Parameter Estimation of IM at Standstill With Magnetic Flux Monitoring

8/14/2019 Parameter Estimation of IM at Standstill With Magnetic Flux Monitoring

1/15

386 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 13, NO. 3, MAY 2005

Parameter Estimation of Induction Motor at StandstillWith Magnetic Flux Monitoring

Paolo Castaldi and Andrea Tilli

AbstractThe paper presents a new method for the estimationof the electric parameters of induction motors (IMs). During theidentification process the rotor flux is also estimated. The proce-dure relies on standstill tests performed with a standard drivearchitecture, hence, it is suitable for self-commissioning drives.The identification scheme is based on the model reference adaptivesystem (MRAS) approach. A novel parallel adaptive observer(PAO) has been designed, starting from the series-parallel Kreis-selmeier observer. The most interesting features of the proposedmethod are the following: 1) rapidity and accuracy of the identi-fication process; 2) low-computational burden; 3) excellent noiserejection, thanks to the adopted parallel structure; 4) avoidanceof incorrect parameter estimation due to magnetic saturation

phenomena, thanks to recursive rotor flux monitoring. The per-formances of the new scheme are shown by means of simulationand experimental tests. The estimation results are validated bycomparison with a powerful batch nonlinear least square (NLS)method and by evaluating the steady-state mechanical curve ofthe IM used in the tests.

Index TermsIdentification, induction motor (IM), magneticsaturation, parallel adaptive observer (PAO), self-commissioningdrives.

I. INTRODUCTION

I

N RECENTyears, the demandfor high-performance electric

drives based on induction motors (IMs) has been constantlygrowing. IMs are particularly attractive for industrial applica-

tions because of their low cost and high reliability. Moreover,

power electronics and control electronics, essential to realize so-

phisticated variable-speed drives, are becoming cheaper every

day. On the other hand, high-performance control of this kind

of electric machine is quite difficult. The IM model is multivari-

able, nonlinear and strongly coupled. The concept of field-orien-

tation, introduced in Blaschkes pioneering work [1], has led to

decoupling torque and flux control in induction machines. This

was the key point in developing direct and indirect field-oriented

control (DFOC and IFOC) algorithms [2], [3], adopted in com-

mercial IM drives for high-performance motion control. Nowa-

days, another kind of control strategy is becoming interestingfor industrial IM drives: the direct torque control (DTC) tech-

nique which directly takes into account the switching nature

of the inverter used to feed the motor [4], [5].

The basic versions of almost all the IM controllers rely on

rotor speed measurement and recently great deal of effort has

Manuscript received July 12, 2003; revised May 5, 2004. Manuscript re-ceived in final form September 13, 2004. Recommended by Associate EditorA. Bazanella.

The authors are with the Department of Electronics, Computer Science andSystems, University of Bologna, Bologna 40136, Italy (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCST.2004.841643

been devoted to developing the so-called sensorless control for

IM, where no speed sensor is used [4]. A final solution for this

hard control task is still to be found. However, different solu-

tions, derived from standard field-oriented controllers and DTC,

are already available in commercial drives, in spite of the open

issues on both methodology and practice.

Unfortunately, field-oriented control and DTC techniques

both require accurate knowledge of electric parameters of the

machine continuous-time model in order to guarantee good

performance. In the case of classic IM control (i.e., with

a speed-sensor), it has been extensively proved [6] that the

control stability is quite robust with respect to variations of the

rotor time constant, which is the most critical IM parameter for

control commissioning. But, in terms of tracking fast variable

speed references, a significant reduction in performance can

be noted when the wrong parameters are adopted. In fact, the

wrong electrical parameters cause flux misalignment leading

to loss of efficiency and effectiveness in torque control. In

particular, besides the rotor time constant, the main inductance

plays an important role, since the wrong value leads to deflux

or to saturate the machine. The effects of errors in other IM

parameters are mitigated by current feedback control. In the

case of sensorless control, the effect of parametrization errors is

even more relevant; in fact, a partial or full IM electrical modelis usually adopted to estimate the rotor speed.

In nonlinear and adaptive control literature a great deal of

work has been devoted to developing other control algorithms

for IM or to improving the previously mentioned well-estab-

lished methods (in particular DFOC and IFOC). Although dif-

ferent approaches have been used [7], [8], only partial and quite

poor results have been obtained in terms of performance ro-

bustness with respect to parameter uncertainties, particularly for

sensorless control. Hence, at the state of the art, good knowl-

edge of the electric parameters of the model is a key point to

realize high-performance control of commercial IM drives. In

addition, also for the purpose of diagnosis the electric parame-ters of a healthy IM must be identified with high accuracy.

Traditionally, the IM electric parameters have been calculated

from the nameplate data and/or using the classical locked-rotor

and no-load tests. The resulting values are not usually enough

accurate to tune a high-performance drive and, moreover, the

no-load test requires the motor to be disconnected from any me-

chanical load. Recently, various parameter identification tech-

niques for IM have been proposed in the literature. These can

be divided into two main classes: the online techniques and

the offline techniques.

The online techniques perform the parameter identification

while the IM drive is operating in normal conditions. This kind

1063-6536/$20.00 2005 IEEE

Authorized licensed use limited to: Reva Institute of Tehnology and Management. Downloaded on October 6, 2008 at 6:55 from IEEE Xplore. Restrictions apply.


2/15

CASTALDI AND TILLI: PARAMETER ESTIMATION OF INDUCTION MOTOR AT STANDSTILL 387

of approach is very interesting since it is possible to track the

slow variation of the electric parameters during normal opera-

tion. In fact, it is well-known that the values of the stator and

rotor resistances are strongly affected by the machine heating

and also the magnetic parameters considerably depend on the

level of the magnetic flux, particularly in the saturation zone

[9]. In [10], different theoretically rigorous, methods are used toidentify stator and rotor resistance during normal operation, but

filtered derivatives of the measurements are required. In [11],

an online method, based on the recursive least-square (RLS)

method, is presented to identify the electrical and mechanical

parameters of the system. A scaled version of the magnetic flux

is also estimated, but the derivatives of the measurements have

to be used and the computational load is quite heavy. A similar

approach is reported in [12], where the time-scale separation be-

tween electric and mechanical dynamics is exploited to obtain

simultaneous speed and parameters estimation. In [13], the gen-

eralized total least-square (GTLS) technique is adopted. Filtered

derivatives of the measured signals are still needed, but partic-

ular attention is devoted to the reduction of the noise effects.A constrained identification procedure is proposed to deal with

low signal-to-noise ratio conditions. In [14], the least-square

(LS) procedure has been applied in an original way to obtain

an estimate of the stator and rotor resistances and reactances.

