closed-loop control impact on the diagnosis of

1318 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 36, NO. 5, SEPTEMBER/OCTOBER 2000

Closed-Loop Control Impact on the Diagnosis ofInduction Motors Faults

Alberto Bellini, Associate Member, IEEE, Fiorenzo Filippetti, Giovanni Franceschini, Associate Member, IEEE,and Carla Tassoni, Senior Member, IEEE

Abstract—In this paper, the impact of control on faulted induc-tion machine behavior is presented. The diagnostic indexes usu-ally used for open-loop operation are no longer effective. Simula-tion and experimental results show that the spectrum of the fieldcurrent component in a field-oriented controlled machine hassuitable features that can lead to an effective diagnostic procedure.Specifically, in the case of stator and rotor faults the spectrumcomponents at frequencies2 and 2 , respectively, are quite in-dependent of control parameters and dependent on the fault ex-tent.

Index Terms—Fault diagnosis, induction motor drives.

I. INTRODUCTION

I N the supervision of electrical equipment, the task of diag-nostic systems is to detect an upcoming machine fault as

soon as possible, in order to save expensive manufacturing pro-cesses or to replace faulty parts. This task is often not trivial,as the impact of many faults is small, and can be masked bythe noise of electrical quantities or by changes in environmentalconditions, therefore, the diagnostic techniques have to be verysensitive.

As far as open-loop induction machines are concerned usu-ally the input current [1]–[4], the stray flux [5] or the electro-magnetic (EM) torque [6] is monitored in quasi-steady-stateconditions, in order to detect machine faults. In the literature,the issue of faults injected by a voltage-source inverter (VSI) inthe motor supply was also tackled in order to diagnose furtheranomalous operating conditions [7], [8]. Addressing diagnostictechniques based on current signature analysis, several proce-dures for the detection and severity classification of both statorshort circuits and rotor bar breakage have been proposed formachines supplied at fixed frequency or at fixed-voltage hertzratio. Usually, the anomalous components introduced by a spe-cific fault in the current spectrum are investigated and the di-agnostic procedure is able to correlate the amplitude of thesecomponents to the fault extent [9]–[14].

As for closed-loop drives, the control itself modifies the be-havior of supply variables and more sophisticated procedures

Paper IPCSD 00–005, presented at the 1999 Industry Applications SocietyAnnual Meeting, Phoenix, AZ, October 3–7, and approved for publication inthe IEEE TRANSACTIONS ONINDUSTRYAPPLICATIONSby the Electric MachinesCommittee of the IEEE Industry Applications Society. Manuscript submitted forreview June 15, 1999 and released for publication March 14, 2000.

A. Bellini, G. Franceschini, and C. Tassoni are with the Dipartimento di In-gegneria dell’Informazione, University of Parma, I-43100 Parma, Italy (e-mail:[email protected]; [email protected]; [email protected]).

F. Filippetti is with the Dipartimento di Ingegneria Elettrica, University ofBologna, I-40136 Bologna, Italy (e-mail: [email protected]).

Publisher Item Identifier S 0093-9994(00)07609-X.

must be adopted in order to assess machine conditions. A recentproposal has been presented in [15]–[17], where the differenceof torque amplitude computed in different ways, as a functionof rotor position, is sensed to detect the presence of rotor faults.The proposed torque computation method aims at producing theindependence of torque ripple produced by the fault of operatingconditions and control parameters.

With the aim of extending the diagnostic procedures devel-oped for open-loop faulted machines to the closed-loop opera-tions, the authors have started in [18] a systematic analysis of thebehavior of controlled induction machines with stator or rotorelectric faults. In this first approach, the faults were introducedas one-side asymmetries, caused by an additional resistance inthe stator or in the rotor windings. Simulation and experimentshave shown that, as expected, the typical spectrum lines pro-duced by asymmetries in the machine input currents are presentin the voltage spectrum as well. The amplitude of these lines de-pends on the control structure and on its parameters, therefore,the usual diagnostic indexes are no longer effective. However,it resulted that the flux control current, i.e. thecurrent in thefield-oriented control structure considered, is quite independentof the control parameters and depends on asymmetry degree.

