Modeling and Analysis of Submerged Arc Weld Power Supply Based on Double Closed-Loop Control

doi:10.4236/jsea.2010.37083

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J. Software Engineering & Applications, 2010, 3, 723-727

doi:10.4236/jsea.2010.37083 Published Online July 2010 (http://www.SciRP.org/journal/jsea)

723

Modeling and Analysis of Submerged Arc Weld

Power Supply Based on Double Closed-Loop Control

Baoshan Shi1, Kuanfang He2, Xuejun Li2, Dongmin Xiao3

1School of Mechanical and Vehicle Engineering, Beijing Institute of Technology, Zhuhai, China; 2Hunan Provincial Key Laboratory of

Health Maintenance for Mechanical Equipment, Xiantan, China; 3College of Electromechanical Engineering, Xiantan, China.

Email: [email protected]

Received January 6th, 2010; revised May 9th, 2010; accepted May 11th, 2010.

ABSTRACT

According to the soft-switching pulsed SAW (Submerged arc weld) weld power supply based on the double closed-loop

constant current control mode, a small signal mathematic model of main circuit of soft-switching SAW inverter was

established by applying the method of three-terminal switching device modeling method, and the mathematic model of

double closed-loop phase-shift control system circuit was established by applying the method of state-space averaging

method. Dynamic performance of the inverter was analyzed on base of the established mathematic model, and the tested

wave of dynamic performance was shown by experimentation. Research and experimentation show that relation be-

tween structure of the power source circuit and dynamic performance of the controlling system can be announced by

the established mathematic model, which provides development of power supply and optimized design of controlling

parameter with theoretical guidance.

Keywords: SAW, Double Loop Control, Soft-Switching, Inverter, Mathematic Model

1. Introduction

The full-bridge phase-shift zero-voltage soft-switching

PWM inverter now is widely used in the weld field for its

many excellent performances. Through establishing ma-

thematic model and transfer function of soft-switching

pulsed metal active gas welding power supply, the rela-

tion between structural parameters of circuit and dynamic

performance of system is obtained, which is an effective

method of designing and development of that power sup-

ply [1,2]. In the field of power electronics, problem of

linear PWM DC-DC converter modeling was solved, there

are many methods of modeling such as three-terminal

switching device modeling method, data-sampling, symbol

analysis and so on [3-6], and method of space state aver-

age applied to inverter modeling [7-10], which provide

mathematic model of soft-switching pulsed metal active

gas welding power supply with theoretical guidance.

This paper proposes a soft-switching SAW weld pow-

er supply based on the double closed-loop constant cur-

rent control mode, which adopts structure of soft-

switching full-bridge circuit and combines the conven-

tional negative feedback of current or voltage and the

peak current control mode. A small signal mathematic

model of main circuit of soft-switching SAW inverter

and the mathematic model of double loop control circuit

are established by applying the method of three-terminal

switching device modeling method and the method of

space state average. According to mathematic model,

dynamic performance of the inverter is analyzed, and

tested wave of dynamic performance is shown to prove

the rationality of the inverter by experimentation.

2. Principles

The sketch map of the double closed-loop feedback con-

trol system is shown in figure1. It uses hall sensor to

sample current signal from primary transformer, and

pouring into control loop after sophisticated high-speed

rectifying. The control loop needs a reasonable slope

compensation circuit to ensure the system to be stable

and get appropriate open-loop frequency.

In the course of operation, the peak current signal

)(tis is sampled from the peak current of the VT, then

plus a peak current slope compensation signal1

)( fa Rti ,

which is a signal substituted traditional triangular wave

signal in voltage mode control. The saw tooth sig-

nal 1

)( fa Rti is synchronized with the signal of inverter

cycle, which is mainly used to improve waveform of the

Modeling and Analysis of Submerged Arc Weld Power Supply Based on Double Closed-Loop Control

724

peak current signal, reduce the noises from the power

circuit, and advance system stability. Meanwhile, aver-

age output current of inductance 2

()

itR is detected,

which is compared to the given signal to get error signal.

The error signal is replaced by the given signal of voltage

mode control after correcting or compensating, and in-

cises the peak current )(tisthat adds saw tooth signal

)( fa Rti to adjust duty cycle of VT, which realizes effec-

tive control of the output current.

The main advantages of inner loop control is to im-

prove the overall dynamic response speed of system,

protect power tube and realize correction of each current

pulse, solve problem of magnetic bias of power trans-

former; the purpose of outer loop control is to improve

control accuracy and technology of power.

