Abstract -- This paper presents an experimental study of

one broken-rotor-bar time-frequency evolution effects, when

the bar is partially broken in an induction motor by gradually

drilling one hole, each three millimeters, from healthy until the

rotor bar is broken. The one phase current startup transient at

each of three partially-broken conditions (0 mm, 3 mm, 6 mm

and 10 mm) are analyzed, using the short-time multiple signal

classification (MUSIC) method that provides a high-resolution

and a time-frequency pseudo-representation of the signals,

where fault-related frequencies and how they evolve in the

time-frequency spectrum are obtained. Results show how the

gradual drilling of one rotor bar produces a shifting in the fault

frequencies as the defect increases. The sideband components

around the supply frequency are shifted with respect to those

from a healthy rotor bar condition obtaining a regular fault

evolution from a healthy rotor bar until the bar is completely

broken.

Index Terms-- Fault diagnosis, Induction motors, Multiple

Signal Classification, Spectral Analysis.

I. INTRODUCTION

OWADAYS, induction motors are in general,

reliable machines requiring minimum maintenance,

robust and with a simple construction. However, they

eventually deteriorate and fail. An induction motor failure

may yield an unexpected interruption at the industry plant,

with consequences in costs, product quality, and safety. This

gave rise to the need for cost-effective preventive

maintenance based on condition monitoring, which can be

addressed by monitoring and analyzing motor signals. The

origins of inherent faults are due to the mechanical or

electrical forces acting on the machine, where the area of

system maintenance cannot realize its full potential if it is

only limited to preventive approaches. Rather, the early

diagnosis of a developing fault is necessary to allow

maintenance personnel to schedule repairs prior to an actual

This work was partially supported by the SEP-CONACYT project

84723 and CONACYT scholarship 201402. A. Garcia-Perez, R. J. Romero-Troncoso, E. Cabal-Yepez, , HSPdigital -

CA Procesamiento Digital de Senales/ Telematica, Division de Ingenierias, Campus Irapuato-Salamanca, Universidad de Guanajuato, Carr. Salamanca-Valle km 3.5+1.8, Comunidad de Palo Blanco, 36700 Salamanca, Guanajuato, Mexico ({agarcia, troncoso, ecabal}@hspdigital.org).

R. A. Osornio-Rios and J. D. J. Rangel-Magdaleno are with HSPdigital - CA Mecatronica, Facultad de Ingenieria, Campus San Juan del Rio, Universidad Autonoma de Queretaro, Rio Moctezuma 249, Col. San Cayetano, 76807 San Juan del Rio, Queretaro, Mexico ({raosornio, jjrangel}@hspdigital.org).

H. Miranda, CA Electronica de Potencia y Control, Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi, Av. Manuel Nava 8, Zona Universitaria, 78290 San Luis Potosi, S. L. P., Mexico (hmirandav@uaslp.mx).

failure. During the last decade, there has been much interest

in early fault detection and diagnosis techniques for use in

condition-based maintenance (CBM) [1]. In contrast to

preventive maintenance, in CBM one does not schedule

maintenance or machine replacement based on previous

records of machine failure. Rather, one relies on information

provided by condition monitoring systems assessing system

condition. This allows better utilization of equipment

components, leading to a considerable reduction of

downtime and maintenance costs. The key for the success of

CBM is the effective early fault condition detection. Thus,

the detection of incipient fault is of great concern. The

Motor current signature analysis (MCSA), can be identified

as one of the most important fault detection methods

nowadays, as it permits to detect the most common machine

faults. For squirrel cage induction motors, broken-rotor bar

faults account for approximately 10% of all failures [2].