In this paper, real electric faults, i.e., stator short circuits androtor bar breakage, are considered (Fig. 1). For the machine withbroken rotor bars, the authors use a simplified dynamic model,developed starting from more complex models, which providessufficiently good results and that is here recalled [19]–[21]. Forthe machine with a stator short circuited, the extension to the dy-namic behavior of a simple steady state model is here presented[22], [23]. These models allow for the consideration of the faulteffects in the dynamic simulation of the whole drive.

By simulations, a map of the amplitude of the specific linesintroduced by the faults in the spectrum of different variablescan be drawn versus control parameters for some fault degrees.Besides machine current and voltages, field currentandtorque current are investigated. The experiments performedwith a digitally controlled drive confirm the effectiveness of thesimulation results and, thus, the effectiveness of the proposedfaulted machine model.

The amplitude of machine current spectrum lines is comparedwith that of the open-loop machine in steady-state conditionsin order to address the different behavior. The features of theother electric variables are monitored, too, and, as expected, theamplitude of the specific component introduced in the current

spectrum by the faults is practically independent of the con-trol parameters, namely, the proportional speed loop gain, anddepends on fault degree. Therefore, it should be possible to de-

0093–9994/00$10.00 © 2000 IEEE

BELLINI et al.: DIAGNOSIS OF INDUCTION MOTORS FAULTS 1319

Fig. 1. Stator short circuit and rotor bar breakage.

Fig. 2. Two-axes simplified model of stator short circuits and rotor bar breakage.

velop new diagnostic indexes, based onspectrum line ampli-tude. However, the authors are not able to state the relationshipbetween the diagnostic index and the fault extent, since the theparameters of other drive components, beyond the machine pa-rameters, affect the control variables.

II. FAULTED MACHINE MODELS

Several models for a machine with broken bars were proposedin the literature [24], [25] while more recently, stator short-cir-cuited machine models have been introduced, too [26], [27].These models are steady-state models and, thus, are not suitablefor dynamic simulation. In the last few years, dynamic modelswere developed both for rotor breakage [19] and stator shortcircuit [28]. However, the complexity of these models leads tounacceptable run time of controlled drive simulation. Therefore,simpler models are needed in order to allow several simulationsin different conditions and to predict the outstanding effects pro-duced by the faults. Specifically, the stator fault model must pro-vide the negative-sequence current at frequencyof the ma-chine input variables, and the rotor fault model must provide thecurrent spectrum line at frequency . These models canbe easily commuted to steady-state models, using the transfor-mation from to symmetrical components [29]–[31]. Addingfurther simplifications, direct diagnostic indexes can be deter-mined which still allow an effective first-level diagnosis of thefaults entity [32].

In the modelization of the controlled machine, the rotor speedis obviously one of the variables, therefore, the faulted machinemodels allow the consideration of the effect of speed ripple dueto the torque ripple, respectively, at frequenciesand . Ifmains supplied machines are considered, the diagnostic proce-dures usually neglect the effect of phenomena atfrequency.

On the contrary, the speed ripple at frequency causes a se-quence of new lines in the current spectrum that cannot be ne-glected [33]. Obviously, in the frequency-controlled machinethe speed ripple at frequency must be considered, too, if thefrequency is low, because it is no more damped by inertia. Inthe following, the models for a stator shorted machine and rotorbar breakage are presented.

A. Stator Shorted Circuit Model

The shorted circuit presence in a stator winding requires theanalysis of a two-poles fundamental flux density wave in themachine air gap. Therefore, no variable transformation couldbe applied and computational methods, accounting for all thetime and spatial harmonics of current and flux density distri-bution, should be used [28]. However, the short-circuit occur-rence allows the machine to operate only if this event affects arestricted number of turns and, thus, when a simplified assump-tion can be adopted. Namely, a machine withshorted turns inone phase with turns can be replaced with a machine with ahealthy stator (three windings with turns) and a dummy statorwinding with shorted turns in the same axis of the shortedwinding. The dynamic behavior of such machine can be ana-lyzed with reference to a two-axes model in a stationary framewith the shorted and, therefore, the dummy winding in theaxis(see Fig. 2). Specifically, the transformation that maintains thecurrent and voltage amplitude and not the power is adopted.

