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

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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.M

2

1Department of Electrical and Electronics Engineering, St. Martins Engineering College,

Hyderabad, India 2Department 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



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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,



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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)



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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



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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.



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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.



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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).



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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



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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.

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

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