Research on Control Strategy of 2-phase Interleaving Magnetic Integrated VRM

doi:10.4236/epe.2013.54B127

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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

Email: [email protected]

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



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:

:00 0

(12 )0

11 1

:00 0

11 1

:00

11 1

LLk

RC RC RC

xxAxb

RC RCRC





 









 





 

 





















 





















 











(12 )0

kAxb





 







*Sponsor: National Natural Science Foundation of China (No.

51177067 and No. 51077125)

R. GUO ET AL.

658

:00 0

11 1

xAx

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]:

(1 )

:00 (1

(12)0

11 1

Lkk

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

)

LLk

CCRC

Ax b







 









 





 

 









k



(1)

Supposed that the output state variables of VRM are

“10 20

[, ,]

dLLo

IIV



”, where “10

” and “20

” 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

” and is trans-

lated to the origin of state space. The error vector is de-

fined as:



 (2)

Substituting equation (1) to (2), the error state equation

of VRM model can be expressed as:

ee d

Axb Ax





 (3)















1LK

2LK









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 “



”

2/0 0

02/0,

000

RL R







 





(4)

and define a matrix “E” as:

E (5)

Substituting equation (5) to (3), we have

ee d

Exb Axx

 (6)

Supposing that the right-hand side of equation (6) is

always equal to zero, then:

xEx

 (7)

A Lyapunov energy function can be established as

follow:

() 2

Vx xPxe

(8)

Selecting P as











then the Lyapunov energy function becomes

22 2

1213

1111

() 0

2222

eeeKeKee

VxxPx LxLxRCx (9)

The derivative of Lyapunov energy function is:

() 0

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

bAx x (11)

Using equation (11), we can derive the expressions of

“λ1” and “λ3” as follow:

111 2

1111 2

2[ ()]

2[( )]

oeee

VRxpxx

VRxIpxx











(12)

122 1

1222 1

2[ ()]

2[( )]

oeee

VRxpxx

VRxIpxx











(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.

REFERENCES

[1] P. L. Wong, P. Xu, P. Yang and F. C. Lee, “Performance

ImProvements of Interleaving VRMs with Coupling In-

ductors,” IEEE Tranctions on Power Electronics, Vol. 16,

No. 4, 2001.

[2] P. Xu, M. Ye and F. C. Lee, “Single Magnetic Push-pull

forward Converter Featuring Built in Input Filter and

Coupled-inductor Current Doubler for 48V VRM,”IEEE

Proceedings of APEC, Vol. 2, No. 3, 2002, pp.843-849.

[3] L. P. Wong,Y. S. Lee and D. K. W. Cheng, “Simulation

and Design of Integrated Magnetics for Power Convert-

ers,” IEEE Transactions on magnetics, Vol. 39, No. 2,

2003, pp.1008-1018. doi:10.1109/TMAG.2003.808579

[4] P. Bolzern and W. Spinelli, “Quadratic Stabilization of A

Switched Affine System about A Nonequilibrium Point,”

Proceedings of the American Control Conference, Vol.

25, No. 3, 2004, pp. 96-101.