The equation of the dummy winding, whose parameters arereferred to with subscript, is added to the the usual equations ofa symmetrical machine referred to stator frame (1). A short-cir-cuit resistance can be introduced, which is included in the oper-ational impedance . The shorted circuit variables and param-eters, like the rotor ones, are all referred to the stator, and toidentify them the superscriptis added. The following symbols


are defined: , whereis the derivative operator, the mutual inductance coeffi-

cient, , , , and the self-inductance and the resistanceof stator and rotor respectively, is the rotor electricalspeed

(1)

The EMF induced in the shorted turns is proportional to,while for the current transformation the ampere turns equiva-lence must be considered. Therefore, defining , therelationships among the actual variables and those referred tothe stator with turns are , , and

.Starting from the dynamic model represented by (1) and in-

troducing suitable simplifications, an approximated relationshipbetween a few machine parameters and the fault percentage

can be obtained. At first, steady-state conditions must beconsidered, i.e., constant speed and sinusoidal symmetrical volt-ages supply. The components can be replaced by symmet-rical components and the stator asymmetry produced by thedummy windings causes a backward-sequence current at fre-quency rotating with respect to rotor at frequency

. The dummy winding being a single-phase one, it featuresforward and backward components of equal amplitude

, and . Naming,

and , (2) is obtained

(2)

Introducing the leakage reactance ,, and ,

expressing the magnetizing terms and dividing the third and thefourth equations respectively byand we obtain thestandstill equivalent model

(3)

Fig. 3. Steady-state equivalent circuit of the machine with a stator shortcircuited.

Fig. 4. Simplified equivalent circuit of the machine with a stator shortcircuited.

As , the above equations correspond to the equivalentcircuit of Fig. 3, where no current flows in the branch and,thus, it can be omitted. Moreover, if the magnetizing currentsare neglected, the circuit becomes as in Fig. 4.

With further assumptions from the circuit of Fig. 4, it stemsthat the stator backward-sequence current is linked to the short-circuit characteristics. Due to the dissimilar resistance values,the voltage drop can be neglected with respect to .This voltage, neglecting stator voltage drop, is equal to the ap-plied voltage , therefore, . This current issplit into the stator and rotor backward components at node.Owing to common parameters values, it can be assumed that theamplitude of these backward currents are quite equal, so that thefollowing relationship holds in terms of amplitude:

(4)

The equivalent impedance is composed by the impedance ofthe shorted turns and by the fault impedance. For zero faultimpedance, a relationship betweenand can be found. In


Fig. 5. Steady-state equivalent circuit of the machine with a rotor additional resistance.

Fig. 6. Simplified equivalent circuit of the machine with a rotor additional resistance.

fact, for a low value of the turns reactance can be neglectedin comparison with the turns resistance, which is and,therefore, . The stator backward-sequence cur-rent becomes

(5)

In spite of the heavy assumptions adopted, this relationship canbe used as a first-level diagnosis of short circuit turns in the caseof no short-circuit resistance [23].

B. Rotor Bar Breakage Model

A breakage of contiguous bars in a rotor with barscan be simulated by the dummy resistancein one of the windings of the three-phase equivalent slip-ringmachine [34]. The additional resistance becomes in thetwo-phase model equal to (Fig. 2). In the following, thesymbol is introduced. The dynamical model ofthe faulted machine referred to rotor frame, which will be usedfor simulation purposes, is, therefore, reported in (6)

(6)

With further simplifications, it is possible to derive an approx-imated relationship among a few machine parameters and thefault percentage from the dynamic model represented by(6). Again, steady-state conditions must be considered, i.e., con-stant speed and sinusoidal symmetrical voltages.components

can be replaced by symmetrical components. Therefore, doingthe asymmetry of the rotor, provoked by the dummy resistance,causes in the rotor windings an additional backward-sequencecurrent rotating at frequency , when referred to thestator. Moreover, the symmetrical component impedance trans-formation introduces the forward impedance and the back-ward impedance , therefore, relationship (7) holds

(7)

where and .Expressing the magnetizing terms, dividing the second equationby and the third and the fourth by, the model equationsbecome

