6i20 Ijaet0520917 V7 Iss2 341 351

International Journal of Advances in Engineering & Technology, May, 2014.

©IJAET ISSN: 22311963

341 Vol. 7, Issue 2, pp. 341-351

BEARINGS FAULT DIAGNOSIS IN DIRECT TORQUE CONTROL

PERMANENT MAGNET SYNCHRONOUS MOTOR BASED ON

DISCRETE WAVELET TRANSFORM AND ARTIFICIAL

NEURAL NETWORK

Abbas H. Abbas, Alaa A. AL-Saffar, and Dhiaa K. Shary

Department of Electrical Engineering, Basrah University, Basrah City, Iraq

Foundation of Technical Education, Basrah Technical College, Basrah City, Iraq

ABSTRACT The paper proposes a novel method, based on wavelet decomposition, for detection and diagnosis of bearings

fault in Direct Torque Control (DTC) Permanent Magnet Synchronous Motor (PMSM). In this technique the

root mean square (RMS) values of the Discrete Wavelet Transform (DWT) coefficients of the quadrature stator

current component are fed to Artificial Neural Network (ANN) to identify the machine state(healthy or faulty).

The dynamic model for PMSM with the bearings fault is derived in dq-variables. This model and the fault

detection algorithms are simulated using Matlab/Simulink environment. The results prove that the effectiveness

of the proposed method for bearing fault detection.

INDEX TERMS: Artificial Neural Network (ANN), Direct Torque Control (DTC), Discrete Wavelet

Transform (DWT), Permanent Synchronous Motor (PMSM), PI-like fuzzy controller.

I. INTRODUCTION

Direct Torque Control (DTC) is a popular control technique widely applied in motor drive

applications since it was proposed by Depenbrock and Takahashi [1], [2]. By directly controlling the

flux and torque, both techniques yield fast dynamic response and high performance [3]. The basic

principle of DTC is to directly select stator voltage vectors according to differences between the

references and actual torque and stator flux linkage [4].

The DTC has many favorable features, such as no need of complicated coordinate transformation and

pulse width modulation (PWM). Also, it is insensitive to motor parameters, which is inevitable in the

vector control scheme. A major problem associated with the popular DTC is the big torque and flux

ripples because of the use of two simple two-value hysteresis controllers for the stator flux linkage

and the torque. In addition, the use of a 600 angular region based signal for choosing the space voltage

vector applied to the stator windings, which is so crude that none of these space voltage vectors

generated by the voltage source inverter (VSI) could offer a precise control of the torque and the

stator flux linkage at the same time. These ripples can be reduced if the errors of the torque and the

flux linkage, and the angular position signal of the flux linkage are subdivided into several smaller

subsections. By choosing a more accurate space voltage vector , more accurate control of torque and

flux linkage can be obtained [5]. In this paper, the DTC of PMSM is proposed and the choice of null-

vectors and vector sequence are properly selected to improve the performance of motor drive system.

In this paper, we focus on the detection of an bearing fault in PMSM. The majority of the electrical

machines use ball or rolling element bearings. Each of these bearings consists of two rings, inner and

outer respectively. A set of balls or rolling elements placed in raceway rotate inside these rings. Even

under normal operating continues with balanced load and a good alignment, fatigue failure may take

place. Flaking or sapling of bearings might occur when fatigue causes small pieces to break loose

from the bearing. A part from normal internal operating stresses, other causes of bearing damages due

to vibration, inherent eccentricity, and bearing currents due to solid state drives appear as well.

Sometimes the ball bearing related defects can be categorized as outer bearing race defect, inner



342 Vol. 7, Issue 2, pp. 341-351

bearing race defect, ball defect, and train defect. All these mechanical defects cause distortions in flux

distribution inside the machine , which in turns leads to new current harmonics in stator windings [6].

In [7], it is proposed to use a dynamic neural network to fault detection and diagnosis (FDD) of

PMSM stator winding short circuit under load fluctuation. In [8], it presented the study of PMSM

running with eccentricity and bearing damage based on wavelet transform decomposition of the stator

current.

In this paper the bearings fault method for DTC PMSM has been presented. The structure of DTC

PMSM is analyzed to improve the motor performance. The paper is organized as follows. In Section

II mathematical model of PMSM. Section III and section IV describe the design and operational

principle of direct torque control of PMSM. Section V describes the construction of Fuzzy logic

controller used in DTC PMSM. Section VI discuss the application of DWT and ANN to detect the

bearings fault . Section VII discusses simulation results and discussion. Section VIII discusses

conclusion and suggests a roadmap for future works.