Broken-rotor bars are easy to detect using steady-state

current monitoring. This is based on monitoring the

amplitudes of the double slip frequency sidebands of the

fundamental supply frequency in the current spectrum [3]. It

has been shown that the greater the rotor bar fault severity,

the higher is the amplitude of these sidebands. Nevertheless,

the sideband amplitudes are also sensitive to the number of

broken-rotor bars. Thus, one partially broken-rotor bar fault

at an early stage can lead to a larger failure or even be

catastrophic, and yet may not be detectable under full load

conditions. Therefore, there is a strong need to develop

condition monitoring techniques to address these issues to

allow earlier detection of rotor faults. An option for the

analysis of partially broken-rotor bar can be during direct-

on-line (DOL) starting, where the rotor current in the

induction motor is very high, typically 5 to 6 times the rated

current. Under these conditions, rotor faults should be much

more evident than under normal running conditions. Another

advantage is that the startup current is less sensitive than the

steady-state current to the load level and then, reliable

conclusions from the data analysis can be obtained even

with motors with no mechanical load.

Several methods and techniques can be used to detect one or

several broken-rotor bars in an induction motor, such as [4]-

[7]. Some few are able to detect the partially broken rotor

bar condition, such as Didier et al. [8] presenting a

technique that permits the detection of incipient broken rotor

bar using the Hilbert transform. Razik et al. [9] proposed a

diagnosis of the signature of a growing broken bar using a

genetic algorithm. Yazidi et al. [10] examined the detection

of one half-broken rotor bar using a flux signature analysis.

Startup Current Analysis of Incipient Broken Rotor Bar in Induction Motors using High-Resolution Spectral Analysis

Arturo Garcia-Perez, Member, IEEE, Rene J. Romero-Troncoso, Member, IEEE, Eduardo Cabal-Yepez, Member, IEEE, Roque A. Osornio-Rios, Member, Jose de Jesus Rangel-Magdaleno, Student

Member, IEEE, Homero Miranda, Member, IEEE.

N

978-1-4244-9303-6/11/$26.00 ©2011 IEEE

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Su and Chong [11] presented the development of a neural

network-based condition monitoring and diagnosis of one

half-broken rotor bar. Wolbank et al. [12] proposed the

monitoring of a partially-broken rotor bar using an

excitation of the machine with voltage pulses and the

measurement of the resulting current reaction. Rangel-

Magdaleno et al. [13] examined the methodology for one

half-broken rotor bar detection, which combines current and

vibration analysis.

This paper presents one broken-rotor-bar time-frequency

evolution effects, when the bar is partially broken in a

standard 1 hp three-phase induction motor by gradually

drilling one hole, each three millimeters, from healthy until

the rotor bar is broken. The current startup transient at each

partially-broken condition is analyzed, using the short-time

multiple signal classification (MUSIC) method that provides

high-resolution, improving the diagnosis by detecting

frequencies in a given bandwidth where the partially-broken

rotor bar condition is present. In this work, fault-related

frequencies and how they evolve in the time-frequency

spectrum are obtained. Experimental results show excellent

identification for the gradual fault evolution of one partially-

broken rotor bar. This technique is able to graphically show

the physical effect of a broken or partially-broken rotor bar,

which is a major advantage compared to classical

approaches. Therefore, the method is proven to be sensitive

enough to early detect even a partially-broken rotor bar,

enabling an improved and reliable diagnosis.

II. THEORETICAL BACKGROUND

A. Broken Rotor Bar Fault

The detection of broken rotor bar faults can be done by

the observation of the space harmonics (fBB) components as a

fault indicator:

1BB s

sf k s f

p (1)

where s is the per-unit motor slip, p is the number of pole pairs of the motor, k/p =1,3,5,… are the characteristic values of the motor, and fs is the electrical supply frequency [7].

B. MUSIC Algorithm

The subspace methods are known as high-resolution methods which detect frequencies with low signal-to-noise ratio. The subspace methods assume that the discrete-time signal x[n] can be represented by m complex sinusoids in noise e[n] [14], i.e.

2

1

[ ] [ ], 0,1,2,...., 1i

mj f n

i

i

x n B e e n n N (2)

with

i

i iB B e (3)

where N is the number of sample data, Bi is the complex amplitude of the i-th complex sinusoid, fi is its frequency, and e[n] is a sequence of white noise with zero mean and a

variance 2 . This method uses the eigenvector

decomposition of x[n] to obtain two orthogonal subspaces.

