On the basis of the analysis of phase-shifted full-
bridge ZVS PWM converter, Corresponding small-signal model is build using of state-space averaging method and the traditional Buck circuit model, Thereof, control block diagram of the system and transfer function are derived, Voltage single-loop control system is designed on the basis of small-signal model of phase-shifted full-bridge ZVS converter, Thus, the system is analyzed and PI compensation network is correctly designed. Finally, it is simulated using of matlab and simulation map is given, The results shows that the mathematical model is rational and design scheme is feasible. 1. Introduction
Phase-shifted full-bridge DC / DC converter has been widely applied in the middle and high-power converter，Soft-switching technology is introduced in the application in order to reduce the wear and tear, Which phase-shifted full-bridge zero-voltage switching converter has been widely used with its simple topology and small voltage and current stress of switching device, etc. The modeling analysis of DC / DC switching converter is basis of studying converter, it has great significance to DC / DC converter analysis and design. After the main circuit determined, the good controller is designed to DC / DC converter to compose of closed-loop control system in order to improve the output accuracy and dynamic characteristics. On the basis of phase-shifted full-bridge ZVS PWM converter proposed in this paper, all aspects of Control system is designed while the realization method of Voltage single-loop control and the simulation analysis of Current-mode dual-loop control are given.
2. The establishment and analysis of small-signal model of Phase-shifted full-bridge ZVS converter
Figure 1 is structure chart of the full-bridge DC / DC converter, On the assumption that power tube VT1-VT4 and rectifier diode DR1-DR2 are the ideal device, Switching frequency is much larger than the corner frequency of output filter disturbing signal arising from the dynamic process, Disturbing signal is much smaller than the steady-state volume, that is small-signal disturbance. An equivalent system has three independent input variables which are respectively control input d, voltage input ug and load current io. Output voltage u0 can be expressed as a linear combination of the above of variables (1), Its equivalent model shows in figure 2.
Fig. 1 The main circuit of full-bridge DC / DC
converter
^
00
^^^
0 )()()()()()()( sisZsusGsdsGsu gugud −⋅+⋅= （1） In while
^
0
^
0)(
0)(^
^
0
)(
)()(
=
==
si
suud
gsd
susG,
^
0
^
0)(
0)(^
^
0
)(
)()(
=
==
si
sdg
ug
su
susG,
^
^
0)(
0)(^
0
^
00
)(
)()(
=
==
su
sd
g
si
susZ
Ug
2D
4D
2C
4C
1D
3D
1C
3C
fL
fC LRDR1
DR2
TR
rL
4VT
1VT
3VT
2VTA B
Uo
ip
*
*
*
2009 Third International Symposium on Intelligent Information Technology Application
So Phase-shifted full-bridge converter can be changed from Buck Converter, the average equation of state of phase-shifted full-bridge ZVS DC / DC converter is established in accordance with the principles of converter and using of state-space averaging method.
Fig. 2 The converter of equivalent model
2.1.The average equation of state of DC / DC converter
Figure 3 shows the equivalent circuit of the full-
bridge DC / DC converter in a switching cycle, It can be divided into two sub-circuits of the state in accordance with the switch tube of the switch state: 0≤ t≤ dTs，dTs ≤ t≤ Ts，They are respectively shown as in Figure 3 (a), (b), The inductor current iL and the capacitor voltage uc are selected to the state variables, the output voltage uo is output variables. linear equation can be listed as follows according to Figure 3.
(a) (b) Fig. 3 The equivalent circuit
In 0 ≤ t ≤ dTs period, VT1, VT4 or VT2, VT3 are
conducted, Figure 3 (a) show s the equivalent circuit, its equation is as follows:
⎪⎪⎩
⎪⎪⎨
⎧
−=
−=
Ru
idt
duC
un
udtdi
L
cL
c
cgL
（2）
In dTs ≤ t≤ T period, VT1, VT4 or VT2, VT3 are turned-off, Figure 3 (a) show s the equivalent circuit, its equation is as follows:
⎪⎩
⎪⎨
⎧
−=
−=
Rui
dtduC
udtdiL
cL
C
cL
（3）
Then, formula (2) and (3) are deal with an average Value: (2) × d + (3) × (1-d),in which d is the duty cycle, under formula is drawn:
⎪⎪⎩
⎪⎪⎨
⎧
−+−=
−+−=
)(2)(2
2)(2
Ru
idRu
iddt
duC
Tu
dun
ud
dtdi
L
cL
cL
c
s
cc
gL (4)
In while：u0=uc.