3. Modeling and Analysis

3.1 Mathematical Model of Main Circuit

In this paper, mathematical model of main circuit of

SAW soft switch inverter is established by the way of

three-terminal switching device modeling method. The

soft-switching circuit is full-bridge circuit in Figure 1; it

is still a typical Buck Converter in essence [11,12].

The main circuit of soft-switching inverter equals to

circuit According to three-terminal switching device

modeling method in Figure 2(a), dynamic low-frequency

small signal circuit model in the pluralism domain is

shown in Figure 2(b).

According to Figure 2(b), dynamic equations of AC

small signal )(

ˆsiL of inductance current in pluralism

domain are expressed as Equations (1) and (2):

ˆ() ()

ˆˆ

()() ()

() ()

iii

usds DUD

isus ds

ZsZs U

















(1)

)(tis

)( fs Rti

)( faRti

)(tiL

)(tis

)(tiL

Figure 1. Block diagram of the control system

(a)

)(



(b)

Figure 2. The AC signal model of main circuit

()

ssLR



 (2)

Equations (3) and (4) are dynamic equations of small

signal of output voltage in pluralism domain.

ˆ()() ()

oLo

us isZs (3)

()



(4)

From above equations, the transfer function for rela-

tion between output current of load and duty cycle can be

denoted as Equation (5):

)(

)( 0)(







 

RsL

sG ii

id i

(5)

The transfer function for relation between output cur-

rent of load and duty cycle can be denoted as Equation

(6):

ˆ() 0

ˆ()

() ()

ˆ() 1

udu sid

us U

Gs GsRL







(6)

In Equations (5) and (6), Ui is the equivalent DC input

voltage; L is the output filter inductance; R is load resis-

tance. Main circuits of inverter are composed of propor-

tional part and inertia part in view of control structure.

3.2 Mathematical Modeling of Inner Loop

Control System

The structure of control circuit of inner loop current is

shown in Figure 3. The inductance current iL(t) is gained

by input voltage ui(t) and output voltage uo(t), iL(t)plus

resistor Rf and then change into voltage signals iL(t)Rf.

iL(t)Rf plus the slope compensated voltage ua(t),which

import to the negative terminal of PWM comparator. uc(t)

is reference voltage of positive terminal of PWM com-

parator. Relations expression of duty cycle d and input

Modeling and Analysis of Submerged Arc Weld Power Supply Based on Double Closed-Loop Control

725

(t)

(t)R

(t)

PWM comparator

Ratio of switch d

(t)

(a)

(t)R

-m

(b)

Figure 3. Model of current-injection controller

voltage ui(t), output voltage uo(t), slope compensation

voltage ua(t), reference voltage uc(t) and inductance cur-

rent iL(t) are derivatived by application of Space State

Average method.

From Figure 3(b), we can indicates expression of av-

erage voltage of inductance sampling current in the

opening of each cycle as Equation (7).



()

fLavg

LABEF ACHBDH

Ri t

Ridt SSS







 (7)

In the Equation (7), SABEF、S ACH and S BDH are

the area of rectangular ABEF, triangle ACH and the tri-

angle BDH in Figure 3(b), according to Equation (7), we

have Equation (8):



()

() 1

fLavg

cas ss

Ri t

utmdTmdTmd T



 

(8)

In Equation (8), we can obtain Equation (10) after

adding disturbing variable and taking into account that

the system state has no relation to the slope compensa-

tion voltage shown in Equation (9).

aa Mtm)( (9)







ˆ()

ˆˆ

()()() ()

fL L

cc ass

RI it

Uut MDdtTMmtDdtT



 



1ˆ

ˆ() 1()

mtDdt T



 



(10)

In Equation (10), )(

ˆtiL、)(

ˆtuc、)(

ˆtd 、)(

ˆ1tm 、and

)(

ˆ2tm are corresponding disturbing variable .We can ob-

tain Equation (11) after linear treatment of Equation (10)



212

ˆ()

ˆˆˆ

()()() 1()

casss

Ri t

utMTdtDTmtD Tmt



 

(11)

In view of equation of L

Rm oi

ˆˆ

ˆ1



and equation

of L

Rm o

ˆ2 in Buck Converter, the transfer function

of inner peak current control circuit shown in Equation

(12) can be obtained from Equation (11).

ˆ()

(1 2 )

1ˆ

ˆˆˆ

() ()()()

fsf s

cfL io

RDTR DT

us Risusus

MTL L













 









(12)

3.3 Mathematical Model of Double Closed-Loop

Control System

In order to improve accuracy of control system, reduce

steady error, the average output current or voltage are

sampled in this control system, and compared to the in-

ner given compensation signal uc(s). Primarily role of

outer loop regulator is to improve and optimize system

performance; PI regulator is used in this paper. Accord-

ing to Subsection 3.1 and Subsection 3.2, overall control

system diagram based on model of double closed-loop

current is shown in Figure 4, the DC signal ui(s) can be

treated as system disturbance.