(8)

The above equations can be represented by the equivalent circuitof Fig. 5. If the magnetizing branches are neglected, it becomesas in Fig. 6. With further assumptions, an approximated rela-tionship between the component at frequencyandof the stator current can be obtained. Neglectingwith re-spect to in the branch with the additional resistance


Fig. 7. Block diagram of a field-oriented motor drive.

and replacing the total impedance of the branch BD by ,the following relationship holds in terms of amplitude:

(9)

The adopted model, based on the generalized rotating fieldtheory, refers to forward- and backward-sequence currents.On the asymmetrical rotor there are effectively forward-and backward-sequence currents at the same frequency.Referring the rotor backward-sequence current to the stator,the corresponding sequence appears at frequency . Ifthis frequency is positive, it is effectively a backward sequence.However, this is not the case for usual slip values, therefore, itappears as an equivalent forward-sequence current at frequency

.The constant-speed assumption required for the above-re-

ported modelization leads to incorrect results. The speed rippleis at low frequency and it is only partially damped by theinertia, and its effect must be introduced. The rotating magneticfield contains a periodical mechanical angular variation whichinduces EMF and currents at frequencies . Therefore,a right sideband current component at frequency isadded, beyond the modification of the left sideband current.

The authors have noted that the sum of the two sideband com-ponents at frequencies depends mainly on the faultdegree and not on the inertia, therefore, relationship (9) can stillbe adopted to determine the faulted bars number, if the sum ofthe amplitude of the two current components is used [33].

III. CONTROL IMPACT ON DIFFERENTVARIABLES

When closed-loop control systems are used, all the manipu-lated variables are available beyond those at the motor termi-nals. These variables, i.e., the outputs of the regulators, can besensed for diagnostic purposes, and the results are very useful,since they show directly the action of control. Namely, a fault inthe machine can be sensed as a plant parameter variation. Sincethe regulators in presence of faults will still force the controlledvariables to the reference value, the controller output changes,reflecting fault entity and type. Therefore, new diagnostic in-dexes can be retrieved from manipulated variables, too.

Drive topology must be considered and, according to theadopted control scheme, machine faults affect specific vari-ables, easing the diagnostic procedure. Obviously, the controlgains affect the behavior of the system, and their effects shouldnot mask the diagnostic procedure.

In this paper, a field-oriented induction motor drive is inves-tigated adopting the common scheme depicted in Fig. 7, limitedto constant flux speed range. Current loops are closed on a ref-erence frame synchronous with the rotor flux. The angle and theamplitude of rotor flux are obtained by means of a flux observerthat allows for the control of the amplitude of rotor flux as well.With this configuration, the output of the flux controller, i.e.,the requested magnetizing current, and the output of the speedcontroller, i.e., the requested torque current, can be monitoredfor diagnostic purposes.

It should be expected that the torque currentis not suf-ficiently robust as a diagnostic index, since it is strongly af-fected by operating conditions. In particular,is affected byload torque value and ripple. Moreover, the amplitude of thespectrum components introduced by anomalies is, in general,dependent on the speed loop bandwidth usually set by the userand on the frequency of electrical quantities.

On the other hand, the field current seems to be very at-tractive. Flux loop bandwidth is set by the manufacturer and,therefore, it usually features fixed and well-known control pa-rameters. It does not depend on operating conditions if decou-pling is correct. Therefore, it should be expected that anomalousspectrum lines appearing in thespectrum depend only on ma-chine troubles, and are independent of operating conditions.

Several simulations have been performed in order to provethese assertions, relying on the dynamic models reportedwith different fault degrees. Then, experiments have beenperformed on real-time-controlled machines by means of adigital-signal-processor (DSP)-based drive. Two identical cagemachines have been used: one for stator faults with windingtaps to realize short circuits, and the other one for rotor faults,introduced by rotor bar breakage. The data of the machines areas follows: 1.5 kW, 50 Hz, 400 V, 4 A, 1410 rpm, ,

, mH, mH, and .The machines are a three slots/pole/phase with a total of 36

stator slots. In every slot, two coils of 44 turns are located,


Fig. 8. Amplitude of�f spectrum lines (%) of~i with different n=Npercentage, simulation (solid line) and experimental (dotted line) results.