The autocorrelation matrix R of the noisy signal x[n] is the

sum of signal and noise autocorrelation matrices (Rs and Rn

respectively):

2 2

1

PH

n i i i n

i

B f fR R R e e Is

(4)

where p is the number of frequencies and the exponent H

denotes Hermitian transpose, I is the identity matrix and H

ife is the signal vector given by:

2 2 ( 1)1 i ij f j f NH

if e ee (5)

From the orthogonality condition of both subspaces, the MUSIC pseudo-spectrum Q is given by:

2

1

1( )MUSIC

H

m

Q f

fe v

(6)

where 1mv is the noise eigen-vector. This expression

exhibits the peaks that are exactly at frequencies of

principal sinusoidal components where 1

H

mfe v =0.

C. Short-time MUSIC algorithm

In this experimental study, it is analyzed only a small

section of the signal at a time, by using a sliding window

and applied to the startup current signal, and then it is

computed the MUSIC pseudo-spectrum of each section of

the signal, realizing a short-time MUSIC pseudo-spectrum.

The features of MUSIC algorithm consist in detecting the

main frequency components of a signal, reducing noise

influence, and extracting useful information for both

stationary and non-stationary signals. The short-time

MUSIC can be represented using surfaces in the time-

frequency space, as is usual in STFT analysis. The short-

time MUSIC provides more regular surfaces, mitigates the

effects of noise, evidences only larger frequency

components making fault diagnosis simpler, and exhibits

how these faults evolve in the time domain.

D. Time-Frequency startup current analysis

The two drawbacks in dealing with the startup current are first, related to the motor speed, which is constantly changing during the starting, meaning that the fault-signal frequency components are changing in both time and

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frequency; and secondly, the startup current only occurs for a short time. The starting time depends on the total motor inertia and load, so it may change from a fraction of a second for small machines up to several seconds for large machines. Therefore, owing to the transient nature of the signal, conventional FFT analysis is not suitable for analyzing startup current. Although the short-time Fourier transform (STFT) can be used for analyzing transient signals in a time–frequency representation, it has a poor frequency resolution. Some of these drawbacks can be improved using advanced methods that can perform time-frequency analysis and compute the PSD (Power Spectral Density) of the stator current. Transient motor current signature analysis (TMCSA) provides a time-frequency representation of harmonic evolution for broken rotor bar fault, where there is a dependence of the harmonic frequency on the per-unit slip during the current startup transient. In this experimental study, the total transient startup current signal x[n] is partitioned into M separate data segments, that are obtained by using overlapping sliding window over the transient current signal. As an example of ST-MUSIC; a synthetic signal that represents the left sideband fault frequency evolution of a broken rotor bar without noise is analyzed. Fig. 1a depicts the whole synthetic signal with 5,120 data points that is partitioned into 16 separate data segments of 320 data points each one. Each segment of 0.1s is analyzed by MUSIC with 13-order model and 60% overlap. The resulting 0.1s pseudo-spectrums make up ST-MUSIC as shown in Fig. 1b and Fig 1c in 3D and time-frequency view, respectively. The resulting pseudo-spectrum depicts the physical effect of one or more broken rotor bars in a time-frequency plane, where it is shown the left sideband frequency evolution of a broken rotor bar during the startup transient. It must be noticed that the pseudo-spectrum is not a true power spectral density (PSD) estimator. This pseudo-spectrum is used for locating the frequency components in the signal.

The features of MUSIC algorithm consist in the ability of detecting the principal frequency components (i.e. those having larger amplitudes) in a signal corrupted by noise; even when the signal-to noise ratio (SNR) is low. ST-MUSIC can be represented using surfaces in the time-frequency space, as it is used in STFT (short-time Fourier transform) analysis. ST-MUSIC provides a high-resolution pseudo-spectrum with more regular surfaces than STFT, which mitigates the effects of noise, and provides high sensitivity.

