FACTA UNIVERSITATIS (NI

?

S)

SER.:ELEC.ENERG.vol.17,December 2004,365-376

Symmetrical Power Supply for 42 V Automotive

Applications

Roberto Giral,Javier Calvente,Ramon Leyva

Abdelali El Aroudi,Goce Arsov,and Luis Mart´nez-Salamero

Abstract:The Positive Channel Two Input Two Output (PCTITO) converter is a third

order MIMODC-to-DCunidirectional and non-isolated switching converter that is de-

rived fromthe non-inverting buck-boost converter.Negative and Dual Channel TITO

converters are also presented.In steady state one of the PCTITO outputs is positive

while the other is negative.Although the outputs could be regulated to provide dif-

ferent absolute values,an interesting application of the new converters is to provide

symmetrical outputs (i.e.,

15 V) to supply balanced loads.Since the absolute value

of the outputs could be greater or smaller than the input voltage,the PCTITO con-

verter will be suitable for present 14 V (from 9 to 16 V) or for future 42 V (from

30 to 50 V) automotive voltage distribution buses.To regulate the outputs,two in-

phase equal-switching frequency PWM-based multivariable control loops have been

designed.The closed-loop systemmust provide lowaudiosusceptibility and good line

and load regulation at both outputs.In addition,the common mode voltage between

the two outputs that could appear in unbalanced load operation has to be minimized.

With these general guidelines,several control parameter adjustments have been con-

sidered,validated using an averaged model of the system,and tested by simulation.

Keywords:MIMO,PWMdc-dc switching converter,symmetrical output regulator,

automotive 42V PowerNet.

Manuscript received June 22,2004.An earlier version of this paper was presented at the Third

Triennial International Conference on Aplied Automatic Systems,AAS’03,September.18-22,3003,

Ohrid,Republic of Macedonia.

R.Giral,J.Calvente,R.Leyva,A.El Aroudi,and L.Mart?nez-Salamero are with Universi-

tat Rovira i Virgili,Escola T?ecnica Superior d’Enginyeria,Departament d’Enginyeria Electr?onica,

El?ectrica i Autom?atica,Campus Sescelades,Av.Pa¤?sos Catalans 26,43007 Tarragona,Spain;(e-

mail:rgiral@etse.urv.es).G.Arsov are with SS Cyril and Methodius University,Faculty of

Electrical Engineering,Institute of Electronics,P.O.Box 574,1000 Skopje,Republic of Macedonia

(e-mail:g.arsov@ieee.org).

365

366 R.Giraletal.:

1 Introduction

The automotive industry is experiencing an electronic revolution.To provide ef-

ciently enough electric power to supply the increasing number of electric and

electronic loads that cars are going to incorporate,car manufacturers are consid-

ering to substitute the actual 14 V alternator-12 V battery set.In the short term,

one of the solutions the automotive industry is going to adopt considers to raise the

DC nominal voltage of the system (42 V PowerNet).According to ISO/CD 21848

draft [1] discussed in SAE2002 Congress,the supply voltage range for 42 Vsystem

devices will be very wide [30 V,48 V].

In this context,as it happens in current vehicles,there will be loads that require

to be supplied by symmetrical voltages like

15 V.There are a large number of so-

lutions,even commercially available,that could provide multiple outputs and that

could be congured for symmetrical voltages.Some solutions use several stages

[2],while others use two separate (isolated or non-isolated) regulators.Other so-

lutions are dual channel and require two unregulated symmetrical input voltages

[3].

Fig.1.The Positive Channel Two Input Two Output (PCTITO) DC-DC

switching converter.

When the loads are also symmetrical,like in the power supply of some class

AB or class D audio ampliers [4],the Positive Channel Two Input Two Output

(PCTITO) unidirectional regulator of Fig.1 could be an interesting solution for

automotive 42 V applications in which isolation among input and outputs is not

required.The PCTITO regulator is a third order MIMO (Multiple Input Multiple

Output) non-isolated dc-dc switching converter that can be derived form a non-

inverting buck-boost converter [5].In fact,instead of connecting the ground node

to the middle output point (Mnode),if the ground is connected to the bottom (B)

node,and switches are simultaneously activated,the converter structure is identical

to the non-inverting buck-boost.On the other hand,if the ground node is connected

to the top node (T) instead of node M,switch Bis superuous and the systemstruc-

SymmetricalPowerSupplyfor42VAutomotiveApplications 367

ture becomes a buck-boost cell.