2.2.The small-signal model of Phase-shifted full-bridge ZVS converter
The loss of duty cycle is an obvious and important
phenomenon in Phase-shifted full-bridge ZVS converter,Converter achieves ZVS load range related the size of original leakage inductance of transformer,While the size of original-side current change rate is decided, Then the effective duty cycle size of transformer Vice-side and the system dynamic characteristics has been affected.
The effective duty cycle Deff of transformer Vice-side can be expressed as follows in Phase-shifted full-bridge ZVS converter:
DDDeff Δ−= （5） In formula (5),D is the size of duty cycle on the
grounds of decision of control signal, △ D is the loss of duty cycle. the loss of duty cycle can be expressed as follows :
)2
)1(2(2 0 s
Lsg
r TD
LU
ITU
nLD −−=Δ （6）
In formula (6), n is a turns ratio of the both sides of the original-side and Vice-side oftransformer , Ug and U0 are respectively the input voltage and output voltage, Ts is the switching cycle, L is the inductor valueof output filter, Lr is the leakage inductance of the transformer, IL is current value the output filter inductor . So the effective duty cycle is as follows :
)2
)1(2(2 sg
Lsg
reff
TD
LU
ITU
nLDDDD −−
⋅−=Δ−= （7）
Formula (7) can be seen that D, U a and IL disturbance will produce Corresponding disturbance
^
ud Deff,So formula (8) is as follows: ∧∧∧∧
++= uieff dddd （8）
Formula (8) can be seen that ^d 、
^
id and ^
ud are the disturbance of effective duty cycle Deff caused by the disturbance of D、IL and Ug. So formula (9) is as follows: ^^
Lg
di i
nUR
d ⋅−= ， ^
2
^
gg
Ldu u
nUIR
d ⋅⋅
= ，
^
2
^^^^^^ 44g
g
LsrL
g
sruieff u
UIfnL
iU
fnLddddd ⋅+⋅−=++= （9）
^
0 )(su ^
)(sd
^
)(sug
^
0 )(si
G ud(s)
G ug(s)Z 0(s)
551550
In formula (9): 24d r sR n L f= ， 1/s sf T= . The disturbance is added to formula (4), And
Dynamic and steady-state volume are separated , duty cycle is lost, second order interchange minterm is omitted, and they are substrated the static state equation,Then we can get that small-signal model are shown as figure 4.
^
gun
^
gi
^
0i^^
dun g )(^^^
uig ddun +
^
dR
nU g )(
^^
uig dd
RnU
+
^
Li
+
+
CR
L
* *
+1: effD
Fig. 4 The small-signal model of phase-shifted ZVS full-bridge converter
3. The system dynamics block diagram and transfer function
It is shown to analyses small-signal model that transfer function )(sGud
for duty cycle d and output
voltage 0u is as follows:
1/)/()( 2 ++++
=RRsCRRLLCs
nUsG
dd
gud
（10）
Transfer function )(sGus for input voltage ug and
output voltage 0u is as follows:
))()(
1(1)/(
1)( 2 RZRRZR
nDsRLLCs
sGei
eideffus +
−+
++= （11）
Transfer function ( )idG s for duty cycle d and
output current oi is as follows:
1/)/(/)1(
)( 2 +++++
=RRsCRRLLCs
RsRCnUsG
dd
inid
（12）
In formula (12): 21// ( 1)
1eiR LZ sL R s LC s
sC sRC R= + = ⋅ + +
+
4. The design and correction of System control program
A major role of control circuit of Phase-shifted full-bridge ZVS converter controls the output voltage value according to controlling the phase-shifting angle between ahead bridge-leg and lagging bridge-leg. The voltage control scheme of system is closed-loop control mode in which the sampling output voltage is taken as feedback value to control, that is also single-loop control mode; Dynamic structure diagram of the system is shown in figure 5, in figure 5:β— feedback
joint-like factor, Kmd — proportional component of Duty cycle output, Gu(s) — Compensation network transfer function of Compensation network; The output of Closed-loop system is as follows known from Figure 5.
0
0
^^
00
0^^
0 1)(
1)(
11)()(
GZsi
GG
suG
Gsusu oug
gref +−
++
+⋅=
β （13 ）
In formula (13): mdudu KsGsGG )()(0 β= is Open-loop transfer function. It is known from formula (13) that all kinds of disturbance of the system reduces the
)(1/(1 0 sG+ times; 0G is Large and result is good in
ensuring stability of the system.