II. PMSM MODEL

The model of the PMSM is derived using direct (d) and quadrature (q) variables in a rotor reference

frame, the voltage equations are:

Vd = Rsid + d(Фd) dt⁄ − wФq (1)

Vq = Rsiq + d(Фq) dt⁄ + wФd + wФf (2)

It is noted that the stator flux linkage components are:

Фd = Ldid + Фf (3)

Фq = Lqiq (4)

where Rs is the stator winding resistance, Ld and Lq are d-q axis inductances, Фf is the rotor flux

linkage generated by the permanent magnets, Vd and Vq are the d-q axis voltages, Фd and Фq are d-q

axis fluxes, id and iq are d-q axis currents and w is the angular speed of the rotor [9], [10].

The mechanical torque equation referred to motor-load system is given by:

Te = (J p)⁄ dw dt + (D P)⁄ w +⁄ TL (5)

with

Te =3

2p(Фdid + ( Ld − Lq)idiq) (6)

where D is the damping torque coefficient, J is the moment of inertia of rotor, TL is the load torque

and P is the number of pole pairs [11], [12].

III. DIRECT TORQUE CONTROL STRATEGY

A- Stator flux linkages sectors

When the motor is fed from a three-phase inverter, the stator voltage is determined by the status of the

power switches. It is noted that there are six non-zero voltage vectors,V1(100), V2(110) ,…, and

V6(101), and two zero voltage vectors, V7(000) and V8(111).Two zero voltage vectors are at the origin

and six non-zero vectors are 600 apart from each other in voltage vector plane as shown in Fig. 1.

Both the amplitude and rotating speed of the stator flux linkage can be controlled by selecting the

proper stator voltage vectors [13].

B- Control of the amplitude of stator flux linkage

The stator flux linkage Фs in stationary reference frame is:

Фs = ∫(vs − Rsis)dt (7)

where vs and is are the stator voltage and the stator current, respectively. To select the voltage

vectors for controlling the amplitude of the stator flux linkage, the voltage vector plane is divided into

six regions. In each region, two adjacent voltage vectors, which give minimum switching frequency,

are selected to increase or decrease the amplitude of stator flux [14].



343 Vol. 7, Issue 2, pp. 341-351

Figure 1. Sectors of stator flux linkage.

C- Control of the rotation of stator flux linkage

In case of PMSM , Фs is changed even when zero voltage vectors are applied since the magnets rotate

with the rotor. Therefore, zero voltage vectors are not used for controlling Фs in PMSM. The

electromagnetic torque can be controlled by controlling the amplitude and rotational speed of Фs.

For counter clockwise operation, if the actual torque is smaller than the reference then the voltage

vectors that keep Фs rotating in the same direction are selected. If the actual torque is greater than the

reference, the voltage vectors that keep Фs in the reverse direction are selected instead of zero

voltage vectors. By selecting the voltage vectors in this way , Фs is rotated all the time and its

rotational direction is determined by the output of the hysteresis controller for torque. The switching

table for controlling both the amplitude and rotating direction of Фs is as follows:

In Table 1, EФ and ET are the outputs of the hysteresis controllers for flux linkage and torque,

respectively. If EФ=1 then the actual flux linkage is smaller than the reference value. The same is true

for the torque. N(1,2,,….6) represents the sector numbers for stator flux linkage [15].

Table 1. Outputs of hysteresis controllers for flux linkage and torque.

ET

EФ

N

1 2 3 4 5 6

1

1

0

V2

V6

V3

V1

V4

V2

V5

V3

V6

V4

V1

V5

0

1

0

V3

V5

V4

V6

V5

V1

V6

V2

V1

V3

V2

V4

IV. DTC IMPLEMENTATION OF PMSM

A- Flux linkage estimator

As shown in the block diagram of DTC of PMSM in Fig. 2., the inverter switching states are

determined according to the error of torque (ET) and the error of flux (EФ) [16].

ET = Teref−Te (8)

EФ = Фeref−Фs (9)

The stator flux linkage can be determined as follows:

)011(4V

α

(100)1V

0)1(12V 0)01(3V

)001(5V )1(106V

00)0(7V )11(18V

β



344 Vol. 7, Issue 2, pp. 341-351

Figure 2. Block diagram of DTC.

Фs = √Фα2 + Фβ

2 (10)

Фα = ∫(uα − Rsiα)dt (11)

Фβ = ∫(uβ − Rsiβ)dt (12)

where Фα and Фβ are α-β axis fluxes, iα and iβ are α-β axis currents.