III. EXPERIMENTAL SETUP

Fig. 2 shows the experiment setup where a three-phase 1-

hp induction motor (model WEG 00136APE48T) is used to

test the performance of the proposed methodology

identifying the fault evolution of the one broken rotor, where

the bar was gradually broken by drilling one hole, each three

millimeters, from healthy until the rotor bar is broken at 10-

mm. The tested motor receives a power supply of 220 VAC,

60 Hz, and the applied mechanical load is 50% from an

ordinary alternator (Fig. 2c). The data acquisition is

synchronized when the motor is switched on. The one phase

current signal is acquired using an AC current clamp model

i200s from Fluke (Fig. 2d). A 16-bit (Fig. 2b), serial-output

analog to digital converter ADS7809 from Burr-Brown, is

used for data acquisition in the data-acquisition system

(DAS); the acquired information is forwarded to a PC

through an RS232 interface for further processing (Fig. 2c).

The instrumentation system uses a sampling frequency

fs=3200 Hz, obtaining 7680 samples for capturing the whole

current startup transient of the induction motor (2.4 s).

Fig. 1. Diagram of a Short-Time MUSIC analysis. a) Time-domain signal. b) 3D time-frequency spectrum. c) Time-frequency decomposition.

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In order to guarantee the accuracy of the partially-broken

rotor bar drilling of successive 3 mm perforations until

breakage, the drilling process was performed in a CNC

(computerized numeric control) machining center as shown

in Fig. 3a. It was also necessary to manufacture a special

mounting device (chuck) to hold the rotor under test during

the drilling process to guarantee the required precision as

can be seen in Fig. 3b.

IV. EXPERIMENT RESULTS

The proposed experimental study is implemented in the Matlab Digital Signal Processing Toolbox. In order to reduce the computation time and to optimize the pseudo-spectrum estimation; after the data acquisition stage, a low-pass filter with a cutoff frequency of 100 Hz is used to limit the frequency region (0-70 Hz) observation to the left sideband fault frequency evolution of rotor broken bar detection so the model order of ST-MUSIC method and computation time are considerably reduced. The low-pass filter is performed by a finite impulse response (FIR) filter of order 64 and a Kaiser window. After filtering, the signal is partitioned into 12 separate data segments of 640 data points each one. Each segment of 0.2s is analyzed by the MUSIC method with model order 12 and overlap of 50%. The resulting pseudo-spectrum of each segment of 0.2s of duration, conform the ST-MUSIC pseudo-spectrum. The proposed method was implemented into an Intel Core 2 Duo personal computer at 2.6 GHz, giving a processing time of 2.43 s. Several works related to the identification of one or more broken rotor bars in induction motors [14]-[17], have established that even for a healthy motor, the stator current always contains spectral components related to the faults, and other frequency components, due to intrinsic asymmetry, air-gap eccentricity, rotor misalignment and other indiscernible factors in a healthy motor. For example, Pereira et al.[15] says “Even for a machine considered as healthy, low amplitude components near the defect frequencies appear. This happens because the process of aluminum alloy injection of the rotor bars results in some degree of irregularity in the cross section of the rotor bars. This intrinsic asymmetry in the rotor circuit leads to small differences in the resistance of rotor bars, which can be considered as defect to some extent. The PSD curves also show a shift in the fault frequencies as the severity of defect increase”. Taking in consideration the obtained results from these works, those are useful to explain the obtained pseudo-spectra from gradual drilling of one rotor bar. Fig. 4 shows the obtained pseudo-spectra from the experimental study for fault evolution of partially broken rotor bar. On each figure, it is shown how the left sideband fault frequency evolves and shifts each time the rotor bar is drilled millimeter by millimeter, until the rotor bar is fully broken at 10 mm drilling. The frequency of the left sideband harmonic during the startup (LSHst), is proposed as a suitable tool for diagnostic of a broken rotor bar condition [18] and is given by,

( ) (1 2 )LSHst sf s s f (7)

According to this equation, LSHstf is equal to 0 when the

per-unit slip equals to 0.5; and from the fully-broken rotor bar condition in Fig. 4d, the per-unit slip is equal to 0.5 at 1.15s approximately. Thus, the frequency of each obtained pseudo-spectrum when the rotor bar is partially broken is analyzed at 1.15s for this experimental study. Fig. 4a shows that even for a healthy rotor bar, it can be seen that there are some spectral components around the supply frequency of

Fig. 2. Test bench used during the experiment: (a) Electric charge, (b) DAS, (c) Motor and alternator, d) Current clamp, e) Personal computer.

