Detection of rotor broken bar and eccentricity faults in induction motors via second order sliding...

7/28/2019 Detection of rotor broken bar and eccentricity faults in induction motors via second order sliding mode observer

1/6

Detection of rotor broken bar and eccentricity faults in induction

motors via second order sliding mode observer

Alessandro Pilloni, Alessandro Pisano, Elio Usai and Ruben Puche-Panadero

Abstract This paper provides a novel approach for de-tecting certain abnormal operating conditions in squirrel cageinduction motors (SCIMs). A mathematical model of the faultyoperating mode is derived with the rotor broken bars and therotor eccentricity being the faults of interest. To detect the faultoccurrence, an appropriate FDI observer, based on second ordersliding modes, is presented and analyzed by Lyapunov methods.

The ability of the suggested FDI observer to produce suitableresidual signals which allow a reliable threshold-based faultdetection is shown. Once the fault is detected, dedicated FFTanalysis of the residuals allows the classification of the fault.The proposed scheme has been verified by real implementationtests using measurements taken from certain commercial three-phase SCIMs intentionally damaged in order to reproduce thefault scenarios of concern. Experimental results confirm thereliability of the suggested framework.

I. INTRODUCTION

Nowadays three-phase Squirrel Cage Induction Motors

(SCIMs) are used in a variety of industrial applications

due to their cheapness, ruggedness and low maintenance

[1]. Voltage stresses, caused by the modern high frequency

power converters, along with the corrosive and dusty industry

environments where motors are used to operate can reduce

the motor lifetime considerably. Rotor has always been

considered the Achilles heel of SCIMs. Although the design

of stator windings has achieved remarkable improvements,

cage rotor design has undergone little change [1].Technical surveys have shown a remarkable percentage of

total SCIM failures is found in the rotor, with, particularly,

broken bars, end-ring faults, and eccentricity, being the most

common failures [2], [3], [4], [5], [6]. Prompt detection

of these abnormal conditions is helpful to avoid costly

disservice, and the potentially catastrophic breakdowns that

can take place if the fault remains undetected.

Even though temperature and vibration monitoring devices

have been utilized for decades, recent research efforts have

been directed towards the inspection of the motor currents,

which is more convenient from the practical implementation

point of view. Up to now Motor Current Signature Analysis

(MCSA) methods are the most popular approaches for SCIM

The research leading to these results has received funding from theEuropean Communitys Seventh Framework Programme FP7/20072013under Grant Agreement n224233 [Research Project PRODI Power PlantRobustification based on fault Detection and Isolation algorithms], andn257462 [Research Project HYCON2Network of excellence].

A. Pilloni, A. Pisano and E. Usai are with the Department of Electricaland Electronic Engineering (DIEE), University of Cagliari, Cagliari 09123,Italy

R. Puche-Panadero is with Department of Electrical E ngineering, Uni-versidad Politecnica de Valencia (UPV), Valencia 46022, Espana

Email addresses: {alessandro.pilloni, pisano,eusai}@diee.unica.it, [email protected]

diagnostics [7]. When broken cage bars, end-ring faults,

or abnormal levels of eccentricity occur, asymmetry in the

rotor air-gap appear and spurious harmonics at well defined

characteristic frequencies coming out in the stator current

spectrum [5], [6], [7], [8], [9]. MCSA is an online diagnosis

family of methods which requires just the measurement of a

single stator phase current and, at least under constant load

condition, allows to correctly classify simultaneous failures.

MCSA has the advantage of dispensing with the knowledge

of the electromechanical motor parameters, and it can be

inexpensively implemented by utilizing a current transformer

or current clamp already in place in most industrial applica-tions. As a result, MCSA has become the current standard

for online motor diagnosis [7]. Modern MCSA method-

ologies based on advanced processing techniques such as

Hilbert, Wavelet transforms or Transient MCSA (T-MCSA)

are continuously developed to enhance the reliability of the

diagnosis process [6].

There are, however, some inherent drawbacks of MCSA,

such as its sensitivity to the spectral leakage caused by

the finite-time measurement window, the need for high

frequency resolution (i.e., small sampling intervals), and its

sensitivity to varying load conditions and to the presence of

additional spurious harmonics caused by mechanical devices,

such as gearboxes, that can often overwhelm the frequencypattern associated to the fault [6], [7]. Furthermore MCSA

methodologies have to be periodically activated due to their

inability to identify the occurrence of the faults.