No derivatives are required, but the proposed method is not

strictly recursive and the computational burden is quite heavy. In

[15][17], a theoretically elegant solution is presented to iden-

tify all the IM drive parameters, but knowledge of all of the state

variables and their derivatives is required. In [18] and [19], an

extended Kalman filter (EKF) has been used to identify the ma-

chine parameters; in [18] particular, attention has been paid to

the selection of noise covariance matrices and initial states. In[20], a sophisticated method, based on nonlinear programming,

is proposed. In [21], neuro-fuzzy technique is applied for online

identification of the rotor time-constant. In [8], a very interesting

technique to tune the stator and rotor resistances in normal op-

erating conditions is presented. The stability characteristics of

the proposed method are formally proved and experimentally

tested, and no derivative of the measurements is required.

The offline identification techniques perform the electric

parameter tuning while the IM drive is not operating normally.

From a philosophical point of view, it seems that the offline

techniques are useless since online techniques are available.

At present, from a control theory point of view, no online

identification method combined with an adaptive control has

been mathematically proved to be globally stable; only partial

simulative and experimental results are given. Moreover, even

if we set aside theoretical issues, the online techniques are usu-

ally characterized by a considerable computational burden, so

they are not suitable for cost-optimized industrial applications.

More important, online identification techniques are quite slow

so they cannot guarantee a safe starting of the drive if the

initial values of the estimated machine parameters are strongly

detuned. Hence, it results that offline methods are useful for

two reasons: 1) they can be used when no online method can

be supported; 2) they can provide a good initialization of the

machine parameters when online methods are adopted. Manyoffline identification methods have been proposed; some of

them require particular tests on the machine with free rotor shaft

and/or special measuring equipment [22][29]. The present

trend in drive technology is to perform the offline identification

at standstill, with the motor shaft connected to the mechanical

load and without any extra hardware. In this way, the set-up

of the control system can be automatically executed (and

repeated) after the drive installation (self-commissioning). In[30], a model reference adaptive system (MRAS) method [31],

[32] is used to perform parameter identification at standstill,

and a classical hyperstability approach is adopted to design

the adaptation law, but the motor torque-constant has to be

assumed known. In [34], the frequency response of the IM

at standstill is exploited, so this approach is suitable to avoid

the effects of inverter nonlinearities. In [35], the motor pa-

rameters are estimated by means of both time and frequency

responses of the stator current at standstill. In [36], the IM

is excited at standstill with a sinusoidal voltage in one of the

two equivalent phases, the equivalent impedance is identified

with RLS techniques and different frequencies are used to

identify the different magnetic parameters. This solution alsoavoids the effect of the inverter nonlinearities. In [37], a similar

approach has been implemented. The main difference is that

a simplified dynamical model replaces the typical steady-state

one. In [38], a standard linear LS technique is adopted to

estimate IM electric parameters similarly to the online methods

reported in [11][13], hence, filtered derivatives of the motor

voltages and currents are required. In [30], [34][38], a linear

model is assumed for the IM at standstill. While, in [9], offline

identification is carried out by relying on a deep knowledge of

the typical nonlinear behavior of the IM. In [39], a method is

proposed to identify the flux saturation curve at standstill. In

[40], the same purpose is pursued using EKF.In this paper, a novel offline identification method of the IM

electric model is proposed. This procedure relies on standstill

tests performed with a standard drive architecture, hence, it

is suitable for self-commissioning drives. Only one phase, in

the two-phases equivalent model, is excited to guarantee the

standstill condition without locked rotor. Under the hypothesis

of linear magnetic circuits, the IM model at standstill is linear

time invariant (LTI). A MRAS approach has been adopted.

The identification procedure is realized by means of a parallel

adaptive observer (PAO) [31], [32], which is based on a non-

minimal statespace representation of the the IM LTI-model,

derived from [41], and an original adaptation law involving

current measurements only (no measurement differentiation is

required). Unlike [30], none of the machine parameters has to

be assumed known. In accordance with the classical adaptive

observers theory, the theoretical analysis and design of the

proposed PAO has been carried out in a deterministic frame-

work. In fact, it is well-known that the parallel structure gives

the adaptive observer excellent noise rejection properties [31],

[43]. From a practical point of view, a key point for the correct

estimate of the IM LTI-model parameters is to avoid saturation

of the magnetic core. In fact, as is well-known [9], [23], the

magnetic parameters depend on the flux level and they can be

reasonably assumed to be constant only if the flux is not greater

than the rated one. On the other hand, it is worth observingthat from nameplate data, usually quite rough, it is possible



3/15


to deduce the nominal flux of the machine with acceptable

accuracy, but very poor information can be obtained about the

level of the magnetizing current [2]. Hence, in order to avoid

magnetic saturation during the identification process, the flux

should be monitored in some way. This requirement, often

neglected, is accomplished by the proposed scheme. In fact, the

adopted PAO gives a recursive estimate of the magnetic flux,during the identification process. Hence, this solution avoids

the incorrect estimation of the magnetic parameters due to

saturation phenomena.

The paper is organized as follows. The IM model at stand-

still, based on the two-phase equivalent representation, is re-

ported in Section II. In this section, the information that can

be deduced from standard nameplate data are discussed. In the

first part of Section III, the general structure of the PAOs is re-

ported. In Section III-A, the nonminimal representation of the

IM model, used in the proposed PAO, is shown. In Section III-B,

the original adaptation law together with the complete structure

of the adopted PAO is reported. In Section IV, simulation re-

sults are given; particular attention is paid to the discretizationmethod which has to be used in order to implement the proposed

algorithm on a real digital controller. Some simulation results

with noisy measurements are also presented. In Section V, it is

shown how the rotor flux estimate given by the proposed scheme

can be effectively used to avoid magnetic saturation during the

identification procedure. In Section VI, the experimental results

are reported. The estimation results of the proposed scheme

are compared with the estimates obtained by applying a pow-

erful batch nonlinear least square (NLS) method. The actual

steady-state mechanical curve of the IM under test and the one

obtained by simulation with the experimentally estimated pa-

rameters are compared to validate the proposed method. In ap-pendices, sketches of the proofs concerning nonminimal repre-

sentation and convergence properties of the proposed solution

are given.

II. INDUCTION MOTOR MODEL AT STANDSTILL AND

NAMEPLATE DATA ANALYSIS

Under the hypothesis of linear magnetic circuits and bal-

anced operating condition, the equivalent two-phase model of a

squirrel-cage IM at standstill, represented in a stator reference

frame , is [2], [44]

(1)

where are stator voltages, stator

currents, and rotor fluxes and is the magnetic torque

produced by the motor. Positive constants in model

(1), related to IM electrical parameters, are defined as:

,

where are stator/rotor resistances and in-

ductances, respectively, while is the mutual inductance

between stator and rotor windings. All the electric variables and

parameters are referred to stator. The transformation adopted

to map the three-phase variables into the two-phases reference

frame maintains the vectors amplitude, as indicated by the

factor in the expression of .From (1), the complete decoupling of the components a and

b of the electrical variables at standstill can be noted. In addi-

tion, the torque expression shows that if only one phase of the

equivalent model is excited then the produced magnetic torque

is null. Hence, if no external torque is applied, the standstill con-

dition is preserved. Therefore, in the following, only the first

two equations in (1) will be considered, while all the variables

of the -phase will be assumed to be equal to zero. From a prac-

tical point of view, this means that no voltage is applied in the

b-phase.

