Sensor Less Control Of Im By Reduced Order Observer With Mca Exin + Based Adaptive Speed Estimation

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Sensorless Control of Induction Motors by Reduced Order Observer With MCA EXIN + Based Adaptive Speed Estimation Maurizio 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 highperformance induction machine drives based on neural networks. It proposes a reduced order speed observer where the speed is estimated with a new generalized least-squares technique based on the minor component analysis (MCA) EXIN + neuron. With this regard, the main original aspects of this work are the development of two original choices of the gain matrix of the observer, one of which guarantees the poles of the observer to be fixed on one point of the negative real semi-axis in spite of rotor speed, and the adoption of a completely new speed estimation law based on the MCA EXIN + neuron. The methodology has been verified experimentally on a rotor flux oriented vector controlled drive and has proven to work at very low operating speed at no-load and rated load (down to 3 rad/s corresponding to 28.6 rpm), to have good estimation accuracy both in speed transient and in steady-state and to work correctly at zero-speed, at no-load, and at medium loads. A comparison with the classic full-order adaptive observer under the same working conditions has proven that the proposed observer exhibits a better performance in terms of lowest working speed and zero-speed operation.

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Index Terms—Field oriented control, induction machines, leastsquares (LS), neural networks, reduced order observer, sensorless control.

NOMENCLATURE

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Space vector of the stator voltages in the stator reference frame. Direct and quadrature components of the stator voltages in the stator reference frame. Space vector of the stator currents in the stator reference frame.

Direct and quadrature components of the stator currents in the stator reference frame. Direct and quadrature components of the stator currents in the rotor-flux oriented reference frame. Space vector of the stator flux-linkages in the stator reference frame. Direct and quadrature component of the stator flux linkage in the stator reference frame. Space vector of the rotor flux-linkages in the stator reference frame. Direct and quadrature component of the rotor flux linkage 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. Rotor time constant. Total leakage factor. Number of pole pairs. Angular rotor speed (in mechanical angles). Angular rotor speed (in electrical angles per second). Sampling time of the control system. I. INTRODUCTION

Manuscript received June 15, 2005; revised October 28, 2005. Abstract published on the Internet November 30, 2006. The work of G. Cirrincione has been supported under a grant from ISSIA-CNR, Italy in the framework of the MIUR project n. 211 entitled “Automazione della gestione intelligente della generazione distribuita di energia elettrica da fonti rinnovabili e non inquinanti e della domanda di energia elettrica, anche con riferimento alle compatibilità interne e ambientali, all’affidabilità e alla sicurezza.” M. Cirrincione was with the ISSIA-CNR, Section of Palermo, Viale delle Scienze snc, 90128 Palermo, Italy. He is now with the Université de Technologie de Belfort-Montbeliard (UTBM), 90010 Belfort Cedex, France (e-mail: [email protected]). M. Pucci is with the ISSIA-CNR Section of Palermo, Institute on Intelligent 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 Engineering, University of Picardie-Jules Verne, 80039 Amiens, France (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TIE.2006.888776

O FAR, sensorless control of induction motors [1]–[3] has been faced with two kinds of methods: those which employ the dynamic model of the induction machine based on the fundamental spatial harmonic of the magnetomotive force (mmf) and those 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], even based on neural networks [6], [7], full-order Luenberger adaptive observers [8]–[11], also with neural networks [12], and reduced order speed observers [13]–[15]. Among the second, some are based on continuous high-frequency signal injection [16]–[18] and some on test vectors [19], [20]. This last kind of methodologies, even if is very promising for position sensorless control thanks to the capability of tracking saliencies, either the saturation

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

of the main flux or the rotor slotting saliencies, is usually machine dependant and sometimes requires a suitable machine design (open or semi-closed rotor slots for rotor slotting tracking). This is not the case for the first kind of techniques, among which the full-order Luenberger observer gives very interesting performances, even if with a significant computational requirement. In this regard, an improvement of this observer based on total least-squares (TLSs) speed estimation has been proposed by the authors [12], which has shown a good performance in the speed estimation during transients, at very low-speed (down to 0.5 rad/s corresponding to 4.77 rpm) and at zero-speed. Moreover, its stability features in regenerating mode at low-speed have been analyzed theoretically and tested experimentally. The main goal of this work is the design of an adaptive speed observer, with a performance comparable to that obtainable with the full-order Luenberger observer. This is achieved by a reduced-order rotor flux observer, which results in lower complexity and computational burden. In fact, the reduced order observer has to solve a problem of order two, while the full-order observer of order four. Particularly, this paper presents a new sensorless technique based on the reduced order observer, where the speed is estimated on the basis of a new generalized leastsquares technique, the MCA EXIN + neuron. Moreover, this work also deals with the development of two original choices of the gain matrix of the observer, one of which ensures that the poles of the observer be fixed on one point of the negative real semi-axis, in spite of the variation of the speed of the motor, with a consequent dynamic behavior of the flux estimation independent of the rotor speed. The adoption of the completely new speed estimation law, based on the MCA EXIN + neuron, ensures very low operating speed at no-load and rated load (down to 3 rad/s corresponding to 28.6 rpm), good estimation accuracy also in speed transient and correct zero-speed operation. Different from [13], which employs a combination of the reduced order observer, used as reference model, and the simple current model, used as adaptive model, to estimate the rotor speed, here only the reduced order observer is employed, while the rotor speed is estimated by the MCA EXIN + algorithm, just on the basis of the stator voltage and current measurements and the estimated flux. It should be remarked that the MCA EXIN + scheduling is more powerful than the other existing techniques, even least-squares based, in terms of smoother convergence transient, shorter settling time, and better accuracy [21]. In addition, the choice of MCA EXIN + neuron allows to take into consideration the measurement flux modeling errors, which influence the accuracy of the speed estimation, since it is inherently robust to the this source of errors. This speed observer has been tested experimentally in a rotor-flux-oriented field oriented control (FOC) drive and compared with the classic full-order adaptive observer of [8]. Also, this paper shows a complexity analysis of the proposed methodology with respect to other observers, both classic and based on neural networks. II. LIMITS OF MODEL-BASED SENSORLESS TECHNIQUES A. Open-Loop Integration One of the main problems of some speed observers, when adopted in high-performance drives, is the open-loop integration