The model-based approach to fault detection and isolation

(FDI) in automated processes growing interest in the last two

decades is studied with [10], [11], [12].

In this paper we present an observer based FDI methodol-

ogy for detecting the occurrence of broken bar or eccentricity

fault conditions. The method requires the measurement of the

stator currents, voltages, shaft speed, and then the knowledge

of the nominal motor electromechanical parameters. To over-

come the uncertainty in the load torque an unknown-input

observation approach, robust to the presence of exogenousinput terms, is taken. The framework of design relies on the

so-called high-order sliding mode observers [12], [13], [14],

[15], [16], [17], [18], [19].

Suitable residuals are computed and processed by a thresh-

old based FDI logic for achieving a quick and compu-

tationally simple detection of the faulty conditions. Once

the occurrence of a fault is detected, additional information

about the nature of the fault occurred can be recovered

by performing a spectral analysis of the faulty residuals.

The main advantage of the method, as compared to the

51st IEEE Conference on Decision and Control

December 10-13, 2012. Maui, Hawaii, USA

7614978-1-4673-2066-5/12/$31.00 2012 IEEE


2/6

MCSA approaches, is that the need of continuous spectral

or transform-based analysis is dispensed with, which reduces

the computational effort of the diagnosis algorithm.

In [20], detection of broken bar faults was considered,

only, by means of a similar approach as that presented in this

paper. Here we extend these previous results by addressing

the possible presence of two types of eccentricity faults as

well, and by providing relevant experimental results.

The paper is organized as follows. In Section II a mathe-

matical model of a SCIM under faulty conditions is presented

along with a brief description of the effects of each faults

in terms of characteristic frequencies. In Section III the pro-

posed FDI observer is outlined. Convergence and estimation

properties are demonstrated, then the suggested FDI logic is

illustrated. Section IV discusses some experimental results

obtained, whilst Section V presents some concluding remarks

and possible lines of investigation for future research.

I I . FAULTY SCIM MODEL

As it is well known, the equations representative of the

nominal (i.e., healthy) operation of a three-phase inductionmotor mathematical model (both Wound or Squirrel-Cage

Rotor) in (, ) reference frame (or stator reference frame)are (see for example [21], [22]):

x1 = a1 (x3x4 x2x5) a2x1 + a3TLx2 = b1x4 b2x2 + b3x1x3 + b4usx3 = b1x5 b2x3 b3x1x2 + b4usx4 = c1x2 c2x4 npx1x5x5 = c1x3 c2x5 + npx1x4

(1)

where ai, bi and ci are coefficients dependent on the machineparameters which take the following form:

a1 =

npLm

JLr

a3 = 1J

b1 =LmRrLsL2r

b3 =npLmLsLr

c1 =RrLr

Lm

a2 =fv

J

= 1 L2mLrLs

b2 =L2mRr+L

2

rRsLsL2r

b4 =1

Ls

c2 =RrLr

(2)

The state-space variables xi with i = 1, . . . , 5 and the elec-tromechanical parameters in (1)-(2) are in Table I. In order

to find out a mathematical representation of the machine in

faulty operating condition we need to identify and considerthe main effects of the faults. Since this paper is focused on

broken bar and eccentricity faults, a brief overview of these

faults is given.

A. Air-Gap Eccentricity Fault

Eccentricity manifests in two different versions, referred

to as static and dynamic eccentricity. Static eccentricity takes

place when the angular position of the minimum radial air-

gap length is fixed in space. It can be caused by stator-core

ovality or incorrect positioning of the rotor in the stator.