Remark 1: In order to mitigate the effects of the machine

asymmetries, the identification procedure described in the next

sections and based on the excitation of the a-phase, can be re-peated with different axis orientation.

The resulting one-phase model is LTI but, as already men-

tioned in the introduction, this condition is admissible only if no

significant magnetic saturation and thermal heating are present.

With respect to the magnetic effects, in general a linear behavior

can be assumed only if the level of the flux is lower than the

nominal value. Since this variable is not directly measurable,

it should be better to express this condition in terms of stator

currents, i.e., the magnetizing current has to be lower than the

rated one. Unfortunately, the nominal value of the magnetizing

current is not usually available from the IM nameplate data. In

fact, the data given by IM manufacturers are related to nominalload conditions and, generally, they are: the mechanical power,

, the stator voltage, , the electric frequency, , the me-

chanical speed, , the stator current, , and the power factor,

. The rated level of the magnetizing current can be de-

duced using a classical no-load test, but it is difficult to deduce

it with acceptable accuracy by means of a simple and fast test

at standstill. On the other hand, it is possible to obtain the nom-

inal stator flux rms value, , by using typical nameplate

data and a simple dc measurement of the stator resistance at

standstill. In fact, the expression of is

(2)

Therefore, it is reasonable to assume that the magnetic core is

not saturated, if the peak value of the rotor flux (referred to

stator) satisfies the following inequality [2], [9], [44]:

(3)

As will be shown in the following sections, the proposed iden-

tification procedure also produces a recursive estimation of the

rotor flux which asymptotically tracks the real one. Hence, this

solution, using the information derived from (2) and (3), is suit-

able to verify that no saturation phenomena occurs during the

estimation process and, consequently, it guarantees that the es-timated magnetic parameters are significant.



4/15


(a) (b)

Fig. 1. (a) Series-parallel and (b) parallel adaptive observer schemes.

III. NEW MRAS PARALLEL IDENTIFIER/OBSERVER FOR THE

IM AT STANDSTILL

During the last three decades, a considerable amount of workhas been done on the design of adaptive state observers with

MRAS configurations [33]. These schemes are suitable for both

state observation and parameter estimation owing to their adap-

tive nature. In the case of IM at standstill considered this kind of

approach can be used for estimating the machine parameters and

monitoring the nonmeasurable state variables during the identi-

fication process.

Fig. 1 shows the two possible classes of MRAS adaptive state

observers: the series-parallel adaptive observer (SPAO) which

uses the input and the output of the observed system in the ob-

server block and the PAO characterized by the absence of the

system output signal in the observer block.

It is well known [31] that the PAO is characterized by ex-

cellent noise-rejection properties, while the SPAO is preferable

only in the case of very high signal-to-noise ratio (SNR) because

of the larger amount of information carried by the output signal.

The solution proposed in the literature for both of the schemes

depends on the possibility of measuring the whole state vector.

For the SPAO several globally asymptotically stable solutions

have been developed both with accessible and not accessible

state [32]; while for the PAO only the solution in the case of ac-

cessible state is well-established. In the case of the IM the whole

state is not directly accessible and only noisy measurements of

the output current are available. In order to improve the robust-

ness of the identification precess with respect to measurementnoise, a PAO structure has been chosen for the proposed estima-

tion scheme. A new adaptation law has been developed to deal

with this case where the full state is not accessible.

A. Nonminimal Realization of the IM Model

The new PAO proposed is based on a nonminimal realiza-

tion of the IM model. This nonminimal form, whose order

is where is the order of the IM model, can be

considered as a generalization of the realization introduced

by Kreisselmeier [41], which is strictly based on the -com-

panion canonical forms. On the contrary, the proposed solution

avoids the use of those canonical forms since they are numer-ically ill-conditioned [42].

According to Section II, consider now the a-phase LTI model

of the IM

(4)

where

where and is the output .

In the following, it will be shown how the previous second-

order model can be represented by the equivalent fourth-order

model:

(5)

where the couple is arbitrary, provided that it is com-

pletely reachable and is Hurwitz; while are relatedto the original model (4) and the choice of .

The remarkable characteristic of (5) is that the relevant model

parameter vectors, and , appear linearly in the output equa-

tion only, while the state dynamics can be defined arbitrary.

Thereby, using this representation, the observation process can

be well separated from the adaptation process [32]. The matrix

is not very important in the model description since the con-

tribution vanishes, owing to the asymptotic

stability of matrix . In addition, note that filters both the

system input and output. This is a useful feature for a robust ob-

server design in a noisy environment.

To obtain the relation between the representations

and Kreisselmeiers result

[41], holding for models in -companion canonical form,

constitutes the starting point. Consider the IM model in K-com-

panion form

(6)

where

In [41], it has been proved that system (6) can also be repre-

sented by the following nonminimal equivalent representation:

(7)

where is the th column of the identity matrix, is in -

companion form and

(8)



5/15


In the following, the conditions for the equivalence of models

(4) and (5) will be presented, using the relation (8), between the

canonical models (6) and (7). Consider the transformations

which sets the triple in the canonical form (6), and a

matrix satisfying relation . Ob-

viously, matrix depends on how the arbitrary and completely

reachable couple is chosen.

The relations between the models (4), (5) and the -com-

panion forms (6), (7) are the following:

(9)

Hence, the output equation of (5) can be rewritten as

Recalling the output expression in (7) and using (8), the fol-

lowing relation between models (4) and (5) can be expressed, in

order to impose the equivalence

(10)

Remark 2: As will be shown in the following, the final aim of

the identification process is to calculate the IM physical param-

eters from the estimation of vectors and . From the first two

equations in (10), it is straightforward to obtain the following

relations:

By solving the previous equations, it is possible to calculate

the system parameters and the product , starting

from and vectors. In order to determine and , it is

necessary to add the hypothesis of , which is usually

verified in practice, however in some types of induction machine

a different ratio is suggested [44], [45]. From that it follows that

then, since is known, it

is possible to determine and separately.

Remark 3: Given the IM physical parameters, it is also pos-

sible to obtain the matrix and the physical state can be

calculated by means of the following formula (the proof is in

the Appendix):

......

...

(11)

where and are matrices built with the polynomial coef-ficient of , for (see the Appendix for

their formal definition). In particular, if is chosen in diagonal

form, , then

and the following simplified expression for the matrixes results

:

B. New PAO for the IM at Standstill

In the previous remarks, it has been shown how the IM dy-

namics (4) can be described with a model of the form reported

in (5). In addition, in Remarks 2 and 3 it has been underlined

how it is possible to calculate the physical state

and the physical parameters , and from the state

and the parameters and of model (5).