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in presence of DC biases. The speed observers suffering from this problem are those which employ open-loop flux estimators, e.g., open-loop speed estimators and those MRAS systems where the reference model is an open-loop flux estimator [5]–[7], while speed estimators employing closed-loop flux integration, like the classic full-order adaptive observer [8], do not have this problem. In particular, DC drifts are always present in the signal before it is integrated, which causes the integrator to saturate with a resulting inadmissible estimation error, and also after the integration because of the initial conditions [22]. In general, low-pass (LP) filters with very low cutoff frequency are used instead of pure integrators; however, since they fail in low-frequency ranges, close to their cutoff frequency, some alternative solutions have been devised to overcome this problem, e.g., the integrator with saturation feedback [22], the integrator based on cascaded LP filters [23], [24], the integrator based on the offset vector estimation and compensation of residual estimation error [4] and the adaptive neural integrator [25]. With regard to the reduced order adaptive observer, the problem of the DC drift in the integrand signal exists only for those choices of the observer gain matrix which transform, at certain working speeds of the machine, the reduced order observer in an open-loop flux estimator, like the current voltage model (CVM) in [26] which gives rise to a smooth transition from the “current” to the “voltage” model according to the increase of the rotor speed (see Section III). With such a choice, below a certain speed and above another one, the observer behaves like a simple open-loop estimator, and therefore suffers from the mentioned problem. It is not the case of the proposed gain matrix choice, which is described in Section III. B. Inverter Nonlinearity The power devices of an inverter present a finite voltage drop in “on-state,” due to their forward nonlinear characteristics. This voltage drop has to be taken into consideration at low-frequency (low-voltage amplitude) where it becomes comparable with the stator voltage itself, giving rise to distortion and discontinuities in the voltage waveform. Here, the compensation method proposed by [4] has been employed. This technique is based on modeling the forward characteristics of each power device with a piecewise linear characteristics, with an average threshold voltage and with an average differential resistance. C. Machine Parameter Mismatch A further source of error in flux estimation is the mismatch of the stator and rotor resistances of the observer with their real values because of the heating/cooling of the machine. The load dependent variations of the winding temperature may lead up to 50% error in the modeled resistance. Stator and rotor resistances should be, therefore, estimated online and tracked during the operation of the drive. A great deal of online parameter estimation algorithms have been devised [4], [8], requiring low complexity and reduced computational burden when used in control systems. In any case, it should be emphasized that steady-state estimation of the rotor resistance cannot be performed in sensorless drives, thus rotor resistance variations must be deduced from stator resistance estimation. In the case under study, differently from [13] where the allocation of the poles of the observer has been chosen to minimize the sensitivity of the ob-

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

server to the rotor resistance variations, the gain matrix choice has been chosen (see Section III) to make the dynamic of the flux estimation constant, by fixing the position of the poles of the observer in a precise point of the negative real semi-axis, in spite of the variation of the speed of the motor, and therefore the sensitivity to the rotor resistance variations has not been considered as a design criterion of the observer. No stator resistance estimation algorithm [4] has been used, since the goal is to develop one observer which is not too complex and computationally cumbersome. III. MCA EXIN + REDUCED ORDER OBSERVER A. Reduced Order Observer Equations The matrix equations of the reduced order flux observer, with a voltage error used for corrective feedback are [13], [26], [27]

(2e) where all space vectors are in the stator reference frame: stator current vector, stator voltage vector, rotor flux vector, ,

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is the rotor speed, and

is the observer gain matrix. For the list of parameters, see the Nomenclature. The proposed MCA EXIN + reduced order observer is based on the classical reduced order flux observer structure, while a new speed estimation law is proposed, which is based on the MCA EXIN + technique. Fig. 1 shows the block diagram of the proposed reduced order observer, whose equations are described in 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 vectors . Moreover, since the gain matrix is time dependant, the correction term which takes into consideration the time derivais also included in the scheme. tive of the gain matrix B. Proposed Choice of the Gain Matrix of the Observer

(1) where

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

(2a)

(2b) (2c) (2d)

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

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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. The FPP choice is proposed as the best for sensorless control for the reasons explained beneath. The FPP gain matrix choice permits the position of the poles of the observer to be fixed on the negative part of the real semiaxis at distance from the origin, according to the variation of the rotor speed, to ensure the stability of the observer itself. and The proposed gain choice is obtained by imposing and gives

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

C. Other Gain Matrix Choices Fig. 3 shows the observer pole locus, the amplitude of poles versus the rotor speed, and the damping factor versus the rotor speed, obtained with five different gain choices of the matrix gain; the first has been developed by the authors and the other four have been proposed in literature. 1) Choice 1: A criterion for choosing the locus of the observer poles is to make their amplitude constant with respect for the rotor speed. This criterion leads either to the above proposed or, if , to a semicircle pole solution if locus with centre in the origin, with radius and lying in the complex semiplane with negative real part. In this last case, the position of the poles varies with the rotor speed and therefore to must be properly avoid instability, a maximum rotor speed chosen, in correspondence to which the poles of the observer lie on the imaginary axis. The matrix gain choice which guarantees this condition is the following:

(4) Fig. 2 shows the observer pole locus, the amplitude of poles versus rotor speed, the damping factor versus rotor speed, and versus ) as obtained with the FPP gain gain locus ( matrix choice. It shows that this solution permits to keep the dynamic of the flux estimation constant, because the amplitude of the poles is the constant and the damping factor is always equal to 1. This last feature is particularly important for sensorless control in high-speed range: in fact, most of the choices of the matrix gain cause a low damping factor at high rotor speed, which can easily cause instability phenomena. Actually, higher values of the damping factor result in low sensitivity to estimated speed perturbations or parameter variations.