Fig.2.The Dual Channel (DCTITO) converter.

Fig.2 shows the Dual Channel TITO (DCTITO),a third order converter that

presents a structure very similar to the ve order dual channel resonant buck-boost

converter presented in [3] being,in fact,a dual channel buck-boost converter.If the

positive input of the DCTITOis made zero,the Negative Channel NCTITOwill be

obtained.In al the TITO converters (DC,PC and NC) there are Two control Inputs

(S

A

,S

B

) and Two voltage Outputs (v

P

,v

N

).

The application of different control laws to the two MOSFET of the TITO

structures will permit,in principle,to regulate independently the converter output

voltages,one positive and one negative,to obtain absolute values greater (step-up)

or smaller (step-down) than the input (or inputs).

In Section 2,the PCTITO circuit is analyzed using an averaged model of the

switches (MOSFETs and diodes).Ageneral control strategy is proposed in Section

3,where several adjustment procedures of the control coefcients are studied by

means of simulations.Finally,some conclusions and proposals for future works

are presented.

2 Time-Averaged Circuit in Open Loop

Substituting the converter MOSFETs and diodes by their time-averaged models

in the form of controlled sources permits to obtain the time-averaged equivalent

circuit model [6] of the PCTITO converter shown in Fig.3,where d

A

and d

B

are

the duty cycles of S

A

and S

B

,respectively.The current i and the voltages v

P

and v

N

are the time-averaged state variables of the circuit.Note that v

N

has been dened

to be positive.

Considering ideal components (without losses,ideal switches),the averaged

368 R.Giraletal.:

system can be described by the following equations in matrix form:

x

A x

Bv

g

(1)

where

x

i v

P

v

N

T

(2)

and

A

0

d

B

1

L

d

A

1

L

1

d

B

C

P

1

R

P

C

P

0

1

d

A

C

P

0

1

R

N

C

N

B

d

A

L

00

(3)

Fig.3.Time-averaged equivalent circuit model of the PCTITO con-

verter.

Let us assume that,around equilibrium,the averaged systemvariables are con-

stituted of a steady-state part plus a small-signal component in the form

i

I

i v

P

V

P

v

P

;v

N

V

N

v

N

v

g

V

g

v

g

;d

A

D

A

d

A

;d

B

D

B

d

B

(4)

where d

A

and d

B

are the two control inputs.The steady-state operating point of the

state variables in open loop is

I

V

g

D

A

1

D

B

2

R

P

1

D

A

2

R

N

V

P

1

D

B

R

P

I

V

N

1

D

A

R

N

I

(5)

Since 0

D

A

1 and 0

D

B

1,all three steady-state values are positive,

and equal (symmetrical) output voltages can be provided.Considering equal loads

(R

P

=R

N

=R),the expressions of the steady-state output voltages become indepen-

dent of load R.In this case,controlling both switches with the same duty-cycle

(D

A

=D

B

=D) results in equal steady-state output voltages.

V

P

V

N

D

1

D

V

g

2

(6)

SymmetricalPowerSupplyfor42VAutomotiveApplications 369

In symmetrical operation,the sum of V

P

and V

N

of (6) yields the same result

of the single-output non-inverting buck-boost of ([5]) as expected.In the general

case,since no losses have been considered,combining (5) and (7) it can be seen

that the steady-state input power is equal to the power delivered to the resistive

loads.

P

in

V

g

D

A

I

P

out

V

2

P

R

P

V

2

N

R

N

(7)

Dening the enlarged small signal input vector of (8) the time-averaged system

can be linearized around its equilibrium point as in (9)-(12).

u

v

g

d

A

d

B

T

(8)

x

A

L

x

B

L

u

(9)

Matrices A

L

and B

L

are

A

L

0

D

B

1

L

D

A

1

L

1

D

B

C

P

1

R

P

C

P

0

1

D

A

C

P

0

1

R

N

C

N

(10)

B

L

D

A

L

B

12

V

g

L

B

13

V

g

L

0 0 B

23

V

g

C

P

0 B

32

V

g

C

N

0

(11)

with the following dimensionless parameters

B

12

1

D

B

2

R

P

1

D

A

R

N

1

D

B

2

R

P

1

D

A

2

R

N

B

13

1

D

B

D

A

R

P

1

D

B

2

R

P

1

D

A

2

R

N

B

23

B

32

D

A

1

D

B

2

R

P

1

D

A

2

R

N

(12)

Previous expressions could be easily simplied assuming equal loads R

P

=R

N

=R.