On the basis of these results, a new MRAS parallel identi-fier/observer (PAO) is presented in this section. Referring to the

IM nonminimal model (5), the structure of the adopted observer

is the following:

(12)

where , and are, respectively, the estimate of the

output, the states, and the parameters of model (5). Note that in

the proposed observer structure no estimate of the initial state

is considered. The reason why is twofold:

the contribution of the initial state disappear expo-

nentially since is Hurwitz;

in the case of the IM model (4) the initial state is

usually null.

The parallel nature of the proposed scheme derives from the

use of the estimated output in the output equation of (12) in-

stead of the actual measurable output ; in this way the state

observation does not depend directly on the actual output.

In order to complete the proposed PAO an adaptation law for

the estimated parameters must be added.

The proposed adaptation law is the following:

(13)

(14)

where and are two filtered versions of the output error,

defined as

(15)

while is an arbitrary positive scalar constant, are arbi-

trary positivedefinite gain matrices, and is a positivedef-

inite matrix which has to satisfy some weak constraints (see the

Appendix).

In the Appendix, it is shown that the PAO given by (12)(15)

guarantees asymptotic convergence of the states and the

output to the actual ones , and . In addition, if per-sistency of excitation is guaranteed for the state variables, also



6/15


TABLE INAMEPLATE DATA AND TRADITIONALLY ESTIMATED PARAMETERS OF THE

ADOPTED INDUCTION MOTOR

the estimated parameters and converge to the actual values.

Some considerations about the choice of the adaptation law are

also reported.

Remark 4: From a theoretical point of view, the choice of

the couple is arbitrary, providing that it is controllable.

Actually, in order to implement a light and well-conditionedalgorithm, it is better to choose matrix in diagonal form.

Remark 5: The scalar and the matrices (usually in

diagonal form) define the adaptation gains. Their values repre-sent a compromise between the speed of convergence and the

noise rejection properties of the PAO.

Remark 6: The PAO scheme shown in (12) (15) does notprovide a direct estimate of the rotor flux. In order to calculate it,(11) has to be used, neglecting the initial state and replacing real

values with estimated ones. Note that the matrix in (11) de-

pends on the physical parameters and . Hence, to obtain a re-

cursive estimate of the flux during the the identification process,it is necessary to calculate an estimate of the previous parame-

ters following the procedure indicated in Remark 2.

IV. SIMULATION RESULTS AND DISCRETIZATION

The aim of this section is twofold: 1) to show, by means of

simulation results, the performances of the proposed PAO (both

ideal and noisy conditions are considered); 2) to introduce a dis-

cretized version of the adopted scheme, suitable for real imple-

mentation, and to show its behavior with respect to the original

continuous-time version.

In order to simulate the actual IM, the LTI model (4) has been

adopted. Hence, no magnetic saturation effect has been taken

into account at this stage. The issue related to the magnetic non-linearity will be discussed in next section. In this part, instead,

it is shown that the rotor flux is well-estimated whenever the

assumption of linear magnetic core is admissible. The IM ac-

tual parameters adopted during the simulations are reported in

Table I. These parameters are related to the motor used in exper-

imental tests. They have been identified by means of traditional

methods based on no-load and locked-rotor tests. The nameplate

data of the motor are also reported in Table I.

The couple adopted in the proposed PAO is the fol-

lowing: and In

this way, the actual parameter values in the nonminimal realiza-

tion (5) are: . These

are the values which have to be identified using the proposedscheme.

Fig. 2. Injected voltage waveform.

A. Simulations of the Continuous-Time Version of the PAO

The simulation tests reported in this part are related to the

PAO in continuous-time version, as introduced in Section III.B.

The adopted gains are the following:

and

In particular, the matrix has been chosen solving the fol-

lowing linear matrix inequality (LMI) problem (see the Ap-

pendix):

(16)

where

(17)

The set has been chosen in order to include the model ma-

trix in canonical form [see (6)] for a wide range of possible

IM. The solution of (16) has been obtained using the LMI

toolbox of Matlab [47].

In all of the tests performed the input voltage is given by the

sum of four sinusoids in order to guarantee the persistency of

excitation. The amplitude is set to 5 V for all the sinusoidal com-

ponents and the following Hz frequencies are adopted: 1, 3.18,

9, and 35 (see Fig. 2). The choice of these values is related to

some insights into the typical behavior of standard IM. In fact,

the transfer function between the stator voltage and stator cur-

rent at standstill is characterized by the slow (15 Hz) and fast(2550 Hz) poles. In addition, a zero is present near the slow



7/15


Fig. 3. Continuous-time PAO, ideal case: estimation of the parameters p and q.

Fig. 4. Continuous-time PAO, ideal case: estimation of current and flux (beginning of the estimation process).

Fig. 5. Continuous-time PAO, ideal case: estimation of current and flux (end of the estimation process).

pole, but structurally on its left in the complex plane. In the firstset offigures (Figs. 35), the results of a simulation in ideal con-

ditions are reported. In Fig. 3, the temporal evolutions of the es-timated parameters are reported. All of the estimations converge



8/15


Fig. 6. Continuous-time PAO, noisy case: estimation of the parameters p and q.

Fig. 7. Continuous-time PAO, noisy case: estimation of current and flux (beginning of the estimation process).

Fig. 8. Continuous-time PAO, noisy case: estimation of current and flux (end of the estimation process).

to the real parameters, independently of their initial value. Theconvergence time is quite long; it can be reduced by increasing

the adaptation gains, but this will lead to larger oscillation inthe transient. In Figs. 4 and 5, the current and flux estimates are



9/15


TABLE IISIMULATION RESULTS FOR CONTINUOUS-TIME PAO IN NOISY ENVIRONMENT

compared with the real values. In Fig. 4, the beginning of the

simulation tests is considered, the estimates of the stator current

and the rotor flux are not very good; in fact, the estimated pa-

rameters are quite far from the real values. Instead, in Fig. 5(c)

and (d), where the end of the simulation is shown, the estimates

of both states are very good. This fact confirms the flux-moni-

toring capability of the proposed scheme.

In Figs. 68, the results of a simulation in noisy conditions

are reported. A white noise has been added on the output (the

stator current ). The adopted standard deviation is 10% of the

RMS value of the stator current in ideal conditions. In Fig. 6,

the temporal evolutions of the estimated parameters are shown.The adaptation process is very similar to the ideal case and the

convergence ratio is not influenced by the measurement noise.

In Figs. 7 and 8, the current and flux estimates are compared

with the actual values. In Fig. 7, the beginning of the simulation

test is considered, while in Fig. 8 the final part is shown. The

state estimate is still very good when the parameters are near

the correct values. Hence, also in a noisy environment the flux

monitoring can be performed. In particular, in Figs. 7(a) and

8(a), the current estimate is compared with the measured one

(impaired by noise). The difference between them represents

the so-called innovation or residual for the adopted identifica-

tion-observation scheme. Other tests have been performed with

different levels of noise, while other conditions are unchanged.