TABLE I

NOMENCLATURE OF SCIM MODEL

State Variables:

Shaft speed x1 [rad/sec]

(,) Stator Currents x2,3 [A]

(,) Rotor Fluxes x4,5 [Wb]

Input Signals:

(,) Stator Voltage Supply u, [V]

Load Torque TL [N m]

Model Parameters:

Pole pairs number np -

Rotor and stator resistance Rr,s []

Rotor, stator and mutual inductance Lr,s,m [H]

Viscous friction coefficient fv [Kg m2/s]

Rotor inertia J [Kg m2]

For these reasons an inherent level of static eccentricity

always occurs due to manufacturing tolerances or specific

design features. Dynamic eccentricity corresponds to the case

where the minimum air-gap revolves with the rotor and is

a function of space and time. This can be caused by a

non-concentric outer rotor diameter or rotor thermal bowing.Static and dynamic eccentricity generate an electromagnetic

force called unbalanced magnetic pull (UMP), respectively

of steady and rotating type in the two cases, that in some

cases can bring rotor and stator in contact [6], [7]. The air-

gap eccentricity specified by manufacturers is the radial air-

gap eccentricity (static plus dynamic) and is normally given

as a percentage of the nominal air-gap length. Levels of air-

gap eccentricity should be kept within a maximum of 10%in three-phase SCIMs to avoid their catastrophic damage.

Static plus dynamic eccentricity is also known as mixed

eccentricity. The sideband spurious frequencies associated

with the eccentricity are given by:

fecc = |fs k fr| , k = 1, 2, 3 . . . (3)

where fs and fr are the electrical and mechanical frequenciesof the machine. From (3) it is clear that these specific side-

band frequencies do not depend on the machine parameters.

B. Broken Bars Fault

Breakages in the rotor cage introduce anomalies in the

air-gap magnetic field, and consequently sideband harmonics

appear in the stator currents [2], [7]. These harmonics of fault

7615


3/6

have well-defined frequencies located respectively at:

fbrb = fs [1 2 k s] , k = 1, 2, 3 . . . (4)

where s = 1 r/s is the motor slip, r = 2fr ands = 2fs represent respectively the mechanical speed andthe synchronous speed of magnetic field. Although broken

bar faults do not cause immediate disservice, they can imply

serious secondary effects (i.e. overheating, bar hitting, dam-aging of motor insulation and consequent winding failure)

and hence prompt detection is mandatory.

C. Faulty machine model

From the above considerations regarding the considered

fault scenarios, we can devise that the insertion of additional

exogenous voltages fs, fs in the current equations of(1) might be a reasonable approach for modeling faulty

SCIM drives. The following mathematical model intends to

represent a Faulty SCIM:

x1 = a1 (x3x4 x2x5) a2x1 + a3TLx2 = b1x4 b2x2 + b3x1x3 + b4 (us + fs)

x3 = b1x5 b2x3 b3x1x2 + b4

us + fs

x4 = c1x2 c2x4 npx1x5x5 = c1x3 c2x5 + npx1x4

(5)

where in absence of fault conditions, the additional entries

fs and fs are identically zero, otherwise when somefault occurs they became nonzero and inject the appropriate

pattern frequencies in the model. The load torque TL beinggenerally not available for measurements in applications, it

is deemed as an unknown input within the observer design

problem using the presented model.

It is worth noting by inspection of (3) and (4) that an

accurate estimation of the speed r is a prerequisite for

reliable MCSA diagnosis.

III. SECOND ORDER SLIDING MODE FDI OBSERVER

FO R SCIMS

An algorithm for FDI in SCIMs, supported by the theory

of model-based FDI [10] shall be presented hereinafter.

Model-based FDI is built upon a number of idealized as-

sumptions, one of which is that the mathematical model

used is a faithful replica of the plant dynamics. This is,

of course, unreasonable in practice. For these reasons a

major objective of model-based FDI is to maximize the fault

detection coverage and at the same time minimize the effect

of modeling errors and disturbances [10].

The approach taken in this paper relies upon the use of arobust observer based on the sliding mode theory. In partic-

ular, the desirable feature of the sliding mode to reconstruct,

in some cases, the unknown inputs acting on the observed

system is exploited [23]. It is clear that the fault signals

fs and fs contain useful information (symptoms) aboutthe faults, and their estimation would be extremely useful

for FDI purposes. We will then devise a scheme that can

reconstruct both the unknown exogenous fault signals fsand fs in (5) while mitigating the effect of modeling errorsby relying on the inherent robustness properties of sliding

mode observers. The detection of faults will be achieved

by a non conventional, threshold based residual evaluation

procedure applied to the reconstructed fault signals.

Hereinafter, we shall explore the two main stages of

the FDI scheme design for the considered case of study,

respectively residual generation and residual evaluation.