Further reasonable simplication considers equal output capacitors (C

P

=C

N

=C).

370 R.Giraletal.:

3 Control Strategies

From the small signal equations at the end of previous section,it is possible to ob-

tain different transfer functions in the Laplace domain that could be used to design

small signal control strategies.

The intended PCTITO application is to provide an automotive symmetrical

power supply.EMC automotive directives make desirable that both switches op-

erate at the same switching frequency,therefore a pulse width modulation (PWM)

based control scheme is preferred.However sliding mode or other hysteretic based

schemes are also easily applicable.

Considering the wide margin and possible noise at the input voltage (42 V

PowerNet) of the converter,line regulation and audiosusceptibility become impor-

tant aspects to be taken into account in the control design which,in principle,will

have a common voltage reference for both outputs.In addition,although the nomi-

nal operation considers balanced operation (symmetrical output voltages and equal

loads),the converter must be able to operate to some extent in unbalanced load

modes,therefore load regulation at both outputs will have to be taken into ac-

count.Finally,related with all the previous subjects,cross regulation effects are

also important.Probably,for supplying high quality symmetrical output voltages,

the common mode voltage of the outputs has to be kept as small as possible in the

case of input voltage and/or load changes.

A general view of the system,that includes the PCTITO converter and the

block diagram of a multivariable PWMcontrol scheme,is depicted in Fig 4.The

control circuit will provide two pulse width modulated digital control signals S

A

and S

B

.The right bottom box in the gure corresponds to the two required PWM

modulators.The gure shows a simplied version of them that omits RS ip-ops

normally used to prevent multiple commutations in one cycle.Aleading-edge saw-

tooth signal with the desired amplitude and frequency is used to generate both con-

trol signals by comparing it with the corresponding control law signals.The use of

a common sawtooth signal will cause simultaneous switch-on of both MOSFETS.

Zero and unity duty cycles are not allowed,they are avoided by limiting the signals

entering the PWMcomparison blocks between 5%and 95%of the sawtooth signal

amplitude (usually normalized to unity).

The multivariable control strategies that have been considered are symmetrical

in structure.Since buck-boost structures have been shown to exhibit right half-

plane zeroes,it is expected that the inclusion of the inductor current in the control

law will improve the stability margins.

The duty cycles of the switches in the open loop system description of (1)-(3)

have to be substituted by the general expressions for d

A

and d

B

shown in (13).

SymmetricalPowerSupplyfor42VAutomotiveApplications 371

Fig.4.PWMmultivariable control scheme for the PCTITO.

d

A

K

IA

i

K

VAP

PI

P

K

VAN

PI

N

d

B

K

IB

i

K

VBP

PI

P

K

VBN

PI

N

(13)

where PI

P

and PI

N

are the outputs of two proportional-integral blocks of the Pos-

itive and Negative error voltages with respect to a common reference V

R

,respec-

tively.K

IA

and K

IB

are respectively the coefcients of the inductor current feedback

for switches A and B (peak current mode control).Accordingly,K

VAP

and K

VBP

are the A and B coefcients for the PI

P

voltage term,and K

VAN

and K

VBN

the cor-

responding coefcients for the PI

N

contribution.Fig.4 shows that two PI blocks

with time constants T

VP

and T

VN

have been considered.

PI

P

die

P

ie

P

T

VP

PI

N

die

N

ie

N

T

VP

die

P

v

R

v

P

die

N

v

R

v

N

(14)

Since ie

P

and ie

N

in (14) are the integrals of the corresponding error voltages

die

P

and die

N

,the dimension of the closed-loop system has been enlarged up to

ve.In this case ie

P

and ie

N

are two additional state variables that have to be added

to the previous ones:i,v

P

and v

N

.The closed-loop state variable vector is (15).

After linearizing the system,the A

L

and B

L

matrices of the closed loop system

372 R.Giraletal.:

description in the form of (9) could be obtained again but they are too large to be

included here.

x

i v

P

v

N

ie

P

ie

N

T

(15)

It has to be pointed out that,in order to get information about the closed-

loop system response to load perturbations,the equations of the output voltage

derivatives have been modied to include two small signal current sources.Each

one of the newinputs is connected in parallel with the corresponding resistive load.