The α-β axis voltages (uα and uβ ) are calculated from the dc-link voltage Vdc and switching

signal Sa, Sb and Sc as follows:

uα = √2

3 Vdc (Sa −

1

2( Sb + Sc ) (13)

uβ = √1

2 Vdc ( Sb − Sc ) (14)

Also

iα = √3

2 ia (15)

iβ = √1

2 (ib − ic ) (16)

B- Torque estimator

The torque can be calculated from the α-β axis voltages and currents as in [17]:

Te =3

2p(Фαiβ − Фβiα) (17)

V. FUZZY LOGIC CONTROL (FLC)

The speed closed loop with PI-Fuzzy controller structure is shown in Fig. 3. The inputs of this FLC

are normalized values of the speed error denoted (e) and its integrated value denoted (ie). Two scaling

factors (Kne and Knie) are used to normalize the actual speed error and its integrated value. The output

of the controller is the normalized change of the motor speed command which generates the actual

value of the motor speed when its multiplied by a third scaling factor (Knc) [18]. .

Figure 3. Simulation model of PI-Like Fuzzy Controller.

U speed 1

neK

nieK

ncK

1 s

Fuzzy Logic Controller

error 1

sФ

Switching

table

Torque and flux

calculation

Voltage

source

inverter

PMSM

erefT

erefФ

eT

error(0,1)

error(0,1)



345 Vol. 7, Issue 2, pp. 341-351

From the speed behavior analysis , Table 2 has been developed to obtain a good performance in the

speed closed loop into which the following fuzzy sets are used in the membership functions: NB is

negative big, NM is negative medium, NS is negative small, Z is equal zero, PB is positive big, PM is

positive medium , and PS is positive small [18].

Table 2. Tabular structure of a linguistic fuzzy rule base.

NB NS Z PS PB

NB NB NB NB NS Z

NS NB NB NS Z PS

Z NB NS Z PS PB

PS NS Z PS PB PB

PB Z PS PB PB PB

Table 3. Frequency level of the wavelet coefficients

.

VI. FAULT DIAGNOSES OF PMSM BASED ON DWT AND ANN

A- Discrete Wavelet Transform (DWT)

DWT actually splits a signal to several band-limited signals, the sum of which is equal to the original

one. In this way, the original signal can be reconstructed as a sum of n detail signals (Dj, 1 ≤ j ≤ n)

and an approximation signal (An). Each detail Dj includes frequency components [2−(𝑗+1). 𝑓𝑠,

2−𝑗. 𝑓𝑠], while the approximation signal includes all the lower frequency components, including the

dominant DC signal. More specifically, at each level of DWT decomposition, low-pass (g[n]) and

high-pass (h[n]) filters are applied, as shown in Fig. 4. [19].

In the present work, DWT uses q-axis stator current component (iq) so as to identify the faults in

PMSM. Daubechies-44 wavelet (db44) has been used as a mother wavelet. The supply frequency in

this paper is taken to be 50 Hz and Table 3 shows the frequency level of the wavelet coefficients.

B- Neural network structure

A neural network is a mapping which uses a dense interconnection of elementals artificial neurons

[20]. ANN comprises connected elements (neurons) working similar to human nervous systems [21].

The network consists of inputs (𝑥𝑖), which are multiplied by weights (𝑤𝑖) and then computed by a

mathematical function f which determines the activation of the neuron where (𝑏) is the bias .

Level Frequency Band with fS=5000 samples/sec

D1 1250-2500 Hz

D2 625-1250 Hz

D3 312.5-625 Hz

D4 156.25-312.5 Hz

D5 78.12-156.25 Hz

D6 39.06-78.12 Hz

A6 0-39.06 Hz

ei

e



346 Vol. 7, Issue 2, pp. 341-351

Figure 4. DWT decomposition.

In ANN, two layers of neuron communicate via a weight connection network. The type of weighted

connections used in this network is the feed-forward neural network, which is composed by: (an input

layer, one or more hidden layers, and an output layer) [22].

The mathematical model of neuron is presented by:

𝑦 = 𝑓 (∑𝑤𝑖𝑥𝑖 − 𝑏

𝑛

𝑖=1

) (18)

In this work, the structure of the neural network consists of an input layer that is fed by one input (the

RMS value of the wavelet coefficient D6), and one hidden layer followed by one output layer which

has two states given by:

Y=0 healthy system

Y=1 bearing fault

The RMS value of the discrete signal 𝑆 can be determined by:

𝑆𝑅𝑀𝑆 = √(1

𝑁∑𝑠𝑖

2

𝑁

𝑖=1

) (19)

where 𝑁 is the number of samples per cycle.