In Table II, the results are summarized. Only the product of

and is reported since these two parameters can be identified

separately only if some additional assumptions are considered

(see Remark 2). The quantity % represents an identification

error index defined as % , where and

are the vectors of the actual and estimated parameters, respec-

tively: and . In

particular, the estimated parameters in are the mean values

of the results given by the proposed PAO over a time interval

from 150 to 180 s, where the convergence transient is always

terminated. In Table II, the variance, over the same time interval,

of the estimated values is also indicated (in brackets). Anotherindex of the identification quality in a noisy environment is the

whiteness of the innovation. This characteristic has always been

computed on the time interval 150180 s, using a whiteness test

based on an eight-degree-of-freedom variable, whose 99%

confidence interval is 020.1 [51]. All the indexes considered

show good performances of the proposed PAO, even with large

noise. Some small differences can be noted among the results

of the simulation tests, owing to the white noise level. In fact,

as is well known, adaptation algorithms are usually biased in a

noisy environment [31]. However, the extensive simulation tests

confirm the robustness of the proposed solution for both identi-

fication and flux monitoring. This is essentially due to the par-

allel structure of the adaptive observer proposed. Moreover, a25 mA-dead-zone has been inserted on the current estimation

error, , in the adaptation law (13)-(14), according to stan-

dard practice of adaptive algorithms. Obviously, the gain

and also plays an important role in noise insensitivity: the

lower the gains, the greater the identification-observation accu-

racy will be(and the larger the convergence time).

B. Discretization of the Proposed Scheme

In order to obtain a really-implementable version of the pro-

posed PAO it is necessary to develop a discrete-time version.

Different discretization methods have been considered: forward

differences, backward differences, Tustin, z-transformationwith different input reconstructors. The sampling time that was

expected to be used in real implementation is s.

This a good a priori tradeoff between the dynamics of the ob-

server (similar to a typical IM) and the computation capability

of a standard DSP or microcontroller used in high-performance

drive. The criterion used to choose between the different dis-

cretization techniques was the following: a) to maximize the

likelihood between the continuous and the discrete version of

the PAO with the sampling time fixed above; b) to minimize

the computational complexity of the algorithm. The best results

were obtained with the following discretization:

(18)(19)



10/15


(20)

(21)

(22)

(23)

(24)

where

and

and , and are the same gains used in the continuousversion. The LTI dynamics (18), (19), and (21) have been dis-

cretized with an exact method in the hypothesis of constant in-

puts between two sampling times (z-transformation with ze-

roth-order reconstructor on the input). The nonlinear dynamic

and static equations (20), (22), (23), (24) have been discretized

using the Euler approximation.

The simulation tests performed for the continuous version

have been repeated for the discrete-time version proposed. The

results are very close to the continuous-time case, both for pa-

rameter estimation and flux observation, even with large noise

on the current measurement. Hence, the proposed discretization

method and the adopted sampling time are suitable for the dig-ital implementation of the original continuous version. (For the

sake of brevity, figures and tables related to the simulations of

the discrete version are not reported)

V. AVOIDANCE OF MAGNETIC SATURATION USING THE

PROPOSED ESTIMATOR

In this section, a procedure to avoid magnetic saturation,

based on the proposed estimator, is illustrated.

In previous paragraphs it was proved that the rotor flux is cor-

rectly estimated when the IM model is LTI, but no results are

available about the observation properties when magnetic satu-

ration occurs. Consequently, the basic idea is to use the rotor fluxlevel estimation to avoid the state of the IM exits from the linear

region during the identification process. From the previous con-

siderations, the following procedure can be defined as:

1) start the identification process with a low-voltage

signal (which guarantees very low flux, far from

saturation) satisfying the persistency of excitation

requirement;

2) wait for the flux and parameters estimation conver-

gence using a suitable innovation whiteness test;

3) slowly increase the voltage as long as a significant level

of the estimated rotor flux [obeying to (3)] is obtained;

4) stop the estimation algorithm when the whiteness testis satisfied.

Note that it is not convenient to stop the parameter identifica-

tion after the estimate convergence with low flux (Step 2 of the

procedure). In fact, in that condition the Signal to Noise Ratio

is very low and the nonideality of the power electronics device

used to feed the motor are relevant. By means of the proposed

procedure, based on flux estimation, the flux level can be con-

sciously increased without producing saturation of the magneticcore (Step 3). Hence, an optimization of the signal to noise ratio

can be safely achieved.

VI. EXPERIMENTAL RESULTS AND VALIDATION

In this section, the performances of the actual implementation

of the proposed identification scheme are shown. The obtained

results are compared with the output of a batch (i.e., nonrecur-

sive) method based on NLS.

The nameplate data of the adopted motor are reported in

Table I. Its electrical parameters, roughly identified with tra-

ditional methods, have been used in the previous section to

perform simulation tests. The stator resistance value, obtainedwith a simple dc test, is equal to 6.6 (as reported in Table I).

Using (2), it can be deduced that the nominal stator flux value is

Wb. Hence, recalling (3), no magnetic saturation

will arise if the rotor flux is maintained under 0.74 Wb.

During experimental tests, the stator currents were measured

using closed-loop Hall sensors. The stator voltages were im-

posed by a standard three-phase inverter with a 10 KHz sym-

metrical-PWM control. Simple techniques based on phase cur-

rent sign [52] were used to compensate for the effects of the

dead-time, set to 1.5 s. The proposed estimation scheme was

implemented on a control board equipped with a floating-point

DSP, TMS320C32. The adopted sampling time was 300 s, aspreviously indicated in Section IV-B. It is worth observing that

the motor shaft was connected to a mechanical load to avoid

rotor movements due to magnetic anisotropy. This solution is

typical for self-commissioning drives.

A set of experimental tests was performed using the proce-

dure shown in Section V to obtain good flux level, avoiding

saturation. That means the flux level was kept under the max-

imum value indicated previously. The voltage signal adopted is

formed by four sinusoids with the same frequencies reported in

Section IV and equal amplitudes of 2 V as starting values. After

stage 3 of the procedure, the amplitude for each of the sinu-

soidal components is 5 V. An additional equality constraint be-

tween the sinusoids amplitude was imposed to simplify the S/N

optimization procedure without impairing the overall estimation

performances. Note that in order to compare the simulations and

the experiments, an amplitude of 5 V was imposed to the sinu-

soids adopted in Section IV and the experimentally estimated

parameters are set to 0 at the end of stage 3 of the procedure

of Section V. The results of one of the experimental tests are

reported in Figs. 911. It can be noted that the temporal evolu-

tion of both state and parameter estimate are very similar to the

simulated ones. Only the final values of the estimated parame-

ters are slightly different. Many other experimental tests were

performed with different frequencies of the exciting sinusoids

(always preserving linearity of the magnetic circuit by meansof the procedure of Section V). The results are summarized in



11/15


Fig. 9. Experimental results: estimation of the parameters p and q.

