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.
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
()
L
f
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
1
)( 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
ˆ() ()
ˆ
ˆˆ
()() ()
() ()
i
i
i
Li
iii
U
usds DUD
D
isus ds
ZsZs U








(1)
)(tis
2f
R
1f
R
1
)( fs Rti
1
)( faRti
)(tiL )(tis
)(tiL
Figure 1. Block diagram of the control system
(a)
)(
0
Su

(b)
Figure 2. The AC signal model of main circuit
()
i
Z
ssLR

 (2)
Equations (3) and (4) are dynamic equations of small
signal of output voltage in pluralism domain.
ˆ
ˆ()() ()
oLo
us isZs (3)
()
o
Z
sR

(4)
From above equations, the transfer function for rela-
tion between output current of load and duty cycle can be
denoted as Equation (5):
1
1
)(
ˆ
)(
ˆ
)( 0)(
ˆ



 
s
R
L
R
U
RsL
U
sd
si
sG ii
su
L
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
i
oi
udu sid
us U
Gs GsRL
ds
s
R



(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
u
o
(t)
u
i
(t)
i
L
(t)R
f
R
f
u
c
(t)
i
L
(t)
PWM comparator
Ratio of switch d
u
a
(t)
(a)
H
0
A
C
E
T
s
v
c
B
F
D
i
L
(t)R
f
u
-m
2
m
1
-m
a
u
c
t
dT
s
(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).

0
()
11
fLavg
Ts
f
LABEF ACHBDH
ss
Ri t
Ridt SSS
TT



 (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):

2
2
12
()
11
() 1
22
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)






2
11
ˆ()
1
ˆˆ
ˆˆ ()()() ()
2
fL L
cc ass
RI it
Uut MDdtTMmtDdtT

 


2
22
1ˆ
ˆ() 1()
2
s
M
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)

2
212
ˆ()
11
ˆ
ˆˆˆ ()()() 1()
22
fL
casss
Ri t
utMTdtDTmtD Tmt

 
(11)
In view of equation of L
uu
Rm oi
f
ˆˆ
ˆ1

and equation
of L
u
Rm o
f
ˆ
ˆ2 in Buck Converter, the transfer function
of inner peak current control circuit shown in Equation
(12) can be obtained from Equation (11).
2
ˆ()
(1 2 )
1ˆ
ˆˆˆ
() ()()()
22
fsf s
cfL io
as
ds
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
i
L
TDR
TM
U
D
f
sa
i
2
2








a
if
sa
i
LM
DUR
RLs
TM
U
2
)21(
1
1
)(siL

S
TSK)1(
2

f
R
1
K
)(si L

)(su
e
)(
ˆsu
c
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
1
(1 2 )
[1 ]
2
fi
fi
aS
a
RU
GS RU D
MT LS RLM


(13)
Equation (14) is inner closed-loop transfer function.
1
()
() ()
(1 2 )
2
L
c
i
fi S
asasf i
is
Ws us
U
RRUDT
M
TLsM RTRU
L


 
(14)
Equation (15) is transfer functions of entire open dou-
ble closed-loop system.
211
12
(1)
()( )
11
(1 2 )
2
ifi s
asasf i
KTS
GsW SK
S
TS
KKU RRUD T
S
M
TLSMRTRU
L



 
(15)
Equation (16) is transfer functions of closed-loop
transfer function for the entire system.
2
12
()
(1)
(1 2 )
()(1)
2
i
fi s
aSasf ii
WS
KU TS
RRUD T
SMTLSM RTRUKKUTS
L




(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( 
c
fjG 
, we
have:
12
(2 )
11
(1 2 )
21
2
c
i
fifi
as
c
a
Gj f
KKU
RVD RU
MT Lj f RLM R






 


(17)
In this paper (1 2 )
21
2
f
ifi
c
a
RVD RU
Lj fRLM R 


 


,
Equation (17) can be taken form as following:
LTM
UKK
f
sa
i
c
 2
21
 (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
1
-
I
:20
0
A/div,
T
:
1
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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