According to Figure 4, open-loop transfer function of

the inner loop current is expressed as Equation (13).

)(

ˆsu

TDR

















DUR

RLs

)21(

)(siL



TSK)1(



)(si



)(su

)(

ˆsu

Figure 4. Block diagram of the double loop system

Modeling and Analysis of Submerged Arc Weld Power Supply Based on Double Closed-Loop Control

726



(1 2 )

[1 ]

GS RU D

MT LS RLM





(13)

Equation (14) is inner closed-loop transfer function.

()

() ()

(1 2 )

fi S

asasf i

Ws us

RRUDT

TLsM RTRU





 

(14)

Equation (15) is transfer functions of entire open dou-

ble closed-loop system.

211

(1)

()( )

(1 2 )

ifi s

asasf i

KTS

GsW SK

KKU RRUD T

TLSMRTRU







 

(15)

Equation (16) is transfer functions of closed-loop

transfer function for the entire system.

()

(1)

(1 2 )

()(1)

fi s

aSasf ii

KU TS

RRUD T

SMTLSM RTRUKKUTS









(16)

In Equation (16), D is duty cycle; Ui is inputting DC

voltage; TS is the inverting cycle; Rf is sampling resistor

of the inner current; Ma is the rising slope of compensa-

tion voltage; L is Output filter inductance; R is pulsed arc

load; K1 is feedback coefficient of outer loop current; K2

is adjusting gain; T is time constants of regulator.

3.4 Analysis of Dynamic Characteristic

The cutoff frequency of open-loop that is an important

characteristic index that is the embodiment of dynamic

response of control system [13]. Dynamic characteristic

of welding power are analyzed as mathematical model

established in Subsection 3.3. Provided outer loop is a

simple proportional control mode, and the open-loop

system fc is frequency when open loop gain equals to1,

according to Equation (15), and set1)2( 

fjG



, we

have:

(2 )

(1 2 )

fifi

Gj f

KKU

RVD RU

MT Lj f RLM R









 





(17)

In this paper (1 2 )

ifi

RVD RU

Lj fRLM R







 





Equation (17) can be taken form as following:

LTM

UKK



 (18)

In Equation (18), open-loop traversing frequencyc

fis

proportional of outer loop resistor, DC input voltage and

gain of outer loop adjuster. But the traversing open-loop

frequency is inversely proportional to the rising rate of

compensation voltage, switching cycle and output induc-

tance. Since outer loop resistor is limited by linear ad-

justment range of voltage of control circuit, opening tra-

versing frequency of control system can be increased by

the way of reducing rising ratio of compensation voltage

and output inductance, and increasing frequency of in-

verter. From above analysis, dynamic response of double

closed loop control system is improved greatly by inner

loop current control.

4. Experimentation

Dynamic characteristics of arc welding inverter are al-

ways defined as the relationship between output current

or output voltage and time when load instantaneous

change, which is a major performance index of arc weld

power source. Two sets of experiments of constant cur-

rent outer characteristic of arc weld power source are

done to prove the effect of theatrical analysis based on

the double closed-loop constant current control mode.

The experiments of arc welding are current response un-

der condition of the instantaneous change of the given

signal and current response under condition of instanta-

neous change of the given load.

The curve of Figure 5 is current response when cur-

rent instantaneous change from 0 A to 430 A under the

simulated load of 0.1 . In figure5, the current instanta-

neous change from 50 A to 320 A just needs time of 2 ms,

which conclude that system has better dynamic perform-

ance through this experimentation.

The curve of Figure 6 is current response curve meas-

ured by given current value of 100A and simulated load

changing from 0.09  to 0.03 . In Figure 6, the given

current instantaneous change from 130 A to 100 A just

needs time of 4 ms, which conclude that system has bet-

ter dynamic performance and a constant current outer

characteristic.

5. Conclusions

Mathematical model of SAW weld soft-switching in-

verter based on a double closed-loop constant voltage

and current control is established. Based on mathematical

model, dynamic performance is analyzed, and dynamic

characteristic curve of arc weld power source is tested in

Modeling and Analysis of Submerged Arc Weld Power Supply Based on Double Closed-Loop Control

727

:20

A/div,

ms/div

Figure 5. The current response curve while instantaneous

change from 0 A to 430 A

1-I:50A/div, T:10ms/div

Figure 6. The current response while the load changing

this paper, it shows that double closed-loop control can

improve dynamic characteristics of arc welding power

source, which can meet request of SAW technology.

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