Fig. 10. Experimental results: estimation of current and flux (beginning of the estimation process.

Fig. 11. Experimental results: estimation of current and flux (end of the estimation process.

Table III. For every different test, the estimated parameters are

the mean values on the time interval between 150 and 180 s.

The whiteness of the residual was checked by means of

the test used for simulations. The mean values and the stan-

dard deviation, reported in the last two rows of Table III, are

computed to evaluate the dispersion of different tests. In partic-

ular, the small standard deviation shows the good precision ofthe proposed method.

As underlined previously, the experimentally estimated pa-

rameters given by the proposed PAO are quite different from

the traditionally estimated data used in simulations as actual

values. In order to verify carefully the performances of the pro-

posed scheme, the experimental data have been processed with

a different identification algorithm, based on the nonrecursive

NLS method. This algorithm has been realized using the fmin-search function of the optimization toolbox of Matlab [48];



12/15


TABLE IIIINDUCTION MOTOR PARAMETERS EXPERIMENTALLY ESTIMATED WITH THE PROPOSED PAO (NO MAGNETIC SATURATION OCCURS)

TABLE IVINDUCTION MOTOR PARAMETERS EXPERIMENTALLY ESTIMATED WITH THE NLS METHOD (NO MAGNETIC SATURATION OCCURS)

fminsearch is a minimization procedure for a generic cost

function, based on the NelderMead method. The cost function,

, has been imposed equal to the difference, in the least square

sense, between the experimental data and the simulation with

the estimated motor parameters, that means

(25)

where is the experimental output, is the vector of the esti-mated parameters and is the output simulated using these pa-

rameters. This method is very powerful so it represents a good

touchstone. Obviously, it cannot be used directly in self-com-

missioning drives, since it has a heavy computational burden

and it can only be used in a batch way, without any recursive

monitoring of the rotor flux. The results obtained with the NLS

method for the experimental tests are reported in Table IV. The

parameters estimated with this approach are very similar to the

ones obtained with the proposed scheme.

The measurements collected during experiments can be cor-

rupted by typical sensor nonidealities such as current sensors

offset or typical actuation troubles such as unperfect dead-time

compensation. Hall sensors offset has been minimized by a stan-

dard zeroing procedure before starting the identification algo-

rithm. However, the robustness with respect to this kind of mea-

surement and actuation trouble cannot checked by the compar-

ison between the proposed scheme and the NLS method re-

ported since the potentially corrupted data are the same for

both algorithms. A practical method to check the correctness

of the estimated values is to compare the actual IM mechan-

ical curve (speed versus torque) with the one simulated using

the estimated parameters. This comparison is reported in Fig. 12

where the mechanical curves are derived by supplying the motor

with a 33.3 Hz253 V sinusoidal three-phase voltage. The

traditionally-estimated parameters are also considered. Verygood matching is obtained between experimental data and the

Fig. 12. IM mechanical curve: from experiments; 3 simulated using theparameters estimated with the proposed scheme in test #2; x simulated usingthe traditionally-estimated parameters.

simulation results based on parameters estimated by the pro-

posed solution, while a significant error can be noted when tradi-

tionally estimated parameters are considered. This result shows

that the robustness of the method presented combined with the

proposed measurements and actuation expedients guarantees a

very reliable IM parameter estimation.

Remark 7: The mechanical curve of an IM is very sensitive

to all of its electrical parameters [2], [44]. Hence, the compar-

ison between the actual speed-torque curve and the one obtained

simulating the IM model is a very effective method to validate

the estimated parameters used in the model. In addition, this val-

idation methods is based on an open-loop experiment, there-

fore its results are not affected by feedback control algorithmswhich usually mitigate the effects of parameters mismatching.



13/15


VII. CONCLUSION

A new method for the estimation of the parameters of IMs at

standstill has been presented. The proposed schemeis based on a

PAO designed using a novel nonminimal representation derived

from Kreisselmeiers canonical form and an original adaptation

law.

It has been proved, both theoretically and by implementation,that the proposed algorithm assures a simultaneous asymptotic

unbiased estimation of both the system parameters and the state

(i.e., stator current and rotor flux).

A discretized version, suitable for digital implementation, has

been developed, preserving the characteristics of the original

continuous-time procedure.

The simulation tests have shown the excellent noise rejection

properties of the proposed solution. This feature is related to

the parallel structure of the adopted adaptive observer and can

be tuned by varying the adaptation law gains.

Experimental results have proved the effectiveness and ra-

pidity of the approach. In particular, it has been shown that mag-netic saturation can be avoided thanks to the good rotor flux es-

timation. The identification results are strongly validated by two

methods: 1) the comparison with a powerful batch NLS method;

2) the comparison of the actual mechanical curve of the IM used

for the test with the one obtained by simulation using the esti-

mated parameters.

Finally, it has been shown that the algorithm is fast and simple

and may be easily implemented in self-commissioning drives.

APPENDIX

Definition 1: Given a generic second-order square matrix ,

the matrix such that

is denoted as the matrix of the polynomial coefficients of

.

Proposition 1: Let

, and be the matrices and vectors de-

fined in Section III-A

, and be the matrices of the polyno-

mial coefficient of and

, respectively;

hence, the following relation holds:

(26)

Proof: Consider the problem

(27)

The extension of (27) to (26) is straightforward. By means of

relations and , it is easy to verify that

(27) can be rewritten as

(28)

where .

Now, recalling the definition of and and the relation

, it is easy to verify

(29)By substituting (29) in (28) and noting that

, the proof is completed.

Proposition 2: [41] The state of the IM model

is linked to the state of the nonminimal representation

by the following relation:

(30)

Proof: [41].

Proposition 3: The state of the IM model is

linked state of the generalized nonminimal representation

by the following relation:

(31)

Proof: Straightforward by means of Propositions 1 and

2.

Now, the convergence properties of the proposed scheme

are discussed. The guidelines for the theoretical proof of

these characteristics are stated avoiding mathematical details.

Starting from the nonminimal parametrization of the IM with

locked rotor, given in (5), and the PAO expression, given in

(12), the following error model can be defined:

(32)

where

(33)

are the state, the estimation, and the output errors. From the first

equation in (32), it results that , hence, the first partof the state can be neglected in the convergence analysis.

Before considering the complete convergence analysis, it is

worth studying the case of perfect knowledge of the parameters

vectors and . In this condition, the error model is

(34)

From (34) it can be deduced that, in this case, the convergence to

zero of error state requires the matrix to be Hurwitz.

Using (10) and the definition of and , it can be shown that

. Then, in order to guarantee

the global asymptotic stability of (34), the matrix must beHurwitz.



14/15


Coming back to the general case reported in (32), the Hurwitz

character of matrix is not strictly necessary in principle to de-

sign an adaptation law that guarantees asymptotic convergence.

