Fuzzy logic approach to control the magnetization level in the magnetic 2

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 3, May - June (2013), © IAEME
19
FUZZY LOGIC APPROACH TO CONTROL THE MAGNETIZATION
LEVEL IN THE MAGNETIC CORE OF A WELDING TRANSFORMER
Rama Subbanna. S.1
, Kamalakar. K.S.K.1
, Dr. Suryakalavarthi.M2
1
Department of Electrical and Electronics Engineering, St. Martins Engineering College,
Hyderabad, India
2
Department of Electrical and Electronics Engineering, Jawaharlal Nehru Technological
University, Hyderabad, India
ABSTRACT
This paper aims to develop a Fuzzy Logic based controller to control the saturation
level in the magnetic core of a welding transformer. The magnetization level controller is a
substantial component of a middle-frequency direct current (MFDC) resistance spot welding
system (RSWS). The basic circuit of a resistance spot welding system consists of an input
rectifier, an inverter, a welding transformer, and a full-wave rectifier which is mounted on the
output of the welding transformer. The presence of unbalanced resistances of the transformer
secondary windings and the difference in characteristics of output rectifier diodes can cause
the transformers magnetic core to become saturated. This produces spikes in the primary
current and finally leads to the over-current protection switch-off of the entire system. To
prevent the occurrence of such a phenomena, the welding system control must detect and
maintain the magnetic core saturation within certain limits. The welding current at the full-
wave rectifier is normally controlled by the pulse width modulated primary voltage of the
transformer supplied by the input converter. Previously, an Artificial Neural Network based
detector was proposed to detect the saturation level. In this paper, a fuzzy logic based
controller is proposed to maintain the saturation within optimal limits. This is achieved by a
combined closed-loop control of the welding current and closed-loop control of the iron core
saturation level.
Keywords: Controllers, Fuzzy logic applications, Hysteresis, Transformers, Welding.
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING
& TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 4, Issue 3, May - June (2013), pp. 19-28
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2013): 5.5028 (Calculated by GISI)
www.jifactor.com
IJEET
© I A E M E

20
I. INTRODUCTION
The aim of this work is to develop and evaluate a novel method to control the
magnetization level in the magnetic core of a welding transformer. It is based on fuzzy logic
and requires the optimum operating values of the flux and welding current across the welding
system. The magnetization level controller is a substantial component of a middle-frequency
direct current (MFDC) resistance spot welding system (RSWS), where the welding current
and the flux density in the welding transformer’s magnetic core are controlled by two
hysteresis controllers [1].
The resistance spot welding systems described in different realizations [2]-[5], are
widely used in the automotive industry. Although the alternating or direct currents (dc) can
be used for welding, this work focuses on the RSWS (Fig.1) with dc welding current. The
resistances of the two secondary windings R2, R3 and characteristics of the rectifier diodes,
connected to these windings, can slightly differ. References [6]-[9] show that combination of
these small differences can result in increased dc component in welding transformer’s
magnetic core flux density. It causes increasing magnetic core saturation with high impact on
the transformer’s primary current i1, where current spikes eventually appear, leading to the
over-current protection switch-off of the entire system. However, the problematic current
spikes can be prevented either passively [6] or actively [7]-[9].
When the current spikes are prevented actively, closed-loop control of the welding
current and magnetic core flux density is required. Thus, the welding current and the
magnetic core flux density must be measured. While the welding current is normally
measured by the Rogowski coil [10], the magnetic core flux density can be measured by the
Hall sensor or by a probe coil wound around the magnetic core. In the latter, the flux density
value is obtained by analogue integration of the voltage induce in the probe coil [7].
Integration of the induced voltage can be unreliable due to the unknown integration constant
in the form of remnant flux and drift in analogue electronic components. The drift can be kept
under control by the use of closed-loop compensated analogue integrator [9].
An advanced, two hysteresis controllers based control of the RSWS, where current
spikes are prevented actively by the closed-loop control of the welding current and flux
density in the welding transformer’s magnetic core, is presented in [9]. This solution requires
measuring of the welding current, while instead of measured flux density only information
about magnetization level in the magnetic core is required. Some methods tested on welding
transformer’s magnetic core, that can be applied for magnetization level detection are
presented in [7], [8]. All these methods require Hall sensor or probe coils which make them
less interesting for applications in industrial RSWS, due to the relatively high sensitivity on
vibrations, mechanical stresses and high temperatures. In order to overcome these problems,
an ANN based magnetic core magnetization level detector was presented previously. Its only
(single) input is the measured transformer’s primary current. The ANN, based on the
magnetic core magnetization level detector, is trained to recognize the waveform of the
current spikes, which appear in the primary current when the magnetic core is approaching
the saturated region. Upon detection of a spike, the ANN target signal makes it possible for
the transformer supply voltage to change direction which also changes the magnetic flux
density accordingly. This way, the system is controlled using the ANN detector and over-
current protection switch-off is prevented.
In this paper, a fuzzy logic based controller is introduced which can be used in place
of the other hysteresis controller. The fuzzy controller supplements the ANN based detector,