The neural network model is trained by using Levenberg-Marquardt algorithm.

VII. SIMULATION RESULTS

The simulink model of the proposed DTC of PMSM is shown in Fig. 5. under the PI-like fuzzy speed

controller which consists of seven blocks as follows:-

A. abc-dq Conversion Block

To convert 3-phase voltages to voltages in the 2-phase synchronously rotating frame, they are first

converted to 2-phase stationary frame (,) and then from the stationary frame to the synchronously

(d-q) rotating frame. The transformation is given by the following equations:

[vα

vβ] = √

2

3[ 1

−1

2

−1

2

0√3

2

−√3

2 ]

[

va

vb

vc

] (20)

[vd

vq] = [

cosθ sinθ

−sinθ cosθ] [

vα

vβ] (21)

B. Motor dq-Model Block

The dq-model of PMSM is represented according to equations (1)-(4).

C. dq-abc Conversion

This conversion does the opposite of the abc-dq conversion for the current variables.

D. Torque and Flux Estimator Block

h(n)

g(n)

2

2 h(n)

g(n)

2

2

X(n) 1st level

coefficients

2nd level

coefficients



347 Vol. 7, Issue 2, pp. 341-351

This block is used to estimate the stator flux which is given in (7). This block is also used to obtain

the developed electromagnetic torque produced by simulated machine using (17).

E. Sector Detector Block

This block is used to detect the sector of the stator flux.

F. State Selector Block

After the sector of stator flux, error of stator flux and error of torque are obtained. These values are

fed to direct torque control block which contains the lookup table which is used to obtain the desired

voltage state vector according to the desired sectors mentioned in Table I.

J. Three Phase Inverter Block

This block contains two-level three-phase voltage source inverter which are controlled by the proper

signal generated by the state selector block. The parameters of PMSM are shown in Table 4.

Figure 5. DTC simulation model of PMSM.

Table 4. Parameters of PMSM.

Motor constants Values

Stator resistance Rs 4.765 Ω

Torque TL 1.7 Nm

d-axis inductance Ld 0.014 H

q-axis inductance Lq 0.014 H

PM flux Фf 0.1848 Wb

Rated speed w 3000 rpm

Rated current is 6.89 A

Number of poles p 2

Moment of inertia J 0.0001051

Friction factor D 4.047e-5

Stator flux reference Фs 0.1848 Wb

Frequency f 50 Hz

Fig. 6. shows the simulated dynamic performance of the torque control loop of DTC system , which is

obtained by applying a step torque command at 1 second from full load (1.7 N.m.) to 1 N.m at 3000

rpm. The simulated result shows that the torque ripples under DTC scheme are much smaller than

state selector

flux state

torque state

selector

Sa

Sb

Sc

selector detector

phase -fluxSector

dq 2 alfabeta

wt

id

iq

ialfa

ibeta

alfabeta 2 abc

ialfa

ibeta

ia

ib

ic

Torque and Flux estimator

Sa

Sb

Sc

ia

ib

ic

magnitude -flux

T

phase - flux

PMSM

va

vb

vc

we

TL

id

iq

rpm

2*pi*50

3000

1.7

0.1848

Clock

3-phase inverter

Sa

Sb

Sc

va

vb

vc

PI-Like Fuzzy Controller

error U speed



348 Vol. 7, Issue 2, pp. 341-351

those of the open loop system shown in Fig. 7. Also, this result confirms that the proposed DTC of

PMSM is an effective method for accurate control of the electromagnetic torque.

Figure 6. Torque response with load change from full load (1.7 N.m.) to(1 N.m.) with DTC sheme.

Figure 7. Torque response with load change from full load (1.7 N.m.) to(1 N.m.) with open loop system

condition.

Fig. 8. shows that the estimated speed can accurately track the change of the real speed with fast

response when speed reference is changed. The proposed DTC system is relatively robust with

respect to the change of speed reference when a step speed command of 2000-3000 rpm is applied at

the rated load torque . The parameters of speed loop PI-like fuzzy controller in this system are

carefully tuned such that the optimal performance is achieved (see Table 5).

Figure 8. Speed response with a step speed command of 2000-3000 rpm.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time (Sec.)

To

rqu

e (N

.m.)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-15

-10

-5

0

5

10

15

Time (Sec.)

To

rq

ue (

N.m

.)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

500

1000

1500

2000

2500

3000

3500

4000

Time (Sec.)

Sp

eed

(r

pm

)



349 Vol. 7, Issue 2, pp. 341-351

Table 5. Parameters of speed loop PI-like fuzzy controller.