By the way, the matrix of the IM model (4) is certainly Hur-

with, even if unknown. This characteristic has been exploited in

the choice of the adaptation law (13), (14) as shown in the fol-

lowing convergence analysis.Now define the following Lyapunov-like function:

(35)

where are arbitrary, and

is the solution of the following Lyapunov equation:

(36)

with arbitrary . The solution of (36) exists,

since is Hurwitz. On the other hand, is unknown and it is

not possible to solve (36) directly. By the way, from a practicalpoint of view, some boundscan be defined on the IM parameters.

Hence, (36) can be translated in a LMI where belongs to a

certain set. Hence, a suitable can be found using the

standard procedure for LMI solving [49].

The function is clearly positive defined on the error

statespace . The time derivative of along the

trajectories of (32) is

(37)

where the contribution of the initial state hasbeen neglected, since exponentially disappears with an arbi-

trary ratio. With simple computation (37) can be rearranged as

follows:

(38)

Considering the adaptation law reported in (13), (14), the defini-tion (15) of the filtered error and recalling (36), the derivative

of results as follows:

(39)

Hence, the error state is bounded and the Barbalats

Lemma [50] can be applied. It results that

(40)

From the definition (15) and the expression of the output error

in the last of (32), it can be derived that

(41)

then, applying standard arguments related to persistency of ex-

citation [32], it can be shown that an exponential convergence

to zero of the parameter estimation error is obtained if the har-

monic content of the input is large enough.

Remark 8

The variable is similar to the augmented error typicallyused in adaptive systems [32]. In particular, it has been intro-

duced in order to have the parameter estimation errors in .

This allows persistency of excitation arguments to be applied

to achieve exponential convergence of the parameter estimates.

The remaining parts of the adaptation law are used to cancel

bad terms in .

ACKNOWLEDGMENT

The authors would like to thank C. Morri and A. Casagrande

for their valuable collaboration in testing the proposed proce-

dure during their degree theses. The experimental tests were car-

ried-out at the Laboratory of Automation and Robotics (LAR)of the University of Bologna. The authors would also like to

thank the anonymous reviewers for their valuable suggestions

about the experiments to test the proposed solution.

REFERENCES

[1] F. Blaschke, The principle of field orientation applied to the newtransvector closed-loop control system for rotating field machines,Siemens-Rev. , vol. 39, pp. 217220, 1972.

[2] W. Leonhard, Control of Electric Drives. Berlin, Germany: Springer-

Verlag, 1995.

[3] B. K.Bose, Power Electronicsand Variable Speed Drives. Piscataway,

NJ: IEEE Press, 1997.

[4] P. Vas, Sensorless Vector and Direct Torque Control. Oxford, U.K.:

Oxford Univ. Press, 1998.[5] G. Buja, D. Casadei, and G. Serra, Direct stator flux and torque

control of an induction motor: Theoretical analysis and experimental

results (Tutorial), in Proc. IEEE-IECON98, Aachen, Germany, pp.T50T64.

[6] A. S. Bazanellaand R. Reginatto, Robustness margins for indirect field-oriented control of induction motors, IEEE Trans. Autom. Control, vol.45, no. 6, pp. 12261231, Jun. 2000.

[7] S. Peresada and A. Tonielli, High performance robust speed-fluxtracking controller for induction motor, Int. J. Adapt. Control SignalProcess., vol. 14, no. 2, pp. 177200, 2000.

[8] R. Marino, S. Peresada, and P. Tomei, online stator and rotor resistenceestimation for induction motors, IEEE Trans. Contr. Syst. Technol., vol.8, no. 3, pp. 570579, May 2000.

[9] N. R. Klaes, Parameter identification of an induction machine with re-gard to dependencies on saturation, IEEE Trans. Ind. Appl., vol. 29, no.

6, pp. 11351140, Nov.-Dec. 1993.[10] S. Sangwongwanich and S. Okuma, A unified approach to speed

and parameter identification of induction motor, in Proc. IECON Int.Conf. Industrial Electronics, Control, and Instrumentation, 1991, pp.

712715.[11] J. Stephan, M. Bodson, and J. Chiasson, Real-time estimation of the

parameters and fluxes of induction motors, IEEE Trans. Ind. Appl., vol.30, no. 3, pp. 746759, May-Jun. 1994.

[12] M. Velez-Reyes, K. Minami, and G. C. Verghese, Recursive speed andparameter estimation for induction machines, in Proc. IAS Conf. Rec.,pp. 607611. 19 889.

[13] C. Moons and B. De Moor, Parameter identification of induction motordrives, Automatica, vol. 31, no. 8, pp. 11371147, 1995.

[14] J. Holtz and T. Thimn, Identification of the machine parameters in avector-controlled induction motor drive, IEEE Trans. Ind. Appl., vol.27, no. 6, pp. 11111118, Nov.-Dec. 1991.

[15] V. Pappano, S. E. Lyshevski, and B. Friedland, Identification of induc-tion motor parameters, in Proc. 37th IEEE Conf. Decision and Control,Tampa, FL, Dec. 1998, pp. 989994.



15/15


[16] , Parameter identification of induction motors part 1: Themodel-based concept, in Proc. IEEE Conf. Control Applications,Trieste, Friuli-Venezia Giulia, Italy, Sep. 14, 1998, pp. 466469.

[17] , Parameter identification of induction motors part 2: Parametersubset identification, in Proc. IEEE Conf.Control Applications, Trieste,Friuli-Venezia Giulia, Italy, Sep. 14, 1998, pp. 470474.

[18] T. Iwasaky and T. Kataoka, Application of an extended Kalman filter toparameter identificationof an induction motor, in Proc.Conf.Rec. IEEE

Industry Applications Society Annu. Meeting , vol. 1, 1989, pp. 248253.[19] L. Zai, C. L. De Marco, and T. A. Lipo, An extended Kalman filterapproach to rotor time constant measurementin PWM induction motor

drives, IEEE Trans. Ind. Appl., vol. 28, no. 1, pp. 96104, Jan.-Feb.1992.

[20] P. Coirault, J. C. Trigeassou, D. Krignard, and J. P. Gaubert, Recur-sive parameter identification of an induction machine using a non linearprogramming method, in Proc. IEEE Int. Conf. Control Applications,Deaborn, MI, Sep. 1518, 1996, pp. 644649.

[21] L. R. Valdenebro, J. R. Hernndez, and E. Bim, A neuro-fuzzy basedparameter identification of an indirect vector controlled induction motordrive, in Proc. IEEE/ASME Int. Conf. Advanced Intelligent Mecha-tronics, Sep. 1923, 1999, pp. 347352.

[22] S. Moon and A. Keyhani, Estimation of induction machine parametersfrom standstill time-domain data, IEEE Trans. Ind. Appl., vol. 30, no.6, pp. 11351140, Nov.-Dec. 1994.

[23] M. Ruff and H. Grotstollen, offline identification of the electrical pa-rameters of an industrial servo drive system, in Proc. 35th IAS Annu.Meeting, vol. 1, 1996, pp. 213220.

