Sensor Less Control of IM by Reduced Order Observer With MCA EXIN + Based Adaptive Speed Estimation

8/14/2019 Sensor Less Control of IM by Reduced Order Observer With MCA EXIN + Based Adaptive Speed Estimation

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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 Grard-Andr Capolino, Fellow, IEEE

AbstractThis 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 the

adoption 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 conditionshas proventhat theproposedobserver ex-hibits a better performance in terms of lowest working speed andzero-speed operation.

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

NOMENCLATURE

Space vector of the stator voltages in

the stator reference frame., Direct and quadrature components of

the stator voltages in the stator refer-

ence frame.Space vector of the stator currents in

the 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 compatibilit interne eambientali, allaffidabilit e alla sicurezza.

M. Cirrincione was with the ISSIA-CNR, Section of Palermo, Viale delleScienze snc, 90128 Palermo,Italy. He is nowwith the Universit 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 of

the stator currents in the stator refer-

ence frame., Direct and quadrature components of

the stator currents in the rotor-flux

oriented reference frame.Space vector of the stator flux-link-

ages 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 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 mechanical

angles).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] has

been faced with two kinds of methods: those which employthe dynamic model of the induction machine based on the funda-

mental 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

basedon 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 method-

ologies, even if is very promising for position sensorless control

thankstothecapabilityoftrackingsaliencies,eitherthesaturation

0278-0046/$25.00 2007 IEEE


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

ofthemainflux or therotorslottingsaliencies,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 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 the

authors [12], which has shown a good performance in the speed

estimationduring transients, at verylow-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 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-order

observer of order four. Particularly, this paper presents a newsensorless technique based on the reduced order observer, where

the speed is estimated on the basis of a new generalized least-

squares 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 inde-

pendent of the rotor speed. The adoption of the completely new

speed estimation law, based on the MCA EXIN + neuron, en-

sures very low operating speed at no-load and rated load (down

to 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 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 es-

timated flux. It should be remarked that the MCA EXIN + sched-

uling 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 ac-

curacy of the speed estimation, since it is inherently robust to the

this 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 observer

of[8]. Also, this paper shows a complexity analysis of the pro-

posed 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, whenadopted in high-performance drives, is the open-loop integration

in presence of DC biases. The speed observers suffering from

this problem are those which employ open-loop flux estimators,

e.g.,open-loopspeed estimatorsand thoseMRAS systems where

the reference model is an open-loop flux estimator [5][7], while

speed estimators employing closed-loopflux integration,like the

classic full-order adaptiveobserver[8], do nothavethis problem.

In particular,DC drifts arealways present in thesignal beforeit isintegrated, whichcausesthe integratorto 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 estima-

tion 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 matrixwhich transform, at certain working speeds of the machine, the

reduced order observer in an open-loop flux estimator, like the

currentvoltagemodel(CVM)in [26] whichgivesrisetoasmooth

transition from the current to the voltage model according

to the increase of the rotor speed (see Section III). With such a

choice, belowa certain speedand aboveanother one, theobserver

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 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 comparable

with the stator voltage itself, giving rise to distortion and dis-

continuities 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 mismatchof 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 estima-

tion algorithms have been devised [4], [8], requiring low com-

plexity 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 sen-

sorless drives, thus rotor resistance variations must be deduced

from 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-


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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 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 be

used in the observer scheme is

(4)

Fig. 2 shows the observer pole locus, the amplitude of poles

versus rotor speed, the damping factor versus rotor speed, and

gain locus ( versus ) as obtained with the FPP gain

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 sensor-

less 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 esti-mated speed perturbations or parameter variations.

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 ob-

server poles is to make their amplitude constant with respect for

the rotor speed. This criterion leads either to the above proposed

solution if or, if , to a semicircle pole

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

avoid instability, a maximum rotor speed must be properly

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:

(5)

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 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)


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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 boththe 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]

(7)


the observer requires the correction term . With such amatrix 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)


the observer requires the correction term . With such a

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

(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 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 ma-chine, based on its stator equations. Between and , the

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 com-

plex 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 prob-

lems. This is not the caseneither of the FPP choice nor the otherfour ones. See [26] for the choice of and .


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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 transi-

tion 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 rotorspeeds 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 fo-

cusing 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, 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 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

page, 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 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

as , can be solved for by using LS techniques. In

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.