Fig. 3. a) CNC machining center for accurate drilling the rotor. b) Holding chuck for precise drilling of successive perforations until breakage to the rotor under test.

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60 Hz that prove the induction motor imperfections and there is a sideband frequency located at 36Hz when s=0.5. Fig. 4b shows the partially-broken rotor bar pseudo-spectrum with a 3 mm of drilling where there is a sideband frequency located at 23 Hz when s=0.5. Fig 4c shows the rotor bar spectra drilled at 6 mm, where there is a sideband frequency located at 13 Hz when s=0.5. Finally, when s=0.5, Fig. 4d shows the pseudo-spectrum of the fully-broken rotor bar at 10 mm |drilling, where the sideband frequency is located at 3 Hz when s=0.5.

Fig. 5 shows the same spectra with a 2D view, where is clearly observed the shift frequency of the left sideband

Fig 4 3D time-frequency Pseudo-spectra of drilled, partially-broken rotorbar: (a) 0 mm (Healthy), (b) 3 mm, (c) 6 mm, (d) 10 mm (one broken rotorbar).

Fig 5 2D time-frequency Pseudo-spectra of drilled, partially-broken rotor bar: (a) 0 mm(Healthy), (b) 3 mm, (c) 6 mm, (d) 10 mm (one broken rotor bar).

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component when the per-unit slip is equals to 0.5. Table 1 show the frequency of the left sideband component when the per-unit slip is equals to 0.5, compared against the level of the partially-broken rotor bar drilling level.

CONCLUSIONS

From results, the proposed experimental work is able to detect the partially-broken rotor bar fault evolution in all obtained pseudo-spectra figures, as the sideband components around the supply frequency are shifted with respect to the healthy rotor bar, when drilled millimeter by millimeter until the bar is completely broken. From Fig. 5d, it is noticed that is in accordance with (7), when the bar is completely broken and the frequency of the left sideband component is 0Hz. From all pseudo-spectra results, it seems that a gradual drilling of one rotor bar produces a shift in the fault frequencies as the severity of defect increases. In this paper, an experimental work for detecting the left sideband fault frequency evolution in one partially broken rotor bar, using a high-resolution and time-frequency analysis is proposed. One-phase startup current was required for time-frequency spectral analysis and obtained results clearly show how it seems that a gradual drilling of one rotor bar produce a shift in the fault frequencies as the severity of defect increases and the fault evolution in all studied cases from a healthy rotor bar until the rotor bar is partially broken with three different levels of drilling. The proposed experimental work provides a view on how the process of partially-broken rotor bar effect is carried out. Thus, this methodology is able to detect a rotor fault in progress in an early stage even before the one bar is fully broken and it is also an excellent diagnosis technique for use in condition-based maintenance (CBM). However, there is still the necessity to make more investigation to clarify the physical processes and establish a theoretical equation that completely defines the gradual fault evolution of one partially-broken rotor bar.

REFERENCES

[1] K. Kim and A.G. Parlos, “Induction Motor Fault Diagnosis Based on Neuropredictors and Wavelet Signal Processing,” IEEE/ASME Trans. Mechatronics, vol. 7, pp. 201–219, June 2002

[2] F. Filippetti, G. Franceschini, C. Tassoni and P. Vas, “Recent developments of induction motor drives fault diagnosis using AI

techniques,” IEEE Transactions on Industrial Electronics, vol.47, pp. 1966-1973, Oct. 2000,

[3] M. E. H. Benbouzid, "A Review of Induction Motor Signature Analysis as a Medium for Faults Detection," IEEE Transactions on Industrial Electronics, vol. 47, pp. 984-993, Oct. 2000.