A. Residual Generation

The aims of residual generation is to reconstruct faultsymptoms using available inputs and outputs token from the

monitored system. The structure of the suggested Unknown-

Input Observer (UIO) is the following:

x1 = a1 (x3x4 x2x5) a2x1 + a31x2 = b1x4 b2x2 + b3x1x5 + b4 (us + 2)x3 = b1x5 b2x3 b3x1x4 + b4 (us + 3)x4 = c1x2 c2x4 npx1x5x5 = c1x3 c2x5 + npx1x4

(6)

Note that the observer equations (6) represent a replica of

the faulty motor model (5) with suitable injection terms 1,

2 and 3 in place of the unknown inputs fs , fs and TL.Shaft speed x1 and stator currents (x2, x3) are supposed tobe available for measurements whereas xi with i = 1, . . . , 5represent the estimated state variables. The observation error

variables are defined as follow

ei(t) = xi(t) xi(t) with i = 1, . . . , 5 , (7)

where e1, e2 and e3 are accessible for measurements, whilee4 and e5 are unknown.

The assumption on the considered exogenous fault signals

are specified as follows.

Assumption 1: Let Fs and FL be a-priory known con-stants, such that, at any t 0, the time derivatives of the

unknown inputs fs, fs andTL satisfy the next inequalities ddt fsi(t)i {,}

Fs ,

ddt TL(t) FL (8)

The observer injection terms are built according to the

following algorithm:

i (t) = i1 (t) + i2 (t) i = 1, 2, 3 (9)

where i1 and i2 are defined as

i1 (t) = ki

| ei (t) | sign(ei (t))

i2 (t) = wi sign(ei (t)) , i2 (0) = 0

(10)

and ki and wi are constants (see [24]).The next theorem sets the underlying tuning rules of the

considered observer and establishes the associated conver-

gence properties.

Theorem 1 Consider the faulty SCIM model (5) and let

Assumption 1 be satisfied. Then, the observer (6), (9), (10)

with the tuning parameters chosen according to

wi > Fi , k2i > 4Fi

wi + Fiwi Fi

i = 1, 2, 3 , (11)

7616


4/6


5/6

TABLE II

SIEMENS 1LA7090 { 2AA10 , 4AA10 } RATINGS

Rated terminal supply voltage: 230 V 400 V Y

Rated frequency/full-load speed: 50 Hz1410 rpm2860 rpm

Rated power :

1.5 kW cos = 0.85

1.1 kW cos = 0.80

Rated supply current with full load:4.60 A 2.70 A Y5.65 A 3.25 A Y

IV. EXPERIMENTAL RESULTS

The suggested methodology has been tested offline by

using real measurements acquired from several healthy and

faulty commercial three-phase SCIMs intentionally damaged

in order to reproduce a broken bar fault and the two consid-

ered types of eccentricity. The broken bar faulty machine has

been realized by drilling a single rotor bar (see right picturein Figure 1). The eccentricity faults have been reproduced by

suitable hardware modification. We have tested respectively

a machine with 0.2mm of static eccentricity, and a second

one with 0.07mm of dynamic eccentricity, too.

The left plot of Figure 1 depicts the structure of the

experimental set-up, where a DC motor is mechanically

coupled to the SCIM under diagnosis in order to apply a

controlled torque. The experimental tests have been per-

formed using several commercial SCIM drives in healthy and

faulty condition. Two 2-pole drives for broken bar tests, and

three 4-pole motors for eccentricity test fed, respectively, at

(230V-, 50Hz) and (400V-Y, 50Hz). Rating parameters

of both SCIMs are reported in the Table II.The electromechanical motor parameters needed for the

observer implementation are derived from the motors data

sheet. After few trial and error tests, devoted to guarantee an

accurate convergence to zero of the measurable estimation

errors e1, e2, and e3 in healthy operating condition, theobserver gains for both tests have been set as follows:

w1 = 14k1 = 80

,w2 = 22k2 = 200

,w3 = 22k3 = 200

, (33)

A suitable value for the time window size T in (31) hasbeen found as

T = 0.3 s . (34)The choice of T turned out to be not critical, satisfactoryperformance has been obtained with different values as well.

The observer (6) has been activated at start-up whereas the

residual evaluation logic (31) is activated after 9 seconds, tolet the machine reach the sinusoidal steady state under the

applied three-phase input voltage.

Figure 2 and Figure 4 show, respectively, the E(t) residualprofiles obtained using measurements from an healthy and a

faulty motor. These figures show that the healthy and faulty

residuals are appreciably different, and a suitable threshold

value , to be used in the fault detection logic (32) forachieving an accurate detection of the fault occurrence, can

be found.

Actually, to perform an affective tuning of the threshold

few experiments with healthy measurements are sufficient,

by selecting the corresponding threshold sufficiently bigger

than the steady state values of E(t). It is apparent from theFigure 2 and Figure 4 that the faulty conditions are diag-

nosed almost instantaneously after that the FDI algorithm is

activated.

Finally, to validate the suggested faulty motor model (5),

and to simultaneously show the effectiveness of the observer

(6) as well, the spectrum of a faulty stator current and one

of the associated injection signal, are compared.

Figures 3 and 5 show that the normalized spectrum of a

stator current (left side) and the spectrum of an injection

signal, e.g. 2(t), (right side) contains the same frequenciesfor broken bar and static eccentricity test respectively. The

satisfactory performances of the suggested FDI observer have

been demonstrated in both the faulty scenarios investigated.

V. CONCLUSIONS AND FUTURE WORKSThis paper has explored a novel approach for fault de-

tection in squirrel cage induction motors based on second

order sliding mode observers. The stability of proposed

unknown input observer has been theoretically proven. Its

effectiveness in detecting the presence of broken cage bars

or eccentricity conditions has been experimentally tested by

offline processing of real motor data taken from several

different commercial 1.1kW an 1.5kW drives.

The computational load of the method is limited, which

makes its online implementation easily feasible with cheap

hardware. The method has provided good performance with

real motor data, which certifies a certain degree of robust-

ness. Noteworthy, the proposed observer allows to recon-

struct, both, the load torque and the direct and quadrature

rotor fluxes.

Among the most interesting directions for next research,

combination of the tested methodology with modern MCSA

classification approaches appears particularly promising.

REFERENCES

[1] A. Bonnett and T. Albers, Squirrel cage rotor options for ac inductionmotors, in Pulp and Paper Industry Technical Conference, 2000.Conference Record of 2000 Annual. IEEE, 2000, pp. 5467.

[2] M. Benbouzid and G. Kliman, What stator current processing-basedtechnique to use for induction motor rotor faults diagnosis? EnergyConversion, IEEE Transactions on, vol. 18, no. 2, pp. 238244, 2003.

[3] A. Bonnett and T. Albers, Squirrel cage rotor options for ac inductionmotors, in Pulp and Paper Industry Technical Conference, 2000.Conference Record of 2000 Annual. IEEE, 2000, pp. 5467.

[4] A. Bonnett and G. Soukup, Rotor failures in squirrel cage inductionmotors, Industry Applications, IEEE Transactions on, no. 6, pp.11651173, 1986.

[5] G. Kliman, R. Koegl, J. Stein, R. Endicott, and M. Madden, Nonin-vasive detection of broken rotor bars in operating induction motors,

Energy Conversion, IEEE Transactions on, vol. 3, no. 4, pp. 873879,1988.

[6] R. Puche-Panadero, M. Pineda-Sanchez, M. Riera-Guasp, J. Roger-Folch, E. Hurtado-Perez, and J. Perez-Cruz, Improved resolution ofthe mcsa method via hilbert transform, enabling the diagnosis of rotorasymmetries at very low slip, Energy Conversion, IEEE Transactionson, vol. 24, no. 1, pp. 5259, 2009.

7618


6/6

Fig. 2. Residuals and chosen threshold (upper plot) and diagnosis signal(lower plot) for the broken bar tests.

Fig. 3. Comparison between the normalized spectra of the faulty motorstator currents (left plot) and that of the observer injection signal 2 (rightplot) for the broken bar test.

[7] M. El Hachemi Benbouzid, A review of induction motors signatureanalysis as a medium for faults detection, Industrial Electronics, IEEE

Transactions on, vol. 47, no. 5, pp. 984993, 2000.[8] G. Didier, E. Ternisien, O. Caspary, and H. Razik, Fault detection

of broken rotor bars in induction motor using a global fault index,Industry Applications, IEEE Transactions on, vol. 42, no. 1, pp. 7988,2006.

[9] W. Thomson and M. Fenger, Current signature analysis to detectinduction motor faults, Industry Applications Magazine, IEEE, vol. 7,no. 4, pp. 2634, 2001.

[10] S. Simani, C. Fantuzzi, and R. Patton, Model-based fault diagnosis indynamic systems using identification techniques, Recherche, vol. 67,p. 02, 2003.

[11] J. Z. Petkovic M., Rapaic M. and P. A., On-line adaptive clusteringfor process monitoring and fault detection, Expert Systems With

Applications, vol. 39, no. 11, pp. 10 22610 235, 2012.[12] N. Orani, A. Pisano, and E. Usai, Fault diagnosis for the vertical

three-tank system via high-order sliding-mode observation, Journalof the Franklin Institute, vol. 347, no. 6, pp. 923939, 2010.

[13] A. Pisano and E. Usai, Sliding mode control: A survey with appli-cations in math, Mathematics and Computers in Simulation, vol. 81,no. 5, pp. 954979, 2011.

[14] A. Pilloni, A. Pisano and E. Usai, Oscillation shaping in uncertainlinear plants with nonlinear pi control: analysis and experimentalresults, in IFAC Conference on Advances in PID Control (PID12.IFAC, 2012.

[15] L. Fridman, J. Davila, and A. Levant, High-order sliding-modeobservation and fault detection, in Decision and Control, 2007 46th

IEEE Conference on. IEEE, 2007, pp. 43174322.[16] T. Floquet, J. Barbot, W. Perruquetti, and M. Djemai, On the robust

fault detection via a sliding mode disturbance observer, InternationalJournal of control, vol. 77, no. 7, pp. 622629, 2004.

[17] E. R. M. Pisano, A. Usai and Z. Jelicic, Second-order sliding mode

Fig. 4. Residuals and chosen threshold (upper plot) and diagnosis signal(lower plot) for the eccentricity tests.

Fig. 5. Comparison between the normalized spectra of the faulty motorstator currents (left plot) and that of the observer injection signal 2 (rightplot) for the eccentricity test.

approaches to disturbance estimation and fault detection in fractional-order systems, in IFAC Conference on Advances in PID Control

(PID12. IFAC, 2012.[18] F. Bejarano and A. Pisano, Switched observers for switched linear

systems with unknown inputs, Automatic Control, IEEE Transactionson, no. 99, pp. 11, 2011.

[19] A. Bejarano, F. PISANO and E. Usai, Finite-time converging jumpobserver for switched linear systems with unknown inputs, Nonlinear

Analysis: Hybrid Systems, vol. 5, no. 2, pp. 174188, 2011.[20] A. Pilloni, A. Pisano, and E. Usai, Robust fdi in induction motors via

second order sliding mode technique, in Variable Structure Systems(VSS), 12th International Workshop on. IEEE, 2012, pp. 467472.

[21] P. Krause and C. Thomas, Simulation of symmetrical inductionmachinery, Power Apparatus and Systems, IEEE Transactions on,vol. 84, no. 11, pp. 10381053, 1965.

[22] R. Marino, S. Peresada, and P. Valigi, Adaptive input-output lineariz-ing control of induction motors, Automatic Control, IEEE Transac-tions on, vol. 38, no. 2, pp. 208221, 1993.

[23] F. Bejarano and L. Fridman, High order sliding mode observer for

linear systems with unbounded unknown inputs, International Journalof Control, vol. 83, no. 9, pp. 19201929, 2010.

[24] A. Levant, Sliding order and sliding accuracy in sliding modecontrol, International journal of control, vol. 58, no. 6, pp. 12471263, 1993.

[25] K. La, M. Shin, and D. Hyun, Direct torque control of inductionmotor with reduction of torque ripple, in Industrial E lectronicsSociety, 2000. IECON 2000. 26th Annual Conference of the IEEE,vol. 2. IEEE, 2000, pp. 10871092.

[26] L. Youb and A. Craciunescu, A comparison of various strategies fordirect torque control of induction motors, in Electrical Machines andPower Electronics, 2007. ACEMP07. International Aegean Confer-

ence on. IEEE, 2007, pp. 403408.

7619

Detection of rotor broken bar and eccentricity faults in induction motors via second order sliding...

Documents

Transcript of Detection of rotor broken bar and eccentricity faults in induction motors via second order sliding...