21
in that it helps to limit the flux and the welding current within optimal operating values. The
inputs and their corresponding outputs are given to the fuzzy controller in the form of
membership functions. While the inputs include flux and welding current, the only output is
the transformer primary voltage. The necessary rules are defined within the fuzzy
interference system so that whenever the flux or welding current exceed the optimal values,
the transformer voltage must reverse its direction. This way, the flux starts to reduce and
finally leading to a suppression of the primary current. The popular and advantageous
Mamdani algorithm was used to employ the proposed controller.
II. DYNAMIC MODEL OF THE RSWS
The RSWS, shown in Fig.1, consists of an input rectifier, an H-bridge inverter, a
single phase transformer and a full-wave output rectifier [9]. The three-phase alternating
current (ac) voltages u1, u2, u3, supplied from the electric grid, are rectified in the input
rectifier in order to produce the direct current (dc) bus voltage. This voltage is used in the H-
bridge inverter, where different switching patterns and modulation techniques can be applied,
to generate ac voltage uH, required for supply of the welding transformer. The welding
transformer has one primary and two secondary windings. They are marked with indices 1, 2
and 3, respectively. The currents, the number of turns, the resistance and the leakage
inductances of the primary and two secondary welding transformer’s windings are denoted by
i1, i2, i3, N1, N2, N3, R1, R2, R3, and Lσ1, Lσ2, Lσ3. The effects of the eddy current losses are
accounted by the resistor RFe.
R1 and L1 are the resistance and inductance of the load. The output rectifier diodes D1
and D2 are connected to both transformer’s secondary coils. They generate the dc welding
current i1 which has a dc value a few times higher than the amplitudes of ac currents i2 and i3
that appear in the transformer’s secondary coils without the rectifier diodes.
Fig.1: Schematic presentation of the RSWS [1]
The dynamic model of the RSWS was built based on the schematic presentation,
shown in Fig.1. In this work the model is built with the programme package Matlab/Simulink
based on the following set of equations (1) – (9).
uH = R1i1+Lσ1(di1/dt)+ N1(dφ /dt)…………………………………………..……...........(1)
0 = R2i2+Lσ2(di2/dt)+ N2(dφ /dt)+dip1+ RLiL+LL(d(i2+ i3)/dt)…….............…….............(2)
0 = R3i3+Lσ3(di3/dt)- N3(dφ /dt)+dip2+ RLiL+LL(d(i2+ i3)/dt)…….............………...........(3)
N1ip+N2i2- N3i3 = H(B)lic+2δB/µ0…………………………………………..……............(4)

22
iL = i2+ i3………………………………………………….………….........................(5)
i1 = iFe+ iP………………………………………………………………….......................(6)
iFe = N1(dφ /dt)/RFe………………………………………………………...…...................(7)
φ = BAFe……………………………………………………….…………........................(8)
θ = N1i1+ N2i2-N3i3.............................................................................................................(9)
The results of simulations, obtained by the dynamic model of the RSWS, show that
small difference in resistances R2, R3 and in characteristics of the rectifier diodes D1 and D2
can cause unbalanced time behaviour of the magnetic core flux density B and the current
spikes in the primary current i1, shown in Fig.2. The a) and b) graphs in Fig. 2 show the same
variables in different time scales. The current spikes appear approximately after 0.06s
(Fig.3(c)). After 0.07s the current spikes become high enough to cause the over-current
protection switch off of the RSWS.
2(a) 2(b)
2(c) 2(d)
Fig.2(a),2(b),2(c): Time behaviour of primary current i1 Fig.2(d): Time behaviour of Flux B
II. FUZZY LOGIC CONTROLLER DEVELOPMENT
This paper proposes a fuzzy logic based controller of magnetization level in the
magnetic core. The inputs for the proposed controller are the flux and the welding current.
The output is the welding transformers primary voltage. The input and output ranges are set
in the corresponding membership functions depending on the data obtained from tests