The u vector for the closed loop system is (16).Also the open loop duty cycles

are no more inputs to the system and should be replaced by the voltage reference

which has been assumed to be the same for both output voltages (v

RP

= v

RN

= v

R

=

V

R

v

R

)

u

v

g

i

OP

i

ON

v

R

T

(16)

The steady-state closed loop equilibrium point for the converter variables will

be

V

P

V

N

V

R

I

R

P

R

N

V

R

R

P

V

g

R

P

R

N

V

R

V

g

(17)

There are eight control coefcients and the integrals of the error voltages in

closed-loop depend on them in a complex form,therefore the corresponding ex-

pressions have been omitted.Instead,it is more useful to include the steady-state

values for the duty cycles,D

A

and D

B

,of both switches (18).Both duty cycles

are equal if the loads are balanced.For unbalanced loads,although D

A

is always

between zero and one,D

B

could become negative for certain values of the voltage

reference smaller than the input voltage if R

P

is also smaller than R

N

.In practice,

this will imply that the control for S

B

could be saturated and that,depending on

the mentioned parameters,the system with unbalanced loads could not always be

regulated as desired.This also suggests that a worst case for checking the effect of

load perturbations could be found for R

N

larger than R

P

D

A

R

P

R

N

V

R

R

P

R

N

V

R

R

P

V

g

D

B

R

P

R

N

V

R

R

P

R

N

V

g

R

P

R

N

V

R

R

P

V

g

(18)

SymmetricalPowerSupplyfor42VAutomotiveApplications 373

3.1 Design example

In order to verify the theoretical analysis,an example with several control possibil-

ities has been designed.The nominal converter parameters have been determined

as follows:

An input voltage of V

g

=42 V accordingly to the PowerNet specications.Ar-

bitrarily,an output voltage reference of V

R

=15 V has been xed.The nominal

output power will be 150 W,which implies an average input current of about 3.6

A and,in balanced load operation,R

P

=R

N

=3 Ω.Steady-state duty-cycles (18)

are about 41.7%.With a switching frequency of 50 kHz (T=20 ms),L

40 mH

and considering simultaneous turn-on of the MOSFETS,the inductor peak-to-peak

current ripple will be 8.75 A over a mean value (17) of about 8.6 A.Since the

peak-to-peak ripple is smaller than 200% of the mean value,the inductor continu-

ous conduction mode operation (CCM) is ensured.Taking C

P

=C

N

500mF,the

voltage ripple will be about 83 mV in each capacitor (166 mV over the 30 V sum

of V

P

and V

N

,0.55%).

Once the plant parameters have been chosen,we have to determine the values

of the control coefcients.First,assuming nominal operation,we can consider

that the contribution of the voltage terms in the control loop is much slower than

the inductor current contribution.We will choose the K

IA

and K

IB

coefcients to

ensure that the slope of the current contribution to the control signal during the

off MOSFET conduction subinterval (m

2

) is approximately equal to the slope of

the sawtooth signal m

a

(compensating ramp criteria to provide deadbeat control

behaviour and to avoid subharmonics,see chapter 12 of [5].In our case,the slope

of the compensating ramp is m

a

=50 V/ms and K

IA

= K

IB

= 80 mV/A,which gives

a slope of about 60 V/ms for the current contribution (maximum current slope

2

V

R

/L;L=40 mH).Higher values of V

R

could require smaller values for the K

I

terms.It is recommended that 0

5

m

2

m

a

m

2

.

As an intuitive approach to adjust the voltage term coefcients,we have ini-

tially considered several assumptions that provide symmetrical expressions of the

control laws.Namely,PI time-constants have been considered to be equal (T

VP

= T

VN

= T

V

).The proportional coefcients of the direct terms have also been

assumed to be equal (K

VAP

= K

VBN

= K

V

),while the proportional coefcients cor-

responding to the crossed terms have been made zero (K

VAN

= K

VBP

= 0).From

the characteristic polynomial of the system,it can be shown that

0

058

K

V

15

603.Aset of root loci taking K

V

as a family parameter,K

V

(0.5,1,1.5,2),

and varying T

V

continuously between 100 ms and 500 ms shows that all the system

poles could be made real and negative for K

V

1.5.Taking K

V

= 1.5 and T

V

=150

ms,the two dominant poles are smaller than z =

1/T

V

corner f requency

-6.7

374 R.Giraletal.:

krad/s.For a nal value of T

V

=220 ms and K

V

=1,the dominant poles are still

real-negative (corner frequency of about -7.2 krad/s).With the obtained set of pa-

rameters,several PSIMsimulations have been carried out.