(5) This matrix gain is dependant on the rotor speed, and therefore . With such a the observer requires the correction term matrix gain choice, the poles are complex with a constant amplitude , 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)

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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 are imaginary with magnitude increasing with the rotor speed and the damping factor drastically reducing at increasing speed, from 1 at zero-speed to about 0 at rated speed and above. This choice cancels the contribution of the stator current from the observer (1). It has the advantage that the gain matrix is not dependent on the rotor speed, and therefore is simpler than both the FPP choice and the others; for the same reason, it does not . even require the correction term 3) Choice 3: Proposes the following matrix gain choice [13]

This matrix gain is dependant on the rotor speed, and therefore . With such a the observer requires the correction term matrix gain choice, the poles of the observer are real and lie on the negative real semi-axis with magnitude increasing with the speed and a damping factor constant with rotor speed and always equal to 1. 5) Choice 5: Proposes the following matrix gain choice [26]: for for for

(7) This matrix gain is dependant on the rotor speed, and therefore the observer requires the correction term . With such a matrix gain choice, the poles of the observer are complex with magnitude increasing with the speed and the damping factor reducing at increasing speed, from 1 at zero-speed to about 0.7 at rated speed and above. However, in [13], it is claimed that this matrix gain choice reduces the sensitivity of the observer to rotor resistance variations. 4) Choice 4: Proposes also the following matrix gain choice [30]:

(8)

(9) and to the rotor speed, Assigned two threshold values the gain matrix has three different values. Below , no correction feedback is given to the observer and it behaves as the simple “current” model of the induction machine, based on its rotor equations. Above , the correction feedback given to the observer is a constant multiplied with the identity matrix, and it behaves as the simple “voltage” model of the induction maand , the chine, based on its stator equations. Between gain matrix linearly varies from the two limit conditions. For this 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 rotor speed. With such a choice, the poles of the observer are complex with magnitude first increasing and then decreasing with the rotor speed, and a damping factor drastically reducing at increasing speed, from 1 at zero-speed to about 0 at rated speed and above. As mentioned above, however, this solution makes the observer work as a simple open-loop estimator both at low and high speeds, with the consequent dc drift integration problems. This is not the case neither of the FPP choice nor the other and . four ones. See [26] for the choice of

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TABLE I ISSUES OF ALL MATRIX GAIN CHOICES

A slightly different approach is presented in [35], which proposes an observer where the rotor flux is estimated as the sum of a high-pass filtered and a LP filtered flux, estimated, respectively, by the “voltage” and the “current” models. This leads to a correction term which depends, differently from the other choices above, on the difference between the two estimated fluxes, which are subsequently processed by a PI controller. The resulting observer presents a smooth transition between “current” and “voltage” model flux estimation which is ruled by the closed-loop eigenvalues of the observer, determined by the parameters of the PI controller. At rotor speeds below the bandwidth of the observer, its sensitivity to the parameters correspond to that of the “current” model, while at high speeds its sensitivity corresponds to that of the “voltage model.” In this sense, it behaves like choice 5. Table I summarizes the features of all six choices, mainly focusing on the variation of the observer pole amplitude with the rotor speed, the variation of the damping factor with the rotor speed, the dependance on the matrix gain by the rotor speed, and the DC drift integration problems. From the standpoint of the pole amplitude variation, the FPP choice and choice 1 are the best, since they permit the amplitude to be constant; choices 2, 4, and 5 permit a low variation of the pole amplitudes, while choice 3 causes a high variation. As for the damping factor variation, the FPP choice and choice 4 are the best since they keep always equal to 1; choice 3 permits a low decrease of at increasing rotor speeds, while choices 1, 2, and 5 cause a strong reduction of . As for the dependance of on the rotor speed, all the choices except choice 2 suffer from this variation. As for the DC drift integration problems, only choice 5 presents this negative issue, especially at low and high rotor speeds. For the above reasons, FPP choice for the gain matrix is the best among the six presented here for sensorless control, and has been therefore adopted in the following experimental tests. IV. MCA EXIN + BASED SPEED ESTIMATION The MCA EXIN + based speed estimation derives from a modification of the complete state equations of the induction motor [8], [12] so that it exploits the two first scalar equations to estimate the rotor speed, as shown below in discrete form for digital implementation, as shown in (10) at the bottom of the is the sampling time of the control algorithm and is page,

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

the current time sample. Note that the is applied on the stator voltage space vector to mean that it is computed from the DC link voltage considering the blanking time of the inverter and the voltage drop on the power devices of the inverter on the basis of the method proposed in [4]. The same symbol on the rotor flux indicates the estimated flux. This matrix equation, which can be written more generally , can be solved for by using LS techniques. In as particular, in literature there exist three LS techniques, i.e., the ordinary 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, this hypothesis does not always correspond to the reality: modeling errors, measurement errors, etc., can cause errors also in . Therefore, in real-world applications, the employment of TLSs would be very often better, as it takes also into consideration the errors in the data matrix. ), which is the case In the monodimensional case ( under study, the resolution of the LS problem consists in determining the angular coefficient of the straight line of equation . The LS technique solves this problem by calculating which minimizes the sum of squares of the disthe value of tances among the elements , with , and the line itself. Fig. 4 shows the difference among the OLS, TLS, and DLS. OLS minimizes the sum of squares of the distances in the direction (error only in the observation vector). TLS minimizes the sum of squares in the direction orthogonal to the line (for this reason, TLS is also called orthogonal regression),

(10)

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while DLS minimizes the sum of squares in the direction (errors only in the data matrix). In particular, it must be expected that, in absence of noise, the results obtained with TLS are equal to those obtained with OLS; however, in presence of increasing noise, the performance of TLS remains higher than that of OLS, as TLS is less sensitive to noise. For these reasons, the TLS algorithm is particularly suitable for estimation processes in which data are affected by noise or modeling errors; this is certainly the case of speed estimation, where the estimated rotor flux, present in , 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 capable to solve a TLS problems recursively online, has been successfully adopted in MRAS speed observers [6]. In this work, a new generalized LS technique, the MCA EXIN + (minor component analysis) neuron, is used for the first time to compute the rotor speed. This technique is a further improvement of the TLS EXIN 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 parameterized formulation (generalized TLS, GeTLS EXIN) of an error function whose minimization yields the corresponding solution. This error is given by