23
performed and from the manufacturer. In this case, the entire dynamic model of the RSWS as
well as the fuzzy logic controller developed have been done so using the MATLAB/
SIMULINK package. Triangular membership functions are chosen in developing this model.
Fig.3: Fuzzy Logic Controller Model for saturation control
The membership function ranges for each variable are set according to the data
obtained from the dynamic model as well as the data obtained from the previously designed
ANN based detector.
(a) (b)
(c)
Fig.4: (a) and (b) represent the Input Membership Function plots of Flux and Welding
Current respectively. (c) represents the Output Membership Function plot of the Transformer
primary voltage.

24
The Rule-base for the proposed operation of the Fuzzy-Logic Saturation Controller is as
shown in Fig.5.
RULE NUMBER CONDITION
Rule 1 IF Flux is “High” THEN Voltage is “Low”
Rule 2 IF Flux is “Low” THEN Voltage is “High”
Rule 3 IF Welding Current is “Moderate” THEN Voltage is “Moderate”
Rule 4
IF Flux is “High” AND Welding Current is “Low” THEN Voltage
is
“Low”
Rule 5
IF Flux is “Low” AND Welding Current is “Low” THEN
Voltage is
“High”
Rule 6 IF Flux is “Moderate” THEN Voltage is “Moderate”
Rule 7 IF Welding Current is “High” THEN Voltage is “Moderate”
Fig.5: Rule-base of the proposed fuzzy-logic Hysteresis Controller
The Rule viewer and surface plots presented in the figures below show that the
controller works well with the presented rules and provides a reliable method to control and
maintain the magnetization levels of the welding transformer under acceptable limits. Thus,
the proposed fuzzy logic based controller can be utilized as an alternative for typically used
hysteresis controllers which possess several drawbacks such as production of noise and
mechanical vibrations.

25
Fig.6(a): Rule viewer of the proposed fuzzy logic saturation controller
Fig.6(b): Surface plot of the fuzzy logic saturation controller
III. OPERATION OF THE PROPOSED CONTROLLER
The proposed controller operates in such a way that whenever the flux or welding
current value exceeds a preset limit, the supply transformer’s primary voltage is either
reversed or made to zero depending on the condition. The welding system with the proposed
fuzzy-logic controller supplemented by an artificial neural network based detector works as a
closed-loop system where the inputs to the welding system are the flux and the welding
current and its output is the supply transformer’s primary voltage. The limiting values are
taken as Bm=1T, Im=14kA, IM=15kA and Udc=560V. The operational circuit is as shown in
Fig.7(a). The flux, welding current and voltage limits are set according to the table in
Fig.7(b). The various mapping values obtained from the proposed controller are as shown in
the table in Fig.7(c).

26
Fig.7(a): The closed loop control of transformer primary current i1 and welding current iL
using the fuzzy logic hysteresis controller and the ANN based saturation detector.
LOW MODERATE HIGH
FLUX <-1 -1 - 1 1<
WELDING <14000 14000-15000 15000<
CURRNT
VOLTAGE -650 - -300 -300 – 300 300 - 650
Fig.7(b): Ranges of each of the Input-Output Membership Functions
FLUX WELDING CURRENT VOLTAGE
-1.43 6680 458
1.8 10200 -474
0 14600 0
-1.72 15100 415
1.21 11600 -446
0 3950 0
-1.91 1230 476
1.54 10500 -464
1.76 29300 -357
Fig.7(c): Input-Output Mapping Values obtained from Fuzzy Controller