In the monodimensional case ( ), which is the case

under 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 calculating

the value of which minimizes the sum of squares of the dis-

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 (er-

rors 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 TLSis less sensitive to noise. For these reasons, the TLSalgo-

rithm is particularly suitable for estimation processes in whichdata 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 ca-

pable to solve a TLS problems recursively online, has been suc-

cessfully adopted in MRAS speed observers [6]. In this work, a

new generalized LS technique, the MCA EXIN + (minor com-

ponent 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 parameter-

ized formulation (generalized TLS, GeTLS EXIN) of an error

function whose minimization yields the corresponding solution.

This error is given by

(11)

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 in-

stant , and is the corresponding observation. The GeTLSEXIN 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

DLS problem. Indeed, define as the augmented ma-

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 eigen-vector associated to the smallest eigenvalue of (MCA).

This eigenvector canbe found by minimizing the following error

function:

(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 applying

MCA 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 of

the system composedof asthe data matrix and of a null obser-

vation vector. In particular, TLS by using MCA can be solved

by using (12) and (13) with and with . The

advantage 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 the

fact that the varying parameter drives toward the solution

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).

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 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

rotor 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 . The

phase voltages have been computed on the basis of the instan-taneous 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 de-

vices has been employed. In the case under study, the employed

IGBT modules, which are the Semikron SMK 50 GB 123, have

been modeled with a threshold voltage and with an

average differential resistance . Finally, the sam-

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 ob-

server in the discrete domain, the pure integrator in the con-tinuous domain has been replaced by the following discrete


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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 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 ofthe state equations, and thus a correct flux estimation with the

adopted value of differently from the simple forward Euler

integrator .

With reference to the MCA EXIN + reduced order observer,

the only two parameters set by the user have been given the

following values: and (kept constant).

With reference to the parameter , the following scheduling has

been adopted: at each speed transient commanded by the con-

trol 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, andwhose 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 con-

vergence 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 trajec-

tory 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 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 the

DC machine of rated power 4 kVA.

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


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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 50050 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 ob-

server dynamics, and thus would highly increase the complexity

of both observers. It can be concluded that with in all

cases the reduced order observer requires fewer flops than the

full-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 have

been compared with those obtained with the full-order classic

adaptive observer proposed in [8]. The parameters of the full-

order classic observer are exactly the same as those suggested

in [8]. Note also that in the full-order classic observer no com-

pensation 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 MatlabSimulink. With regard to the ex-

perimental tests the speed observer as well as the whole control

algorithm have been implemented by software on the DSP ofthe 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 constantspeed 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, esti-mated (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 wave-

forms 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 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 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 reduc-

tion 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 measuredspeed 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 of6 5 N m

(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. 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


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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 positionat 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 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 the

MCA 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 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 tran-

sient caused by the torque step, the estimated speed follows thereal one very well.


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Fig. 14. Reference,estimated, measured speed,and speed estimation error during zero-speed operation at no-loadwith theclassic 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 at

zero-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 not

perceptible movement of the rotor during this test, which is con-

firmed 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 ob-

server [8] at zero-speed with no-load. The classic observer at

almost 15 s after the magnetization of the machine, has an un-

stable behavior and the machine eventually runs at 45 rad/s

with a mean speed estimation error of 13.74 rad/s. The com-

parison 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 techniquewhich is based

on 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 induction

machine 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 target

of 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 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 es-

timation 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 in-

fluence the accuracy of the speed estimation.

A suitable test setup has been developed for the experimental

assessment of the methodology. An experimental compar-

ison 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 ob-

server 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 tuningproposed in [8].


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Marcello Pucci (M03) 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 Researcher

at 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 (M03) received the Laureadegree in electrical engineering from the Politec-nico of Turin, Turin, Italy, in 1991 and the Ph.Ddegree from the Laboratoire dInformatique etSignaux (LIS) de lInstitut 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.

Grard-Andr Capolino (A77M82SM89F02) received the B.Sc. degree in electrical en-gineering from Ecole Suprieure dIngnieurs deMarseille, Marseille, France, in 1974, the M.Sc.degree from Ecole Suprieure dElectricit, Paris,France, in 1975, thePh.D. degreefrom theUniversityAix-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 Yaound(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 of

Electrical Engineering (19951998), and Director of the Energy Conversionand Intelligent Systems Laboratory (19962000). 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 bookSimulation & CAD for Electrical Machines, Power

Electronics 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 the

Vice-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.

Documents

Sensor Less Control of IM by Reduced Order Observer With MCA EXIN + Based Adaptive Speed Estimation