This eigenvector can be found by minimizing the following error function: (14) which is the Rayleigh quotient of . Hence, the TLS solution is found by normalizing in order to have the last com. Resuming, TLS can be solved by applying ponent equal to MCA to the augmented matrix . [21] also proves the equivalence between MCA and DLS in a very specific case. Indeed, and (DLS) in (11) yields (14) with . setting Hence, the MCA for the matrix is equivalent to the DLS of the system composed of as the data matrix and of a null observation vector. In particular, TLS by using MCA can be solved and with . The by using (12) and (13) with advantage of this approach is the possibility of using the scheduling. This technique is the learning law of the MCA EXIN + neuron [21], which is an iterative algorithm from a numerical point of view. It yields better results than other MCA iterative techniques because of its smoother dynamics, faster convergence, and better accuracy, which are the consequence of the toward the solution fact that the varying parameter drives in a smooth way. These features allow higher learning rates for accelerating the convergence and smaller initial conditions (in [21], it is proven that very low initial conditions speed up the algorithm).

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

(12) where (13) where is the learning rate, is the row of fed at instant , and is the corresponding observation. The GeTLS EXIN learning law becomes the TLS EXIN learning law for equal to 0.5 [38]. The TLS EXIN problem can also be solved by scheduling the value of the parameter in GeTLS EXIN, e.g., it can vary linearly from 0 to 0.5, and then remains constant. This scheduling improves the transient, the speed, and the accuracy of the iterative technique [38]. [21] shows that a TLS problem corresponds to a MCA problem and is equivalent to a particular as the augmented maDLS problem. Indeed, define trix built by appending the observation vector to the right of the data 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 eigenvector associated to the smallest eigenvalue of (MCA).

A. Control System The MCA EXIN + reduced order observer has been tested on a “voltage” rotor flux oriented vector control scheme [6], [7] (Fig. 5). For control purposes, the estimated speed has been fedback to a PI speed controller and instantaneously compared with the measured one to compute the speed error at each instant and in each working condition. Inside the speed loop there is the loop. On the direct axis, the voltage is controlled at a constant value to make the drive automatically work in the field-weakening region. Inside the loop are, respectively, the loop. The voltage source inrotor flux-linkage loop and the verter (VSI) is driven by an asynchronous space vector modula. The tion algorithm with a switching frequency phase voltages have been computed on the basis of the instantaneous measurement of the DC link voltage and the switching state of the inverter. Moreover, the method proposed in [4] for the compensation of the on-state voltage drops of the inverter devices has been employed. In the case under study, the employed IGBT modules, which are the Semikron SMK 50 GB 123, have and with an been modeled with a threshold voltage . Finally, the samaverage differential resistance pling frequency of the acquired signals has been set to 10 kHz, at which also all control loops work. For reproducibility reasons, Table II shows all the parameters of the control system adopted for the experimental implementation. As for the integration of state (1) of the reduced order obin the conserver in the discrete domain, the pure integrator tinuous domain has been replaced by the following discrete

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Fig. 5. Implemented FOC scheme. TABLE II PARAMETERS OF THE CONTROL SYSTEM

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

where is the integrator input at the current time sample and is the corresponding integrator output. This formula is the sum of a simple Euler integrator and an additional term taking into consideration the values of the integrand variables in two previous time steps; it guarantees a correct integration of the state equations, and thus a correct flux estimation with the differently from the simple forward Euler adopted value of integrator . With reference to the MCA EXIN + reduced order observer, the only two parameters set by the user have been given the and (kept constant). following values: With reference to the parameter , the following scheduling has been adopted: at each speed transient commanded by the control system, a linear variation of from 0 to 1 in 0.3 s has been given. This scheduling has been implemented in software by a discrete integrator with the constant value 1/0.3 in input, which permits the output to get the value 1 in 0.3 s with linear law, and whose output is reset to zero at each change of the reference speed of the drive. With the above scheduling, the flatness of the OLS error surface around its minimum, which prevents the algorithm from being fast, is smoothly replaced by a ravine in the corresponding DLS error surface, which speeds up the convergence to the solution [minimum of (14)] as well as its final accuracy. Fig. 6 shows the error surfaces obtained with (OLS) and (DLS) and the MCA EXIN + error trajectory versus the two components of with regard to the DLS error surface, obtained when a speed step reference from 0 to 150 rad/s has been given to the drive without load. It should be remarked that the proposed speed observer does not need any LP filtering of the estimated speed to be fed back to the control system, with consequent higher bandwidth of the speed loop.

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

TABLE III PARAMETERS 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 parameters shown in Table IV. • An electronic AC-DC converter (three-phase diode rectifier and a full-bridge DC-DC converter) for supplying the DC machine of rated power 4 kVA. • A dSPACE card (DS1103) with a PowerPC 604e at 400 MHz and a floating-point DSP TMS320F240.

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TABLE IV PARAMETERS OF THE DC MACHINE