Controller constants Values

Kne 0.28

Knie 0.0089

Knc 50

Fig. 9. shows the wavelet coefficients signals resulting from the wavelet decomposition of the stator

q-axis current of the healthy system while Fig. 10. shows the wavelet signals for bearing fault.

Figure 9. Wavelet coefficients of stator q-axis current component for healthy machine with full load.

Figure 10. Wavelet coefficients of stator q-axis current component for bearing fault with full load.

0 100 200 300 400 500 600 70005

10

original signal iq

0 100 200 300 400 500 600 700-10

010

A6 (0-39.0625 Hz) ( RMS=5.8599 )

0 100 200 300 400 500 600 700-101

D6 (39.0625-78.125 Hz) ( RMS=0.2122 )

0 100 200 300 400 500 600 700-101

D5 (78.125-156.25 Hz) ( RMS=0.12995 )

0 100 200 300 400 500 600 700-0.5

00.5

D4 (156.25-312.5 Hz) ( RMS=0.068988 )

0 100 200 300 400 500 600 700-0.5

00.5

D3 (312.5-625 Hz) ( RMS=0.030889 )

0 100 200 300 400 500 600 700-0.1

00.1

D2 (625-1250 Hz) ( RMS=0.0090889 )

0 100 200 300 400 500 600 700-0.05

00.05

D1 (1250-2500 Hz) ( RMS=0.0039649 )

Sample Number

0 500 1000 1500 2000 2500 300005

10

original signal iq

0 500 1000 1500 2000 2500 3000-10

010

A6 (0-39.0625 Hz) ( RMS=6.0422 )

0 500 1000 1500 2000 2500 3000-101

D6 (39.0625-78.125 Hz) ( RMS=0.10602 )

0 500 1000 1500 2000 2500 3000-101

D5 (78.125-156.25 Hz) ( RMS=0.072095 )

0 500 1000 1500 2000 2500 3000-0.5

00.5

D4 (156.25-312.5 Hz) ( RMS=0.035054 )

0 500 1000 1500 2000 2500 3000-0.5

00.5

D3 (312.5-625 Hz) ( RMS=0.012638 )

0 500 1000 1500 2000 2500 3000-0.1

00.1

D2 (625-1250 Hz) ( RMS=0.0057335 )

0 500 1000 1500 2000 2500 3000-0.05

00.05

D1 (1250-2500 Hz) ( RMS=0.0020181 )

Sample Number



350 Vol. 7, Issue 2, pp. 341-351

The comparison between Fig. 9. and Fig. 10. shows clearly that the bearing fault can be identified by

means of the RMS values of the wavelet coefficient (D6) between the different studied cases (0.2122

V for healthy machine and 0.10602 V for bearing fault case).

The RMS values of the wavelet coefficients for level 6 are used as the input of the neural network to

give an output which identifies the machine case.

VIII. CONCLUSION AND FUTURE WORK

In this paper bearings fault detection was simulated by means of Matlab/Simulink environment for

DTC PMSM drive system. The simulation results proved that the torque response of the proposed

DTC scheme is faster much than open loop system with low ripple. Also, the results showed the

feasibility and validity of the proposed Fuzzy speed controller for wide range of motor speed. It

also, presented the detection of the bearings fault for a PMSM in which the quadrature component of

the stator current has been analyzed using DWT and application of ANN to identify the machine

state. For the future work the proposed design for the artificial neural network can be easily and

successfully extended to get a compact design using fuzzy logic system to identify the machine

condition in short time. The scheme can also be improved using Neuro-Fuzzy system to control the

motor speed taking into account uncertainties.

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AUTHORS

Abbas H. Abbas was born in Basrah, Iraq, in 1958. He received the B.Sc from the

University of Technology/Baghdad in 1980. He received the PHD from Technical

University/Sofia/Bulgaria in 1991. His current research interests include electrical

engineering power systems and electrical machines.

Alaa A. Al-Saffar was born in Basrah, Iraq, in 1957. He received the B.Sc, M.Sc and

PHD from the University of Basarh, College of Engineering, Electrical Engineering

Department in 1979, 1982 and 2001, respectively. His current research interests include

optical computing and robotic control.

Dhiaa K. Shary was born in Basrah, Iraq, in 1976. He received the B.Sc, and M.Sc

from the University of Basrah, College of Engineering, Electrical Engineering

Department in 1999, 2002, respectively . Currently He is PHD student in University of

Basrah, College of Engineering, Electrical Engineering Department.

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