[24] J. Seok, S. Moon, and S. Sul, Induction machine parameter identifica-tion using PWM inverter at standstill, IEEE Trans. Energy Convers.,vol. 12, no. 2, pp. 127132, Jun. 1997.

[25] J. Seok and S. Sul, Induction motor parameter tuning for high per-formance drives, IEEE Trans. Ind. Appl., vol. 37, no. 1, pp. 3541,Jan.-Feb. 2001.

[26] T. C.Chen,J. S.Chen,andC. C.Tsai, Measurement of induction motorparameter identification, in Proc. 8th IEEE Instrumentation and Mea-surement Technology Conf., 1991, pp. 288291.

[27] S.R. Shawand S.B. Leeb, Identification of induction motor parametersfrom transient statorcurrent measurements,IEEE Trans. Ind. Electron.,vol. 46, no. 1, pp. 139149, Feb. 1999.

[28] F. Alonge, F. DIppolito, S. La Barbera, and F. M. Raimondi, Param-eter identification of a mathematical model of induction motors via leastsquare techniques, in Proc. IEEE Int. Conf. Control Applications, Tri-este, Friuli-Venezia Giulia, Italy, Sep. 14, 1998, pp. 491496.

[29] F. Alonge, F. DIppolito, G. Ferrante, and F. M. Raimondi, Parameteridentification of induction motor model using genetic algorithms, in

Inst.Elect. Eng. Proc. Control Theory, vol.145,Nov. 1998,pp.587593.[30] G. S. Buja, R. Menis, and M. I. Valla, MRAS identification of the in-

duction motor parameters in PWM inverter drives at standstill, in Proc.IEEE IECON 21st Int. Conf. Industrial Electronics, Control, and Instru-

mentation, vol. 2, 610, 1995, pp. 10411047.[31] I. D. Landau, Adaptive Control: The Model Reference Approach. New

York: Marcel Dekker, 1979.

[32] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. En-

glewood Cliffs, NJ: Prentice-Hall, 1989.

[33] K. S. Narendra, Parameter adaptive control-the end . . . or the begin-ning?, in Proc. IEEE CDC, vol. 3, 1994, pp. 491496.

[34] A. Bilate and H. Grottstollen, Parameter identification of inverter-fed

induction motor at standstill with correlation method, in Proc. 5th Eur.Conf. Power Electronics and Applications, vol. 5, 1993, pp. 97102.

[35] T. Caussat, X. Roboam, J. C. Hapiot, J. Faucher, and M. Tientcheu, Selfcommissioning for PWM voltage source inverter-fed induction motor at

standstill, in Proc. 20th IECON Int. Conf. Industrial Electronics, Con-trol and Instrumentation, vol. 1, 1994, pp. 198203.

[36] M. Bertoluzzo, G. S. Buja, and R. Menis, Inverter voltage drop-freerecursive least squares parameter identification of PWM inverter-fed in-duction motor at standstill, in Proc. IEEE Int. Symp. Industrial Elec-tronics, vol. 2, 1997, pp. 649654.

[37] M. Sumner and G. M. Asher, Autocommissioning for voltage-refer-enced voltage-fed vector-controlled induction motor drives, in Inst.

Elect. Eng. Proc. Control Theory, vol. 140, May 1993, pp. 187200.

[38] C.B. Jacobina, J.E. C.Filho,and A.M. N.Lima, Estimating the param-eters of induction machines at standstill, IEEE Trans. Energy Convers.,vol. 17, no. 1, pp. 8589, Mar. 2002.

[39] H. Pan, J. Jiang, and J. Holtz, Decoupling control and parameter identi-ficationoffield-orientedinduction motor with saturation, in Proc. IEEE

Int. Conf. Industrial Technology, 1996, pp. 757761.[40] M. Summer, Estimation of the magnetising curve of a cage induction

motor using extended kalman filter, in Proc. IEEE Int. Symp. Industrial

Electronics, vol. 1, 1995, pp. 321326.[41] G. Kreisselmeier, Adaptive observers with exponential rate of conver-gence, IEEE Trans. Autom. Control, vol. 22, pp. 28, Feb. 1977.

[42] M. Gevers and G. Li, Parametrization in Control, Estimation, and Fil-

tering Problems. Berlin, Germany: Springer-Verlag, 1993.

[43] I. D. Landau, R. Lozano, and M. MSaad, Adaptive Control. Berlin,Germany: Springer-Verlag, 1997.

[44] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric

Machinery. Piscataway, NJ: IEEE Press, 1995.

[45] IEEE Standard Test Procedure for Polyphase Induction Motorsand Gen-

erators, 1996. IEEE Std. 112-1996.

[46] I. D. Landau, Unbiased recursive identification using model referenceadaptive techniques, IEEE Trans. Autom. Control, vol. AC21, no. 2,pp. 194202, Apr. 1976.

[47] P. Gahinet, A. Nemirovski, and A. J. Laub, Matlab LMI Control Toolbox

Users Guide: The MatWorks Inc., 2000.

[48] T. Coleman, M. A. Branch, and A. Grace, Matlab Optimization ToolboxUsers Guide: The MatWorks Inc., 1999.

[49] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix

Inequalities in System and Control Theory. Philadelphia, PA: SIAM,

1994.

[50] H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1994.

[51] Y. Bar-Shalom and T. E. Fortmann, Tracking and Data Associa-

tion. New York: Accademic, 1987, vol. 179.

[52] S. G. Jeong and M. H. Park, The analysis and compensation of dead-time effects in PWM inverters, IEEE Trans. Ind. Electron., vol. 38, no.2, pp. 108114, Apr. 1991.

Paolo Castaldiwas born in Bologna, Italy. He re-ceived the Laurea degree in electronic engineering

and the Ph.D. degree in system engineering from theUniversity of Bologna, Italy, in 1990 and 1994, re-spectively.

Since 1995, he has been a Research Associate inthe Department of Electronics, Computer Science,and Systems (DEIS), University of Bologna. Hisresearch interests include adaptive filtering, systemidentification, fault diagnosis and their applicationsto mechanical and aerospace systems.

Andrea Tilli was born in Bologna, Italy, on April 4,1971. He received the Laurea degree in electronic en-gineering and thePh.D. degreein system engineering

from the University of Bologna, Italy, in 1996 and2000, respectively.

Since 1997, he has been with the Department ofElectronics, Computer Science, and Systems (DEIS),University of Bologna. Since 2001, he has been a Re-search Associate at DEIS. He is also a Member of theCenterfor Research on ComplexAutomated Systems

Giuseppe Evangelisti (CASY), established withinDEIS. His current research interests include applied nonlinear control tech-niques, adaptive observers, variable structure systems, electric drives, automo-tive systems, active power filters, and DSP-based control architectures.

Documents

Parameter Estimation of IM at Standstill With Magnetic Flux Monitoring