C. Hardware Choice With regard to the hardware implementation of the proposed sensorless control technique, a floating point DSP (TMS320F240) has been employed, since its programming needs a lower development time than a fixed point DSP. In general, the choice between floating or fixed point DSPs is highly dependent on the application at hand, its complexity, and its cost reduction needs. For industry products, the production volumes play a relevant role in this choice: for high volumes, the lower cost of a fixed point DSP justifies the amount of any nonrecurring engineering (NRE) cost [39], like control software development, while for low volumes, the NRE cost dominates and thereby floating point choice seems to be the best, as it reduces the development costs. In the industrial drives market, where high production volumes dominate, the cost issue is important, and thus the potential implementation of each technique on fixed point DSP is a real advantage. The big difference between floating and fixed point DSPs is the coding of the numbers. Fixed point chips, differently from floating point ones, need a scaling factor to be managed by the user. If all variables of the program are normalized between and 1, not even the scaling factor is needed. Moreover, fixed point DSPs are also capable of a finer resolution than fixed point ones (of the same word length) because of the extra bits in the mantissa. In drive control, the development of the entire control system, including the observer, can be performed by working in per-unit (p.u.), i.e., by dividing each values by the corresponding base value: this assumption highly simplifies the transport of the software from floating point to fixed point format, exploiting also its better resolution. In addition to this, many development tools have been recently proposed to convert control software from floating point to fixed point representation [39]. Some specific suggestions for the implementation on fixed point DSPs of an MRAC speed controller for a FOC induction motor drive with a LSs-based parameter estimator are given in [40]. [40] explicitly addresses the difficulties associated with the large dynamic range of the covariance matrix (used by the LSs algorithm) with respect to the finite length of the DSP word. The proposed solution is the adoption of a double-word fixed point representation, which increases the dynamic range of the processed data, and consequently reduces the rounding/truncation errors, at the expense of higher execution time. With regard to the proposed technique, the state equations of the reduced order observer can be implemented in software by simple operations (sums and multiplications/divisions) between quantities in p.u. With specific regard to the MCA EXIN + algorithm, any quantization error, which is larger in fixed point than in floating point DSPs, can degradate its solution (typical of all of gradient-based algorithms), with respect to the performance

achievable in infinite precision (see [36] for more details). This kind of error accumulates in time without bound, leading in the long run (ten of million of iterations) to an eventual overflow (the so called numerical divergence). The source of this divergence is both the analog-to-digital (A/D) conversion and the finite word length used to store all internal algorithmic quantities. The degradation of the solution is proportional to the conditioning of the input, i.e., to the eigenvalue spectrum of the input autocorrelation matrix [36]. Decreasing the learning rate in the infinite precision algorithm leads to improved performance. Neverthless, this decrease increases the deviation from infinite precision performance, while its increase magnifies numerical errors, so a tradeoff is required [41]. A technique for avoiding overflows caused by this kind of divergence, at the expense of some increase of complexity and small degradation of the solution, is the technique called leakage (see [36] for its details). Finally, the MCA EXIN + algorithm does not need particularly critical operations (the most complex operation is a dot product between vectors of dimension two) and explicitly employs neither the covariance matrix [40] nor its inverse computation, as needed in some versions of the recursive least-squares (RLSs). In any case, it should be remarked that, independently of the DSP choice, the elements of data matrix and the observation vector (both bidimensional vectors) processed by the MCA EXIN + algorithm must be properly scaled before processing, so that the estimated will result in a quantity ranging between and 1, otherwise, the effect of the parameter in (11) is null. This intrinsic algorithm demand further facilitates the potential conversion of the software into fixed point format. D. Computational Complexity From the computational point of view, the MCA EXIN + reduced order observer has been compared here with some neural network-based observers, in particular, the TLS EXIN full-order observer [12] and the TLS EXIN MRAS observer with adaptive neural integrator [6], and with the classic full-order observer [8]. This comparison has been done on the basis of the number of floating operations (flops) needed by each algorithm for every iteration. The comparison is shown in Table V. If the is not adopted in the proposed observer, correction term the most demanding observer is the TLS EXIN full-order observer which requires 126 flops + 3 IF-THEN instructions and then there is the MCA EXIN + reduced order speed observer with 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 of experimental tests performed with and without this term have shown that the MCA EXIN + reduced order observer can be imwithout a significant worsplemented either without the ening of the performance of the flux and speed estimation. Then, there is the TLS EXIN MRAS observer with the adaptive neural integrator 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 EXIN full-order observer in [12] and the classic full-order observer in [8] are implemented with a matrix gain correction term which is null, i.e., without any feedback term. The adoption of such a term would require the product of a (2 4) matrix for a (4 1)

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TABLE V COMPLEXITY 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 variable with the speed of the machine in dependence on the desired observer dynamics, and thus would highly increase the complexity in all of both observers. It can be concluded that with cases the reduced order observer requires fewer flops than the full-order ones. In any case, the total flops of the different observers is of the same order. VI. EXPERIMENTAL RESULTS The proposed MCA EXIN + reduced order observer has been verified in simulation and experimentally on a test setup (see

appendix). Moreover the results obtained experimentally have been compared with those obtained with the full-order classic adaptive observer proposed in [8]. The parameters of the fullorder classic observer are exactly the same as those suggested in [8]. Note also that in the full-order classic observer no compensation of the inverter nonlinearity has been considered. On the other hand, the parameter estimation method of [8] has been adopted in the full-order classic observer only. Simulations have been performed in Matlab®–Simulink®. With regard to the experimental tests the speed observer as well as the whole control algorithm have been implemented by software on the DSP of the dSPACE 1103.

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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 constant speed of 50 rad/s at no-load, then a zero step reference has been given and the drive has been operated at zero-speed for almost 2 s, and then a step speed reference of 50 rad/s at no-load has been given. Fig. 7 shows the waveforms of the reference, estimated (used in the feedback loop), and measured speed during this test. It shows that the measured speed and the estimated one both follow correctly the reference, even at zero-speed. Subsequently, the transient behavior of the observer at very low speeds has been tested. First, the drive has been given a set of 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 waveforms of the reference, estimated and measured speed during this test, and Table VI shows the 3 dB bandwidth of the speed loop versus the reference speed of the drive. Both Fig. 8 and Table VI show a very good dynamic behavior of the drive with a bandwidth which, however, decreases from 69.3 rad/s at the reference speed of 6 rad/s to 12.3 rad/s at 3 rad/s. This consideration is confirmed by Fig. 9 which shows the reference,

TABLE VI BANDWIDTH 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 5 to , and from 6 to . These last figures show that the drive is able to perform a speed reversal also at very low speeds, i.e., in very challenging conditions. However, it should be noted that the lower the speed reference, the higher the time needed for the speed reversal, as expected, because of the reduction of the speed bandwidth of the observer at decreasing speed references, which is typical of all observers. B. Low-Speed Limits In this test, the drive has been operated at a constant very low-speed (3 rad/s corresponding to 28.65 rpm), at no-load and rated load. Fig. 10 shows the reference, estimated, and measured speed during these tests. It shows that the steady-state speed

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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).