[4] A. Stefani, F. Filippetti and A. Bellini, “Diagnosis of induction machines in time-varying conditions,” in Proceedings of IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, SDEMPED, pp.126-131, 2007.

[5] M. Riera-Guasp, J. A. Antonino, J. Roger-Folch and M. P. Molina;

“The use of the wavelet approximation signal as a tool for the diagnosis of rotor bar failures,” in Proceedings of IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, SDEMPED, pp.1-6, 2005.

[6] Y. Gritli, A, Stefani, C. Rossi, F. Filippetti and A. Chatti, “Doubly Fed Induction Machine stator fault diagnosis under time-varying conditions based on frequency sliding and wavelet analysis,” in Proceedings of IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, SDEMPED, pp.1-7, 2009.

[7] A. Garcia-Perez, R. de J. Romero-Troncoso, E. Cabal-Yepez, R.A. Osornio-Rios; “The Application of High-Resolution Spectral Analysis for Identifying Multiple Combined Faults in Induction Motors,” IEEE Trans. Ind. Electron., vol. 58 , pp. 2002-2210, May. 2011.

[8] G. Didier, E. Ternisien, O. Caspary and H. Razik, “A new approach to

detect broken rotor bars in induction machines by current spectrum analysis,” Elsevier Mechanical Systems and Signal Processing, vol. 21, pp. 1127-1142, Feb. 2007.

[9] H. Razik, M.B.R. Correa and E.R.C. Silva, “A Novel Monitoring of Load Level and Broken Bar Fault Severity Applied to Squirrel-Cage Induction Motors Using a Genetic Algorithm,” IEEE Trans. Ind. Electron., vol. 56, pp. 4615–4626, Nov. 2009.

[10] A. Yazidi, H. Henao and G.-A. Capolino, “Broken Rotor Bars Fault Detection in Squirrel Cage Induction Machines,” in Proceedings of IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, SDEMPED, pp. 741-747, 2005.

[11] H. Su and K.T. Chong, “Induction Machine Condition Monitoring Using Neural Network Modeling,” IEEE Trans. Ind. Electron., vol. 54, pp. 241–249, Feb. 2007.

[12] T.M. Wolbank, G. Stojicic and P. Nussbaumer, “Monitoring of partially rotor broken rotor bars in induction machine drives,” in 36thAnnu. Conf. on IEEE Industrial Electronics Society, 2010, pp. 912-917.

[13] J.J Rangel-Magdaleno, R.J. Romero-Troncoso, R.A. Osornio-Rios, E. Cabal-Yepez and L.M. Contreras-Medina, “Novel Methodology for Online Half-Broken-Bar Detection on Induction Motors,” IEEE Trans. Instrum. Meas., vol. 58, pp. 1690-1698, May 2009.

[14] S.H. Kia, H. Henao, and G.-A. Capolino, “A High-Resolution Frequency Estimation Method for Three-Phase Induction Machine Fault Detection,” IEEE Trans. Ind. Appl., vol. 54, pp. 2305-2314, Aug. 2007.

[15] L.A. Pereira, D. Fernandes, D.S. Gazzana, F.B. Libano and S. Haffner, “Performance Evaluation of Nonparametric, Parametric, and the MUSIC Methods to Detection of Rotor Cage Faults of Induction Motors,” In: Proceedings of the 32nd Annual Conference of the IEEE Industrial Electronics Society, v. 1. pp. 1-6, 2006.

[16] F. Cupertino, E. de Vanna, G. Forcella, L Salvatore, S. Stasi, “Detection of IM broken rotor bars using MUSIC pseudo-spectrum and pattern recognition,” In the 29th Annual Conference of the IEEE Industrial Electronics Society, 2003. IECON '03, v.1, pp.2829-2834, Nov. 2003.

[17] F. Cupertino, V. Giordano, “competitive learning applied to detect broken rotor bars in induction motors,” In the 2004 IEEE International Symposium on Industrial Electronics, v.2, pp.1485-1490, 2004.