27
IV. CONCLUSION
A novel fuzzy logic based controller is developed to control the magnetization levels in
the core of a welding transformer. The controller developed works in conjunction with an ANN
based saturation detector presented in [11]. By employing the proposed ANN based saturation
detector and the fuzzy logic based magnetization controller, the welding system can operate
efficiently and properly. The proposed Fuzzy Controller works well and can be used to obtain
closed-loop control. The rules used work well and the input-output mapping obtained is just as
required. From the surface and from the above table, the values obtained are appropriate for the
controller to be used as a closed loop saturation controller. The system works such that whenever
any specified limit of flux or welding current is exceeded, the primary voltage is reversed in its
direction or made to zero.
REFERENCES
[1] K. Deželak, J. Pihler, G. Štumberger, B. Klopčič and D. Dolinar, “Artificial Neural Network
Applied for Detection of Magnetization Level in the Magnetic Core of a Welding Transformer,”
IEEE Transactions on Magnetics, vol. 46, no. 2, pp. 634–637, February 2010.
[2] W. Li, E. Feng, D. Cerjanec, and G. A. Grzazinski, “A comparison of AC and DC resistance
welding of automotive steels,” in Sheet Metal Welding Conf. XI, Sterling Heights, MI, May
2004.
[3] A.Canova, G. Gruosso, and B. Vusini, “Electromagnetic modelling of resistance spot
welding system,” in ISEF 2007, XIII Int. Symp. Electromagnetic Fields in Mechatronics, Czech
Republic, 2007.
[4] B. M. Brown, “A comparison of AC and DC resistance welding of automotive steels,”
Welding J., vol. 66, no. 1, pp. 18-23, Jan. 1987.
[5] W. Li, D. Cerjanec, and G. A. Grzadzinski, “A comparative study of single AC and
multiphase DC resistance spot welding,” ASME Trans. J. Manuf. Sci. Eng., vol. 127, no. 3,pp.
583-889, 2005.
[6] B. Klopčič, G. Štumberger, and D. Dolinar, “Iron core saturation of a welding transformer
in a medium frequency resistance spot welding system caused by the asymmetric output rectifier
characteristics,” in Conf. Rec. IAS 2007 Annu. Meeting, New Orleans, LA, Sep. 2007, pp. 2319–
2326.
[7] K. Deželak, B. Klopčič, G. Štumberger, and D. Dolinar, “Detecting saturation level in the
iron core of a welding transformer in a resistance spot-welding system,” J. Magn. Magn. Mater.
vol. 320, no. 20, pp. 878–883, Oct. 2008.
[8] K. Deželak, G. Štumberger, B. Klopčič, D. Dolinar, and J. Pihler, “Iron core saturation
detector supplemented by an artificial neural network,” Prz. Elektrotech., vol. 84, no. 12, pp.
157–159, 2008.
[9] B. Klopčič, D. Dolinar, and G. Štumberger, “Advanced control of a resistance spot welding
system,” IEEE Trans. Power Electron., vol. 23, no. 1, pp. 144–152, Jan. 2008.
[10] D. J. Ramboz, “Machinable Rogowski coil, design, and calibration,” IEEE Trans. Instrum.
Meas., vol. 45, no. 2, Apr. 1996.
[11] Rama Subbanna,S., Kamalakar,K.S.K., Dr.Suryakalavathi,M., “Artificial Neural network for
the detection of Magnetization level in the magnetic core of a welding Transformer”,IJAER,Vol8,
no.6, pp.56-60, 2013.
[12] J. M. Mendel, “Fuzzy Logic Systems for Engineering: A Tutorial”, Proc. IEEE, Vol. 83,
pp. 345-377, 1995.

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AUTHOR’S BIBLIOGRAPHY
RAMA SUBBANNA,S. graduated from Jawahalal Nehru Technological
University in the year 2003. M.Tech from Jawahalal Nehru Technological
University, Hyderabad, in the year 2006. Currently, He is pursuing Ph.D from
Jawahalal Nehru Technological University, Anatapur, India. Presently, he is
working as Assistant Professor in St.Martin’s Engineering College. His
research includes Transformer, Hysteresis, Controllers, ANN Techniques and
Fuzzy Logic Methods.
KAMALAKAR,K.S.K is a final year student of B.Tech in Electrical and
Electronics Engineering at St. Martins Engineering College, J.N.T.U-
Hyderabad. His research interests are mainly concerned with applications of
artificial intelligence and software aspects of Computer Engineering.
Dr.SURYAKALAVATHI,M. graduated from S.V.University, Tirupati in the
year 1988 . M.Tech from S.V.University, Tirupati in the year 1992. Ph.D from
J.N.T.University, Hyderabad in the year 2006 and Post Doctoral from CMU,
USA. She is presently professor of Electrical and Electronics Engineering
department, J.N.T.U.College of Engineering, Hyderabad. She presented more
than 50 research papers in various national and international conferences and
Journals. Her research area includes High Voltage Engineering, Power
Systems, Artificial Intelligence Methods.

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