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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 (experimental).

estimation error is very low, equal to 2.45% at no-load and to 7.67% with rated load. For comparison reasons, the test has been also performed with the full-order classic observer [8]: Fig. 11 shows the reference, estimated, and measured speed, obtained

65 Nm

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% at no-load and 30.5% at rated load. The comparison shows a better

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

accuracy in the speed estimation of the MCA EXIN + reduced order observer than the one the classic full-order adaptive observer, even at a higher reference speed (4 rad/s against 3 rad/s). Below 2 rad/s, however, the speed accuracy estimation of the MCA EXIN + reduced order observer drastically reduces. C. Rejection to Load Perturbations In this test, to verify the robustness of the speed response of the proposed observer to a sudden torque perturbation, the drive

has been operated at the constant speed of 30 rad/s and two subsequent load torque square waveforms of amplitude have been applied. Fig. 12 shows the reference, measured, and estimated speed during this test, as well as the applied load torque, created by the torque of a controlled DC machine. These figures show that the drive response occurs immediately when the torque steps are given. Moreover, even during the speed transient caused by the torque step, the estimated speed follows the real one very well.

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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 observer, the drive has been operated for 60 s fully magnetized at zero-speed with no-load. Fig. 13(a), which shows the reference, estimated, measured speed and position during this test shows the zero-speed capability of this observer, and highlights a not perceptible movement of the rotor during this test, which is confirmed from the graph of the measured position. The same kind of test has been performed at the constant load torque of 5 Nm. Fig. 13(b) shows the reference, estimated, measured speed and position during this test, and highlights that the measured speed is in average close to zero and the rotor has an undesired angular movement of 2 rad, achieved in 60 s with a constant applied load torque of 5 Nm. This is the ultimate working condition at zero-speed. Above 5 Nm load torque, the rotor begins to move and instability occurs. For comparison reasons, Fig. 14 shows the reference, estimated, measured speed, and the instantaneous speed estimation error obtained with the classic full-order observer [8] at zero-speed with no-load. The classic observer at almost 15 s after the magnetization of the machine, has an unstable behavior and the machine eventually runs at 45 rad/s with a mean speed estimation error of 13.74 rad/s. The comparison shows a better accuracy in the speed estimation of the MCA EXIN + reduced order observer than the classic full-order adaptive observer, which has an unstable behavior after a few seconds. VII. CONCLUSION This paper presents a new sensorless technique which is based on a reduced order observer where the speed is estimated by a new neural LSs-based technique, the MCA EXIN + neuron.

This work deals with those sensorless techniques of induction machine drives based on the fundamental harmonic of the mmf. In particular, it is in the framework of previous LSs based sensorless techniques developed by the authors. However, the target of this work is the design of an observer with performances comparable to those obtainable with the full-order Luenberger observer, but with lower computational burden. The main original aspects of this work are the following: 1) the development of two original choices of a gain matrix of the observer, one of which (the FPP choice) ensures the poles of the observer to be fixed on one point of the real axis, in spite of the variation of the speed of the motor, with a resulting dynamic behavior of the flux estimation of the observer independent of the rotor speed and 2) the adoption of a completely new speed estimation law based on the MCA EXIN + neuron, which guarantees lower operating speed at no-load and rated load, good estimation accuracy also in speed transient and correct zero-speed operation. The choice of the MCA EXIN + neuron allows the observer to take into consideration the measurement flux modeling errors, which influence the accuracy of the speed estimation. A suitable test setup has been developed for the experimental assessment of the methodology. An experimental comparison with the classic full-order observer has shown that the MCA EXIN + reduced order observer can work correctly down to 3 rad/s (28.65 rpm), while the classic full-order observer presents a worse speed estimation accuracy at 4 rad/s (38.19 rpm). Moreover, the MCA EXIN + reduced order observer works properly at zero-speed without load and with medium/low loads, whereas the classic full-order observer has not the same performance, at least with the observer tuning proposed in [8].

