer to be fixed onone point of the real axis, in spite of the variation of the speedof the motor, with a resulting dynamic behavior of the flux es-timation of the observer independent of the rotor speed and 2)the adoption of a completely new speed estimation law basedon the MCA EXIN + neuron, which guarantees lower operatingspeed at no-load and rated load, good estimation accuracy alsoin speed transient and correct zero-speed operation. The choiceof the MCA EXIN + neuron allows the observer to take intoconsideration the measurement flux modeling errors, which in-fluence the accuracy of the speed estimation.

A suitable test setup has been developed for the experimentalassessment of the methodology. An experimental compar-ison with the classic full-order observer has shown that theMCA EXIN + reduced order observer can work correctlydown to 3 rad/s (28.65 rpm), while the classic full-order ob-server presents a worse speed estimation accuracy at 4 rad/s(38.19 rpm). Moreover, the MCA EXIN + reduced orderobserver works properly at zero-speed without load and withmedium/low loads, whereas the classic full-order observer hasnot the same performance, at least with the observer tuningproposed in [8].


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Maurizio Cirrincione (M’03) received the Laureadegree in electrical engineering from the Politecnicoof Turin, Turin, Italy, in 1991 and the Ph.D. degreein electrical engineering from the University ofPalermo, Palermo, Italy.

From 1996 to 2005, he has been a Researcher atthe Section of Palermo, ISSIA-CNR (Institute onIntelligent Systems for the Automation), Palermo.Since 2005, he has been a Full Professor of Con-trol Systems at the Technological University ofBelfort-Montbéliard, France His current research

interests are neural networks for modeling and control, system identification,intelligent control, electrical machines, and drives.

Dr. Cirrincione was awarded the prize “E.R.Caianiello” for the Best ItalianPh.D. Thesis on neural networks.


Marcello Pucci (M’03) received the Laurea degreeand Ph.D. degree in electrical engineering from theUniversity of Palermo, Palermo, Italy, in 1997 and2002, respectively.

In 2000, he was a host student at the Institut ofAutomatic Control, Technical University of Braun-schweig, Germany, working in the field of control ofAC machines. Since 2001, he has been a Researcherat the Section of Palermo, ISSIA-CNR (Institute onIntelligent Systems for the Automation), Palermo.His current research interests are electrical machines,

control, diagnosis and identification techniques of electrical drives, intelligentcontrol, and power converters.

Giansalvo Cirrincione (M’03) received the Laureadegree in electrical engineering from the Politec-nico of Turin, Turin, Italy, in 1991 and the Ph.Ddegree from the Laboratoire d’Informatique etSignaux (LIS) de l’Institut National Polytechniquede Grenoble (INPG), Grenoble, France, in 1998.

He was a Postdoctoral at the Department of Sig-nals, identification, system theory and automation(SISTA), Leuven University, Leuven, Belgium,in 1999 and since 2000, he has been an AssistantProfessor at the University of Picardie-Jules Verne,

Amiens, France. Since 2005, he has been Visiting Professor at the Section ofPalermo, ISSIA-CNR (Institute on Intelligent Systems for the Automation),Palermo, Italy. His current research interests are neural networks, data analysis,computer vision, brain models, and system identification.

Gérard-André Capolino (A’77–M’82–SM’89–F’02) received the B.Sc. degree in electrical en-gineering from Ecole Supérieure d’Ingénieurs deMarseille, Marseille, France, in 1974, the M.Sc.degree from Ecole Supérieure d’Electricité, Paris,France, in 1975, the Ph.D. degree from the UniversityAix-Marseille I, Marseille, in 1978, and the D.Sc.degree from the Institut National Polytechnique deGrenoble, Grenoble, France, in 1987.

In 1978, he joined the University of Yaoundé(Cameroon) as an Associate Professor and Head

of the Department of Electrical Engineering. From 1981 to 1994, he hasbeen Associate Professor at the University of Dijon, Dijon, France, and theMediterranean Institute of Technology, Marseille, where he was founder andDirector of the Modeling and Control Systems Laboratory. From 1983 to1985, he was Visiting Professor at the University of Tunis, Tunisia. From 1987to 1989, he was the Scientific Advisor of the Technicatome SA Company,Aix-en-Provence, France. In 1994, he joined the University of Picardie “JulesVerne,” Amiens, France, as a Full Professor, Head of the Department ofElectrical Engineering (1995–1998), and Director of the Energy Conversionand Intelligent Systems Laboratory (1996–2000). He is now Director of theGraduate School in Electrical Engineering, University of Picardie “JulesVerne.” In 1995, he was a Fellow European Union Distinguished Professorof Electrical Engineering at Polytechnic University of Catalunya, Barcelona,Spain. Since 1999, he has been the Director of the Open European Labora-tory on Electrical Machines (OELEM), a network of excellence between 50partners from the European Union. He has published more than 250 papersin scientific journals and conference proceedings since 1975. He has been theAdvisor of 13 Ph.D. and numerous M.Sc. students. In 1990, he has foundedthe European Community Group for teaching electromagnetic transients andhe has coauthored the book Simulation & CAD for Electrical Machines, PowerElectronics and Drives (ERASMUS Program Edition). His research interestsare electrical machines, electrical drives power electronics, and control systemsrelated to power electrical engineering.

Prof. Capolino is the Chairman of the France Chapter of the IEEE PowerElectronics, Industrial Electronics and Industry Applications Societies and theVice-Chairman of the IEEE France Section. He is also member of the AdComof the IEEE Industrial Electronics Society. He is the co-founder of the IEEEInternational Symposium for Diagnostics of Electrical Machines Power Elec-tronics and Drives (IEEE-SDEMPED) that was held for the first time in 1997.He is a member of steering committees for several high reputation internationalconferences. Since November 1999, he has been Associate Editor of the IEEETRANSACTIONS ON INDUSTRIAL ELECTRONICS.

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