2.101.0102.10.2)( 250 ++×
= − sssG (14)
Fig. 5 Thedynamic structure diagram of
system
4.1.The system analysis when not adding corrected link
The actual parameters of converter are input voltage
Ug=640V ， n=1/1.3 ， L=1.8mH ， C=6580μF ，
Uo=220V，Lr=38μH，fs=20kHZ，R=2202/5500=8.8， 8.14 2 == srd fLnR ，β =0.014.Formula (14) is given when these parameters are taken into the open-loop transfer function.
Figure 6 is Bode plots When not adding corrected link Simulated in using Matlab software,It is known from figure 6 that System frequency is 140 rad/s，Phase margin is 116o..Although phase margin is a large, open-loop system is stable, gain is very small, open-loop system bandwidth is quite narrow, dynamic is worse in low-band system.
Fig. 6 The Bode plots When not adding corrected link
G u(s) K m d G ud(s)
β
G ug(s)Z 0(s)
^
)(su f - ^
u^
)(sd
^
)(su
^
0 )(si
^
0 )(su-
552551
4.2.The system analysis when adding PI controller
The system gain is improved in Series revising by PI
controller, the system bandwidth is increased to improve system performance, the PI controller added is kp=1 ,ki=306.2, Formula (14) is given when these parameters are taken into the open-loop transfer function.
2.101.0102.1)/2.3061(0.2)( 250 ++×
+= − ssssG
（15） Figure 7 is Bode plots after adding corrected link,
The across frequency of gain function of system original circuit is250rad/s, Phase margin is 48.3o，Amplitude margin is greater than 90dB, the low-band gain is Significantly increased, System bandwidth is slightly increased, dynamic performance is better.
Fig. 7 The bode plots adding corrected link
4.3.Experimental waveforms
The main parameters of the experimental circuit is
DC input voltage: Uin ＝ 360V~640V ； DC output voltage: U0=220V ； Output power: 5.5kW ； the original side winding turns of transformer:N1=22 turns, the vice side winding turns of transformer:N2=17 turns；Parallel capacitance: C1＝C3＝4.4nF，C2＝C4＝8nF；Resonant inductor: Lr =28uH ， Output filter inductor:Lf=1.8mH ； Output filter capacitor: Cf＝6580uF；Switching frequency: fs=20kHz; TMS320F2812 chip is used of Control chip, System uses a control of single-loop voltage. Figure 8shows the waveform of system output voltage (channel 1) and output current (channel 2) in that input voltage is 400V, output current is 10A. Figure 9 shows the drive waveform of switch VT1, VT3, It can be seen from the chart switch driver two-leg is complementary relationship, The dead zone between the two drivers is 1.2us To ensure safe work of switch tube.
(Vertical axis:90V/div, Horizontal axis:10us)
Fig. 8 The waveforms of Output voltage and current
Small signal model of phase-shifted full-bridge ZVS converter is established using state-space averaging method, the transfer function is derived from small-signal model, Voltage single-loop control system is designed on the basis of small-signal model of phase-shifted full-bridge ZVS converter, Thus, the system is analyzed and PI compensation network is correctly designed. Finally, it is simulated and experimented, The results demonstrates that the model is correct.
6.Acknowledgment
Sponsored by Hubei Provincial Department of Education (B20083001).
The authors would like to acknowledge support for the project from Hubei Provincial Key Discipline on Machine Electron. References [1] YungtaeckJang，MilanM Jovanovic，Yu-MingChang.A new ZVS-PWM full-bridge converters[J].IEEE Transaction on Power Electronics,2003,18(5):1122-1129. [2] Cho J G,Sabate J,Lee F.Novel zero-voltage-transition PWM dc/dc converter for high power applications[C]. IEEE APEC Rec.,Orlando,USA,1994:143-49. [3] Forsyth A J ,Ellis I K. Adaptive Control of a High-frequency DC-DC Converter by Oarameter Scheduling [J]. IEE Proc. Electr. Power Appl.,1999,146(4):447-454. [4] A. J. Forsyth，S. V. Mollov. Modelling and control of DC/DC converters. Power Engineering Journal October,1998:229~236. [5] YUAN Jin-xing,MA Rui-qing,FAN Ping.Research on Phase-shifted Full-bridge ZVS DC/DC Converter with Auxiliary Branch.Power Eletronics,2008(5):23~25. [6] Broeck H W .Analysis and Realization of a Pulsewidth Modulator Based on Voltage Space Vectors. IEEE Trans.on IA, 2002, 24(1): 142-150. [7] Chenjian. Power Electronics—Power Electronics Transformation and Control Technology .Beijing :China Higher Education Press,2002.
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