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REFERENCES [1] K. Rajashekara, A. Kawamura, and K. Matsuse, Sensorless Control of AC Motor Drives. Piscataway, NJ: IEEE Press, 1996. [2] P. Vas, Sensorless Vector and Direct Torque Control. Oxford, U.K.: Oxford Science, 1998. [3] Holtz, “Sensorless control of induction motor drives,” Proc. IEEE, vol. 90, pp. 1359–1394, Aug. 2002. [4] J. Holtz and Q. Juntao, “Drift- and parameter-compensated flux estimator for persistent zero-stator-frequency operation of sensorless-controlled induction motors,” IEEE Trans. Ind. Appl., vol. 39, pp. 1052–1060, Jul.-Aug. 2003. [5] C. Shauder, “Adaptive speed identification for vector control of induction motors without rotational transducers,” IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1054–1061, Sep./Oct. 1992. [6] M. Cirrincione, M. Pucci, G. Cirrincione, and G. A. Capolino, “A new TLS based MRAS speed estimation with adaptive integration for high performance induction motor drives,” IEEE Trans. Ind. Appl., pp. 1–22, Jul./Aug. 2004. [7] M. Cirrincione and M. Pucci, “An MRAS speed sensorless high performance induction motor drive with a predictive adaptive model,” IEEE Trans. Ind. Electron., vol. 52, pp. 532–551, Apr. 2005. [8] H. Kubota, K. Matsuse, and T. Nakano, “DSP-based speed adaptive flux observer of induction motor,” IEEE Trans. Ind. Appl., vol. 29, pp. 344–348, Mar./Apr. 1993. [9] H. Kubota, I. Sato, Y. Tamura, K. Matsuse, H. Ohta, and Y. Hori, “Stable operation of adaptive observer based sensorless induction motor drives in regenerating mode at low speeds,” in Proc. IAS Annu. Meeting, Oct. 2001, pp. 469–474. [10] H. Kubota, K. Matsuse, and Y. Hori, “Behavior of sensorless induction motor drives in regenerating mode,” in Proc. PCC , Japan, 1997, pp. 549–552. [11] C. Lascu, I. Boldea, and F. Blaabjerg, “A modified direct torque control for induction motor sensorless drive,” IEEE Trans. Ind. Appl., vol. 36, pp. 122–130, Jan.-Feb. 2000. [12] M. Cirrincione, M. Pucci, G. Cirrincione, and G. Capolino, “An adaptive speed observer based on a new total least-squares neuron for induction machine drives,” IEEE Trans. Ind. Appl., vol. 42, no. 1, pp. 89–104, Jan./Feb. 2006. [13] H. Tajima and Y. Hori, “Speed sensorless field-orientation of the induction machine,” IEEE Trans. Ind. Appl., vol. 29, no. 1, pp. 175–180, Jan./Feb. 1993. [14] Y.-N. Lin and C.-L. Chen, “Adaptive pseudoreduced-order flux observer for speed sensorless field-oriented control of IM,” IEEE Trans. Ind. Electron., vol. 46, pp. 1042–1045, Oct. 1999. [15] J. Song, K.-B. Lee, J.-H. Song, I. Choy, and K.-B. Kim, “Sensorless vector control of induction motor using a novel reduced-order extended Luenberger observer,” in Proc. Record IEEE Conf. Industry Appl., Oct. 2000, vol. 3, pp. 1828–1834. [16] P. L. Jansen and R. D. Lorenz, “Transducerless position and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Appl., vol. 31, pp. 240–247, Mar./Apr. 1995. [17] F. Briz, M. W. Degner, A. Diez, and R. D. Lorenz, “Static and dynamic behavior of saturation-induced saliencies and their effect on carrier–signal–based sensorless AC drives,” IEEE Trans. Ind. Appl., vol. 38, pp. 670–678, May/Jun. 2002. [18] N. Teske, G. M. Asher, M. Sumner, and K. J. Bradley, “Analysis and suppression of high-frequency inverter modulation in sensorless position-controlled induction machine drives,” IEEE Trans. Ind. Appl., vol. 39, pp. 10–18, Jan./Feb. 2003. [19] C. S. Staines, G. M. Asher, and M. Sumner, “Rotor position estimation for induction machines at zero and low frequency utilising zero sequence currents,” in Proc. Record IEEE 39th IAS Annu. Meeting Conf. Industry Appl. , Oct. 3–7, 2004, vol. 2, pp. 1313–1320. [20] J. Holtz and H. Pan, “Acquisition of rotor anisotropy signals in sensorless position control systems,” IEEE Trans. Ind. Appl., vol. 40, no. 5, pp. 1379–1387, Sep./Oct. 2004. [21] G. Cirrincione, “A Neural Approach to the Structure from Motion Problem,” Ph.D. dissertation, INPG (Institut National Polytechnique de Grenoble), Grenoble, France, 1998. [22] J. Hu and B. Wu, “New integration algorithms for estimating motor flux over a wide speed range,” IEEE Trans. Power Electron., vol. 13, pp. 969–977, Sep. 1998. [23] L. E. Borges de Silva, B. K. Bose, and J. O. P. Pinto, “Recurrentneural-network-based implementation of a programmable cascaded LP filter used in stator flux synthesis of vector-controlled induction motor drive,” IEEE Trans. Ind. Electron., vol. 46, pp. 662–665, Jun. 1999.

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[24] J. O. P. Pinto, B. K. Bose, and L. E. Borges de Silva, “A stator-flux-oriented vector-controlled induction motor drive with space-vector PWM and flux-vector synthesis by neural network,” IEEE Trans. Ind. Appl., vol. 37, no. 5, pp. 1308–1318, Sep./Oct. 2001. [25] M. Cirrincione, M. Pucci, G. Cirrincione, and G. A. Capolino, “A new adaptive integration methodology for estimating flux in induction machine drives,” IEEE Trans. Power Electron., vol. 19, pp. 25–34, Jan. 2004. [26] L. Harnefors, “Design and analysis of general rotor-flux-oriented vector control systems,” IEEE Trans. Ind. Electron., vol. 48, pp. 383–390, Apr. 2001. [27] G. C. Verghese and S. R. Sanders, “Observers for flux estimation in induction machines,” IEEE Trans. Ind. Electron., vol. 35, pp. 85–94, Feb. 1988. [28] R. Nilsen and M. P. Kazmierkowski, “Reduced-order observer with parameter adaption for fast rotor flux estimation in induction machines,” Proc. Inst. Elect. Eng. D, Control Theory Appl., vol. 136, no. 1, pp. 35–43, Jan. 1989. [29] ——, “New reduced-order observer with parameter adaptation for flux estimation in induction motors,” in Proc. IEEE Power Electron. Specialists Conf., Jun.-Jul. 29–3, 1992, vol. 1, pp. 245–252. [30] G. Franceschini, M. Pastorelli, F. Profumo, C. Tassoni, and A. Vagati, “About the gain choice of flux observer in induction servo-motors,” in Proc. Conf. Record IEEE Industry Appl. Soc. Annu. Meeting,, Oct. 7–12, 1990, vol. 1, pp. 601–606. [31] A. Damiano, G. Gatto, I. Marongiu, and A. Pisano, “Synthesis and digital implementation of a reduced order rotor flux observer for IM drive,” in Proc. IEEE ISIE, Bled, Slovenia, pp. 729–734. [32] C. Zell and A. Medvedev, “Reduced-order flux observers with arbitrary convergence rate,” in Proc. 4th IEEE Conf. Control Appl., Sep. 28–29, 1995, pp. 793–798. [33] S.-U. Kim, I.-W. Yang, E.-J. Lee, Y.-B. Kim, J.-T. Lee, and Y.-S. Kim, “Robust speed estimation for speed sensorless vector control of induction motors,” in Proc. Record IEEE Ind. Appl. Conf., Oct. 3–7, 1999, vol. 2, pp. 1267–1277. [34] C.-M. Lee and C.-L. Chen, “Observer-based speed estimation method for sensorless vector control of induction motors,” Proc. Inst. Elect. Eng. D, Control Theory Appl., vol. 145, no. 3, pp. 359–363, May 199. [35] P. J. Jansen and R. D. Lorenz, “Observer-based direct field orientation: Analysis and comparison of alternative methods,” IEEE Trans. Ind. Appl., vol. 30, pp. 945–953, Jul./Aug. 1994. [36] G. Cirrincione, M. Cirrincione, J. Hérault, and S. Van Huffel, “The MCA EXIN neuron for the minor component analysis: Fundamentals and comparisons,” IEEE Trans. Neural Netw., vol. 13, no. 1, pp. 160–187, Jan. 2002. [37] G. Cirrincione and M. Cirrincione, “Linear system identification by using the TLS EXIN neuron,” Neurocomputing, vol. 28, no. 1-3, pp. 53–74, Oct. 1999. [38] G. Cirrincione, M. Cirrincione, and S. Van Huffel, “The GeTLS EXIN neuron for linear regression,” in Proc. IJCNN, Como, Italy, Jul. 2000, pp. 285–289. [39] C. Inacio and D. Ombres, “The DSP decision: Fixed point or floating?,” IEEE SPECTRUM, vol. 33, no. 9, pp. 72–74, Sep. 1996. [40] L. Chen, J. C. Balda, and K. J. Olejniczak, “Model reference adaptive control-implementation considerations on an integer-based DSP,” in Proc. 30th IEEE Ind. Appl. Conf. IAS Annu. Meeting, Oct. 8–12, 1995, vol. 2, pp. 1612–1618. [41] R. D. Gitlin, J. E. Mazo, and M. G. Taylor, “On the design of gradient algorithms for digitally implemented adaptive filters,” IEEE Trans. Circuits Syst., vol. 20, no. 2, pp. 125–136, Mar. 1973.