Fig. 9. Amplitude of�f spectrum lines (%) of~v with different n=Npercentage, simulation (solid line) and experimental (dotted line) results.

resulting in 264 turns/phase. The terminal connections oftwo coils are available and two shorted circuit tests, respec-tively, involving 22 turns, %, and 44 turns,

%, have been performed. The amplitude of thecurrent flowing in the short-circuited turns is very high and theJoule losses could damage insulation [22]. In fact, the currentcan be expressed as the ratio between the EMF induced in theshort-circuited turns, and the turns resistance, neglecting thereactance. A suitable choice of the speed set point, that leads toa frequency lower than the rated one, limits the EMF, which isdependent on frequency and, therefore, the current. However,in order to further reduce the current amplitude, an externaladditional resistance of 1.5is added, which can be consideredas a fault resistance. As for rotor faults, a breakage of one barand then of another contiguous one are operated in sequence.

The speed reference values forced for stator and rotorbreakage are, respectively, 41 and 141 rad/s; this choice anda load equal to 60% of the rated one result in frequenciesrespectively close to 15 and 45 Hz. Therefore, the anomalous

Fig. 10. Amplitude of2f spectrum lines (%) ofi with different n=Npercentage, simulation (solid line) and experimental (dotted line) results.

Fig. 11. Amplitude of2f spectrum lines (%) ofi with different n=Npercentage, simulation (solid line) and experimental (dotted line) results.

spectrum components, respectively, at frequenciesand, are close to 30 Hz and 6 Hz.

The speed loop proportional gainis used as a parameter,in order to analyze the different impact of regulator parameterson the anomalous harmonics contents, while the integrative gainis set to zero. Specifically, the speed loop bandwidth is variedfrom 10 up to 40 Hz. The fixed speed reference value leadsobviously to a shift of supply frequency as speed control gain orfault degree changes. The bandwidths of the current loops areset to 600 Hz.

The field-oriented induction motor drive was simulated withMatlab and the different variables are examined. Obviously, inrotor faults simulation the transformation and inverse transfor-mation blocks from fixed frame to rotor frame are needed, sincethe model is in that reference frame.

Considering stator faults simulation, the space vector of cur-rents must be computed in order to span the whole frequencyrange in order to account for both negative and positive se-quences. The space phasors are built from currents and voltages


Fig. 12. Amplitude of(1� 2s)f spectrum lines (%) ofi with one and twobroken bars, simulation (solid line) and experimental (dotted line) results.

Fig. 13. Amplitude of(1� 2s)f spectrum lines (%) ofv with one and twobroken bars, simulation (solid line) and experimental (dotted line) results.

Fig. 14. Amplitude of2sf spectrum lines (%) ofi andi with one and twobroken bars, simulation (solid line) and experimental (dotted line) results.

Fig. 15. FFT spectrum of~i for a faulted machine (stator) with differentkvalues,n=N = 8:3%.

Fig. 16. FFT spectrum of~v for a faulted machine (stator) with differentkvalues,n=N = 8:3%.

in the stator reference frame and are indicated in the followingas and . The amplitude of spectrumlines at frequency of the current and voltage space phasorsas a function of the proportional gainare reported in Figs. 8and 9, while the correspondent amplitude at frequencyofand current spectrum are in Figs. 10 and 11.

The two above-noted fault percentages are considered. Noticethat the theoretical steady-state rms values of backward currentcomponents according to the relationship (4) are, respectively,normalized by the test current, and .

These results address that the component of the currentspace phasor is no more effective as a diagnostic index for statorfaults as far as closed-loop systems are concerned: the currentcomponent is not constant with proportional gain variation andis not consistent with (4). Relying also on the correspondingvoltage component, a mixed benchmark should be investigatedto retrieve a new diagnostic index from the combination of cur-rent and voltage components.


Fig. 17. FFT spectrum ofi current varying thek parameter,n=N = 8:3%.

Fig. 18. FFT spectrum ofi current varying thek parameter,n=N = 8:3%.

Figs. 10 and 11 report simulation results for thespectrumcomponents of the controlled variablesand , and addresstheir peculiarities. As is known, the currents in thecompo-nents are referred to a reference frame rotating with the rotorflux, therefore, the spectrum is shifted in frequency. It resultsthat the harmonic amplitude of the current can lead to anew diagnostic index, quite robust with the control parametersand dependent on the fault extent. On the contrary, thehar-monic amplitude of the is strongly dependent on the propor-tional gain .

As far as rotor faults are concerned, the usual slip values leadto positive values of the critical spectrum components at fre-quency , therefore, the negative range of frequencydoes not contribute to an effective fault analysis. This is thereason why only the spectrum of one phase voltage and cur-rent is analyzed. Results are reported in Figs. 12–14 for oneand two broken bars. The same consideration reported above for

Fig. 19. FFT spectrum of~i for a faulted machine (stator) with differentn=Npercentage,k = 10.

Fig. 20. FFT spectrum of~v for a faulted machine (stator) with differentn=Npercentages,k = 10.

stator faults on input current and voltage space vectors can beadopted in this case, simply referring current and voltage spec-trum components at frequencies . Notice that the theo-retical steady-state values of backward current components ac-cording to the relationship (9) are, respectively,and .

Again, the features of the spectrum component at fre-quency seem very attractive for diagnostic purposes. Infact, this component is independent of control parameters andis dependent quite linearly on the fault degree. Notice that, inFig. 14, the same chart reports bothand shapes, that havethe same order of magnitude, since the speed ripple is withinthe control bandwidth for the considered value of frequency.


Fig. 21. FFT spectrum ofi for a faulted machine (stator) with differentn=Npercentages,k = 10.

Fig. 22. FFT spectrum ofi for a faulted machine (stator) with differentn=Npercentage,k = 10.

IV. EXPERIMENTAL RESULTS

Using a fully digitally controlled drive, the experiments cor-responding to the simulated conditions have been performed andthe different variables have been sampled for fast Fourier trans-form (FFT) computation.

As for stator faults, different values of the proportional gainhave been used and the electrical quantities, , , and(in order to build the phasors and ), , and have beenprocessed. Some FFT spectra of the different variables are re-ported in Figs. 15–18 for different proportional gain values anda fixed fault percentage and in Figs. 19–22 for the two fault per-centages and a fixedvalue. The healthy machine has also beenanalyzed for comparison, showing the intrinsic anomalies of the

Fig. 23. FFT spectrum ofi for a faulted machine (rotor) with differentkvalues and two broken bars.

Fig. 24. FFT spectrum ofv for a faulted machine (rotor) with differentkvalues and two broken bars.

manufacturing process. Notice that the amplitudes of the spacephasors are normalized.

Experimental results confirm that the component at fre-quency changes in function of control gainwhile theharmonics of the current is constant with variations andshould be a better diagnostic index. So far, it is not possible toprovide a quantitative evaluation of the fault degree, since thenumber of parameters is too high. Moreover, the additional re-sistance avoids stating a proportional relationship with the faultpercentage . Notice that, in the experimental results, spec-trum lines appears in correspondence of mechanical speed andof converters bias.

As for rotor faults, Figs. 23–26 report the FFT spectra of inputcurrent, voltage, and of controlled variables for different valuesof proportional speed gain. Figs. 27–30 report the results ob-tained with one or two broken bars and with the healthy machine


Fig. 25. FFT spectrum ofi current varying thek parameter and two brokenbars.

Fig. 26. FFT spectrum ofi current varying thek parameter and two brokenbars.

for a constant value of proportional gain. The experimental re-sults, indicated by the dots in Figs. 8–14, confirm that the onlyeffective quantity to be considered for diagnostic purposes in acontrolled machine is still the current spectrum.

Notice that for rotor faults the speed ripple is slightly dampedby mechanical inertia and, thus, the amplitude of thecompo-nents at frequency is comparable with the correspondingcomponents for the considered fault percentages and frequency.On the contrary, for stator faults mechanical inertia stronglysmoothes the amplitude of thecomponent at frequency .

It should also be considered that the information containedin the sideband components introduced by the speed ripple is

Fig. 27. FFT spectrum ofi for a faulted machine (rotor) with zero, one, andtwo broken bars,k = 10.

Fig. 28. FFT spectrum ofv for a faulted machine (rotor) with zero, one, andtwo broken bars,k = 10.

lost when the frequencies of the input variables are shifted byand the manipulated variables are analyzed. This considera-

tion holds both for rotor faults, for which the components at fre-quencies become a single component at , and forstator faults, for which the sideband components at frequencies

, corresponding to the speed ripple, become a singlecomponent at .

V. CONCLUSION

As far as voltage-supplied machines are concerned, suitablecomponents of the current space-vector spectrum can be used todetect electrical faults and to evaluate their entity. Specifically,the negative-sequence component at frequencycan diagnosestator faults, while the sideband components at frequencies

can diagnose rotor faults.


Fig. 29. FFT spectrum ofi current with zero, one, and two broken bars,k =

10.

Fig. 30. FFT spectrum ofi current with zero, one, and two broken bars,k =

10.

As for controlled machines, these indexes are no more effec-tive, as their information is masked by control action. There-fore, the behavior of other variables have been investigated withthe aim of finding new indexes suitable for diagnostic purposes.Simulation and experimental results have proved that the spec-trum of the field current can be an effective diagnostic indexwhen the field-oriented control scheme is adopted. In fact, theamplitudes of the spectrum components at frequenciesand

are almost constant with proportional gain variations andthey seem quite linearly dependent on stator and rotor faults de-grees, respectively. On the contrary, the corresponding compo-nent of torque current is dependent on control gain, load con-ditions and, overall, on the frequency.

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Alberto Bellini (S’96–A’98) was born in Forlì, Italy,in 1969. He received the M.S. and Ph.D. degreesin electronics engineering from the Universityof Bologna, Bologna, Italy, in 1994 and 1998,respectively.

Since 1997, he has been with the Universityof Parma, Parma, Italy, where he currently is anAssistant Professor of Electrical Engineering. Hisresearch interests include applications of artificialintelligence to nonlinear signal processing, industrialdrive control, and diagnostics. He has coauthored

more than 30 published scientific conference and journal papers.

Fiorenzo Filippetti was born in Fano, Italy, in 1945.He received the Master’s degree in electrical engi-neering from the University of Bologna, Bologna,Italy, in 1970.

He joined the University of Bologna in 1976 as anAssistant Professor and is currently an Associate Pro-fessor of Electrotechnics in the Department of Elec-tric Engineering. He has authored or coauthored morethan 90 published scientific papers and is the holderof an industrial patent. His main research interests in-clude the simulation and modeling of electric circuits

and systems and the application of diagnostic techniques to circuits and systems.Prof. Filippetti is a member of the Italian Association of Electric and Elec-

tronics Engineers (AEI) and of the European Consortium for Research on Con-dition Monitoring of Electric Systems and Drives (CRCM).

Giovanni Franceschini (A’97) was born in Castel-novo ne’ Monti, Italy, in 1960. He received theMaster’s degree in electronic engineering from theUniversity of Bologna, Bologna, Italy.

He is currently an Associate Professor at the Uni-versity of Parma, Parma, Italy. His current researchinterests include high-performance electric drivesand diagnostic techniques for industrial electricsystems. He has authored or coauthored more than60 published technical papers on these topics.

Carla Tassoni (A’90–SM’92) was born in Bologna,Italy, in 1942. She received the Master’s degreein electrical engineering from the University ofBologna, Bologna, Italy, in 1966.

She joined the University of Bologna as anAssistant Professor and then became an AssociateProfessor of Electrical Machines in the Departmentof Electric Engineering. She is currently a Full Pro-fessor of Electrical Engineering at the University ofParma, Parma, Italy. She has authored or coauthoredmore than 100 published scientific papers and is

the holder of an industrial patent. Her main research interests include thesimulation and modeling of electric systems and applications of diagnostictechniques.

Prof. Tassoni is a senior member of the European Consortium for Researchon Condition Monitoring of Electric Systems and Drives (CRCM).

closed-loop control impact on the diagnosis of

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