[18] M. Pineda-Sanchez, M. Riera-Guasp, J.A. Antonino-Daviu, J. Roger-Folch, J. Perez-Cruz and R. Puche-Panadero, “Instantaneous frequency of the left sideband harmonic during the startup transient: a new method for diagnosis of broken bars,” IEEE Trans. Ind. Electron., vol. 56, pp. 4557-4570, 2009.

TABLE IFREQUENCY OF LEFT SIDEBAND COMPONENT AGAINST THE LEVEL OF

PARTIALLY-BROKEN ROTOR BAR DRILLING WHEN THE PER-UNIT SLIP IS

EQUALS TO 0.5.

Level of Drilling (mm) Frequency of

LSHst (Hz)

0 (Healthy) 36 3 23 6 13 10 (Broken Rotor Bar) 3

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BIOGRAPHIES

Arturo Garcia-Perez (M’10) received the B.E. and M.E. degrees in electronics from the University of Guanajuato, Guanajuato, Mexico, and the Ph.D. degree in electrical engineering from the University of Texas at Dallas, Dallas, USA, in 1994 and 2005, respectively. He is currently an Associate Professor with the Department of Electronic Engineering, University of Guanajuato. He has been an Adviser of over 40 theses. His fields of interest include digital signal processing for applications in mechatronics.

Rene J. Romero-Troncoso received the B.E. and M.E. degrees in electronics from the University of Guanajuato, Guanajuato, Mexico, and the Ph.D. degree in mechatronics from the University of Queretaro, Queretaro, Mexico. He is a National Researcher with CONACYT. He is currently a

Head Professor with the University of Guanajuato and an Invited Researcher with the University of Queretaro. He has been an Adviser of over 150 theses, an author of two books on digital systems (in Spanish), and a coauthor of over 40 technical papers in international journals and conferences. His fields of interest include hardware signal processing and mechatronics. He received the ‘‘2004 ADIAT National Award on Innovation” for his works in applied mechatronics and the ‘‘2005 IEEE ReConFig’05” award for his works in digital systems.

Eduardo Cabal-Yepez received his B.Eng. and M.Eng. degrees from the University of Guanajuato, Guanajuato, Mexico, and his D.Phil. degree from the University of Sussex, Brighton, UK. He is an Associate Professor at the Department of Engineering, Campus Irapuato-Salamanca, University of Guanajuato. He develops research work at the HSPdigital Group (http://www.hspdigital.org). His fields of interest include hardware signal processing on field-programmable gate arrays for applications in

mechatronics.

Roque A. Osornio-Rios (M’10) received the B.E.from Instituto Tecnologico de Queretaro, M.E. and the Ph.D. degrees from the University of Queretaro, Queretaro, Mexico. He is a National Researcher with CONACYT. He is currently a Head Professor with the University of Queretaro. He has been an Adviser of over 20 theses, and a coauthor of over 23 technical papers in international journals and conferences. His fields of interest include hardware signal processing and mechatronics. He received the “2004 ADIAT National Award on Innovation” for his works in applied mechatronics.

Jose de Jesus Rangel-Magdaleno (S’08) received the B.E. degree (cum laude) in electronics engineering and the M.E. degree (summa cum laude) in electrical engineering on hardware signal processing applications from the University of Guanajuato, Guanajuato, Mexico, in 2006 and 2008, respectively. He is currently working toward the Ph.D. degree with the Autonomous University of Queretaro, Queretaro, Mexico. His research

interests include mechatronics, instrumentation, and digital systems applied to solutions for industrial problems.

Homero Miranda was born in San Luis Potosí, México. He received the engineering degree in electronics engineering from Technological Institute of San Luis Potosi in 2000, and the M.Sc. and Ph.D degree in Electrical Engineering (with emphasis in Automatic Control and Power Electronics) in University of San Luis Potosí in 2003 and 2007 respectively. Since 2008, he has been with de Engineering Department, University of San Luis Potosi, where he is currently a Professor and he is engaged in teaching and research areas of power electronics and automatic control. His main areas of interests are in power quality, active power filters, multilevel converters and PWM techniques. Dr. Miranda is member of the IEEE.

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