Maurizio Cirrincione (M’03) received the Laurea degree in electrical engineering from the Politecnico of Turin, Turin, Italy, in 1991 and the Ph.D. degree in electrical engineering from the University of Palermo, Palermo, Italy. From 1996 to 2005, he has been a Researcher at the Section of Palermo, ISSIA-CNR (Institute on Intelligent Systems for the Automation), Palermo. Since 2005, he has been a Full Professor of Control Systems at the Technological University of Belfort-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 Italian Ph.D. Thesis on neural networks.

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Marcello Pucci (M’03) received the Laurea degree and Ph.D. degree in electrical engineering from the University of Palermo, Palermo, Italy, in 1997 and 2002, respectively. In 2000, he was a host student at the Institut of Automatic Control, Technical University of Braunschweig, Germany, working in the field of control of AC machines. Since 2001, he has been a Researcher at the Section of Palermo, ISSIA-CNR (Institute on Intelligent Systems for the Automation), Palermo. His current research interests are electrical machines, control, diagnosis and identification techniques of electrical drives, intelligent control, and power converters.

Giansalvo Cirrincione (M’03) received the Laurea degree in electrical engineering from the Politecnico of Turin, Turin, Italy, in 1991 and the Ph.D degree from the Laboratoire d’Informatique et Signaux (LIS) de l’Institut National Polytechnique de Grenoble (INPG), Grenoble, France, in 1998. He was a Postdoctoral at the Department of Signals, identification, system theory and automation (SISTA), Leuven University, Leuven, Belgium, in 1999 and since 2000, he has been an Assistant Professor at the University of Picardie-Jules Verne, Amiens, France. Since 2005, he has been Visiting Professor at the Section of Palermo, 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 engineering from Ecole Supérieure d’Ingénieurs de Marseille, Marseille, France, in 1974, the M.Sc. degree from Ecole Supérieure d’Electricité, Paris, France, in 1975, the Ph.D. degree from the University Aix-Marseille I, Marseille, in 1978, and the D.Sc. degree from the Institut National Polytechnique de Grenoble, 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 has been Associate Professor at the University of Dijon, Dijon, France, and the Mediterranean Institute of Technology, Marseille, where he was founder and Director of the Modeling and Control Systems Laboratory. From 1983 to 1985, he was Visiting Professor at the University of Tunis, Tunisia. From 1987 to 1989, he was the Scientific Advisor of the Technicatome SA Company, Aix-en-Provence, France. In 1994, he joined the University of Picardie “Jules Verne,” Amiens, France, as a Full Professor, Head of the Department of Electrical Engineering (1995–1998), and Director of the Energy Conversion and Intelligent Systems Laboratory (1996–2000). He is now Director of the Graduate School in Electrical Engineering, University of Picardie “Jules Verne.” In 1995, he was a Fellow European Union Distinguished Professor of Electrical Engineering at Polytechnic University of Catalunya, Barcelona, Spain. Since 1999, he has been the Director of the Open European Laboratory on Electrical Machines (OELEM), a network of excellence between 50 partners from the European Union. He has published more than 250 papers in scientific journals and conference proceedings since 1975. He has been the Advisor of 13 Ph.D. and numerous M.Sc. students. In 1990, he has founded the European Community Group for teaching electromagnetic transients and he has coauthored the book Simulation & CAD for Electrical Machines, Power Electronics and Drives (ERASMUS Program Edition). His research interests are electrical machines, electrical drives power electronics, and control systems related to power electrical engineering. Prof. Capolino is the Chairman of the France Chapter of the IEEE Power Electronics, Industrial Electronics and Industry Applications Societies and the Vice-Chairman of the IEEE France Section. He is also member of the AdCom of the IEEE Industrial Electronics Society. He is the co-founder of the IEEE International Symposium for Diagnostics of Electrical Machines Power Electronics and Drives (IEEE-SDEMPED) that was held for the first time in 1997. He is a member of steering committees for several high reputation international conferences. Since November 1999, he has been Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS.