Energy and Power Engineering, 2013, 5, 657-660
doi:10.4236/epe.2013.54B127 Published Online July 2013 (http://www.scirp.org/journal/epe)
Research on Con t rol Strategy of 2 - p h a s e
Interleaving Magnetic Integrated VRM
Rui Guo1,2, Con g Wang 1,Yugang Yang2
1School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing, China
2Faculty of Electrical and Control Engineering, Liaoning Technical University, Huludao, Liaoning, China
Received February, 2013
ABSTRACT
A kind of 2-phase interleaving coupled magnetic integrated VRM is studied and the corresponding passivity-based con-
trol strategy is put forward. The model of this kind of magnetic integrated VRM is constructed, and the performance of
this 2-phase interleaving magnetic integrated VRM of passivity-based control is verified by simulation experiments.
The results proved that this kind of passivity-based control strategy can decrease the steady state current ripple and the
dynamic output voltage under load disturbance.
Keywords: VRM; Magnetic Integrated; Interleaving; Coupled Inductors
1. Introduction
Nowadays, the topology used in VRM is mostly multi-
phase interleaving Buck converter, in which the magnetic
components have important effect on the performance of
VRM. In order to increase the power density and effi-
ciency of VRM, the magnetic integration technology is
applied to it [1-3]. However, each phase winding of the
multi-phase magnetic integrated VRM has a self induc-
tance, meanwhile, it can form coupled magnetic circuit
with the other phase windings. Therefore, it is difficult to
construct the model of VRM and the traditional linear
control methods can not meet the demand of the per-
formance [4]. A kind of 2-phase negative coupling mag-
netic integrated VRM is studied in this paper and its cir-
cuit model is constructed using linear system control
theory, what’s more, the corresponding nonlinear passiv-
ity-based control strategy is put forward to realize the
equality of each phase current and to improve the dy-
namic performance of VRM.
2. Model Building of 2-phase Interleaving
Magnetic Integrated VRM
The model of 2-phase interleaving negative coupled
magnetic integrated VRM is shown in Figure 1. There
are 4 operation modes in each switch cycle, and the cor-
responding equivalent circuits are shown in Figure 2.
Supposed that VRM operates in the mode of continu-
ous current, and the 4 operating modes of VRM are de-
fined as “Σ1”, “Σ2”, “Σ3” and “Σ4”. The state variables are
selected as

123
T
x

x
xx, where “x1” and “x3” are cur-
rents “i1” and “i2”, “x3” is voltage “uc” , “Lk” is leakage
inductance, “k” is coupling coefficient, and “R” is the
load resistance. The models of the 4 modes “Σ1”, “Σ2”,
“Σ3” and “Σ4” are as follow:
11
22
3
1
00
1
1
:00 0
(12 )0
11 1
1
00
0
1
:00 0
0
11 1
1
00
1
:00
11 1
K
in
oo
KK
K
oo
K
K
in
KK
Lk
V
1
2
x
xA
LLk
RC RC RC
L
xxAxb
L
RC RCRC
L
V
xx
LL
RC RCRC


 




 

  
 










 



 









 








xb
33
0
1
(12 )0
oo
kAxb
k


 



*Sponsor: National Natural Science Foundation of China (No.
51177067 and No. 51077125)

R. GUO ET AL.
658
4
1
00
0
1
:00 0
0
11 1
K
oo
K
L
44
x
xAx
L
RC RCRC







 



 



b
This is a typical switch affine linear system. Its oper-
ating process is switched in 4 modes. The convex scheme
“Σeq” of 2-phase planar magnetic integrated VRM can be
constructed as [4]:
13
13
1
00
(1 )
1
:00 (1
(12)0
11 1
K
in
eq
KK
Lkk
V
Equation (1) is the state equation model of 2-phase
magnetic integrated VRM, and “λ1” and “λ3” are duty
cycles of switch device “Q1H” and “Q2H”, respectively.
3. Passivity-based Control Strategy of
2-phase Interleaving Planar Magnetic
Integrated VRM
)
x
xk
LLk
CCRC
Ax b




 




 

  
 




k

(1)
Supposed that the output state variables of VRM are
“10 20
[, ,]
T
dLLo
x
IIV

”, where “10
L
I
” and “20
L
I
” are
steady state average currents and “o” is static state
output voltage. The equilibrium state of the system de-
fined by equation (1) is supposed as “d
V
x
” and is trans-
lated to the origin of state space. The error vector is de-
fined as:
ed
x
xx

 (2)
Substituting equation (1) to (2), the error state equation
of VRM model can be expressed as:
ee d
x
Axb Ax


 (3)
1a
Q
2a
Q
1b
Q
2b
Q
o
C
o
R
o
V
in
V




m
V


m
V
1
i
2
i
o
i


m
i
1
i
1LK
L
2LK
L
m
L
1
V
2
V




Figure 1. Equivalent circuit of two-phase negative coupled planar magnetic integrated VRM.
Figure 2. Four operating modes of 2-phase negative coupled planar magnetic integrated VRM.

R. GUO ET AL. 659
Introduce a damping term “

”
1
11
2/0 0
02/0,
000
K
K
RL
RL R



 


0
A
e
(4)
and define a matrix “E” as:
E (5)
Substituting equation (5) to (3), we have
ee d
x
Exb Axx
 (6)
Supposing that the right-hand side of equation (6) is
always equal to zero, then:
0
ee
xEx
 (7)
A Lyapunov energy function can be established as
follow:
1
() 2
T
ee
Vx xPxe
0
(8)
Selecting P as
1
00
00
00
K
K
L
PL
RC






then the Lyapunov energy function becomes
22 2
1213
1111
() 0
2222
T
eeeKeKee
VxxPx LxLxRCx (9)
The derivative of Lyapunov energy function is:
1
() 0
2
T
eee
Vx xQx 
 (10)
According to the asymptotic stability criterion of the
control theory, the origin is asymptotically stable in the
system defined by equation (8).That is to say, if and only
if the right-hand side of equation (6) is constantly equal
to zero, the error zero point is the system’s intrinsic
steady point, then
0
de
bAx x (11)
Using equation (11), we can derive the expressions of
“λ1” and “λ3” as follow:
111 2
1
1111 2
2[ ()]
2[( )]
oeee
in
oL
in
VRxpxx
V
VRxIpxx
V





(12)
122 1
3
1222 1
2[ ()]
2[( )]
oeee
in
oL
in
VRxpxx
V
VRxIpxx
V





(13)
Equation (12) and (13) are the passivity-based control
strategy of 2-phase planar magnetic integrated VRM.
With this strategy, if the input voltage “Vin”, the output
voltage “Vo” and the coupling coefficient “k” are known,
the VRM can be controlled precisely to be on the steady
operation point and is passive. This can guarantee that
the VRM has a global stability. In addition, the dynamic
response speed of the VRM can be regulated in certain
range by adjusting the damping parameter “R1”.
4. Simulation Verifying
4.1. Steady Performance Simulation
The input voltage is “Vin=12 V”, output voltage is
“Vo=1.2 V”, switch frequency is “fs=200 kHz”, output
filter capacitance is “C=680μF”, load resistance is
“RL=0.05 Ω”, leakage inductance is “Lk=3 μH”, mutual
inductance is “Lm=3 μH”, and the coupling coefficient is
“k=0.5”.
According to equation (12) and (13), the steady state
performance of the 2-phase magnetic integrated VRM
with passivity-based control is simulated and compared
with that of 2-phase discrete inductor VRM, as shown in
Figure 3. The blue curves (If1, If2 and Ifo) are the current
waveforms of discrete inductor VRM, and the green
curves (Ih1, Ih2 and Iho) are the current waveforms of pla-
nar magnetic integrated VRM. It can be seen that the
current ripples of magnetic integrated VRM are smaller
than that of discrete inductor VRM, and this means that
the negative coupling magnetic integrated VRM of pas-
sivity-based control has better steady state performance
than that of the discrete inductor VRM.
4.2. Load Disturbance Simulation
The simulation waveforms shown in Figure 4 are the
simulation results of the process that the load resistance
jumps from light load (Rload=0.05Ω) to full load (Rload=
0.025Ω) at the moment of 1ms and falls from full load to
Figure 3. Steady state current waveforms of 2-phase VRM
with passivity-based control strategy.

R. GUO ET AL.
660
Figure 4. Dynamic response of output voltages of 2-phase
VRM with passivity-based control strategy.
light load at the moment of 1.5 ms. The blue curve (Vf) is
output voltage waveform of discrete inductor VRM un-
der load disturbance, and the green curves (Vh) is output
voltage waveform of magnetic integrated VRM under
load disturbance. It can be seen that the drop value and
over-modulation of dynamic output voltage of 2-phase
magnetic integrated VRM are smaller than that of 2-
phase discrete inductor VRM.
5. Conclusions
This paper brings passivity-based control method into
2-phase interleaving magnetic integrated VRM and puts
forward a kind of passivity-based control strategy. The
passivity-based control strategy is verified with MAT-
LAB simulation. The simulation results prove that
2-phase interleaving magnetic integrated VRM with pas-
sivity-based control strategy can improve the steady state
performance and the dynamic performance. Passiv-
ity-based control is a perfect control scheme for magnetic
integrated VRM.
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