Fig.5 shows the simulated waveforms of the output voltages v

P

and -v

N

of

the regulator.The (a) arrows point out the small overshoots that appear at start-up

fromzero initial conditions for the nominal 42 Vinput,3 Ωbalanced load case.The

reference voltage raises from 0 to 15 V in 1 ms.At point (b) there is a step change

in the input voltage that goes from 42 V to 30 V.A +1 ampere step perturbation

in the positive output is applied at t=5 ms (c).Finally,from 7 ms to 7.5 ms,the

reference voltage rises from15 V to 18 V (d).

Fig.5.Simulated output voltages of the regulator.(a) start-up for

nominal conditions.(b) input voltage step change from 42 V to

30 V.(c) unbalanced load change:+1 A step at i

OP

(Fig.4).(d)

reference change from15 V to 18 V.

Fig.6 shows the ripple amplitude for different operating points.In the 2 to 3

ms interval the ripples are in agreement with the expected 83 mVpp in each output

for nominal operation.A detailed exploration of the interval (not shown) reveals

that both output ripple waveforms are in phase and exhibit a peak-to-peak ripple of

83.4 mV.In the interval 3 ms-5 ms,the step change in the input voltage from 42

V to 30 V at 3 ms causes an undershoot of about 150 mV in both v

P

and v

N

.The

duration of the transient is about 600 ms,which is consistent with the dominant

poles (

4 times the time constant).The ripple amplitude in steady state is about

100 mV.The duration of the transients caused by the +1 A step change at 5 ms

(c) is slightly shorter than the corresponding duration at (b).The main effect of

the change is that the load becomes unbalanced and this causes the increase of the

common mode voltage as it can be seen in Fig.7.The unbalance in the loads

breaks the symmetry observed in the transients.

SymmetricalPowerSupplyfor42VAutomotiveApplications 375

Fig.6.Detail of the simulated output wave-

forms of Fig.5 showing ripples.

Fig.7.Common mode voltage between positive

and negative outputs corresponding to Figs.5

and 6.

Fig.8.Detail of the simulated output wave-

forms for K

VAP

=K

VBN

=3,K

VAN

=K

VBP

=

1.

Fig.9.Common mode voltage between positive

and negative outputs corresponding to Fig.8.

Other parameter adjustments are possible.Considering again symmetrical co-

efcients,Figs.8 and 9 show the results corresponding to simulations in which the

K

V

parameters have been adjusted to K

VAP

=K

VBN

=3,K

VAN

=K

VBP

1.All the

results have been slightly improved with these coefcients.

4 Conclusions and Future Works

The PCTITO is a two-input two-output DC-DC switching converter that has been

controlled to provide two symmetrical outputs from a positive input voltage in the

42 V PowerNet automotive standard range (30 - 50 V).Although the main results

have been obtained by means of computer simulations,some theoretical analyses

have been performed.The system has been modelled in open loop.Steady-state

expressions for the state variables and a small signal time-domain averaged model

have been presented.A general full state feedback control strategy yields a system

376 R.Giraletal.:

with symmetrical output voltages with excellent line and load regulation.Good

audiosusceptibility and acceptable response to load changes are also obtained for

two different sets of control coefcients.With balanced loads,the common mode

voltage is completely eliminated and kept very small for unbalanced loads.

Future studies will address some theoretical aspects like the justication of the

control parameters adjustment.Experimental verication will be also carried out.

Acknowledgments

This work was supported by the Spanish Ministerio de Ciencia y Tecnologa under

Grant TIC2000-1019-C02-02.

References

[1] W.Bremer,Standardization of the 42V PowerNet,(Chairman-ISO

TC22/SC3/WG14).In 42-Volt Executive Panel, in SAE World Congress,2002.

[Online].Available:http://www.sae.org/42volt/

[2] Y.Xi and P.Jain,A forward converter topology with independent and precisely regu-

lated multiple outputs, IEEE Trans.on Power Electronics,vol.18,2003.

[3] J.Hamar and I.Nagy,Asymmetrical operation of dual channel resonant DC-DC con-

verters, IEEE Trans.on Power Electronics,vol.18,pp.8394,2003.

[4] A.Ginart,R.Bass,W.Leach,and T.Habetler,Analysis of the class AD audio am-

plier including hysteresis effects, IEEE Trans.on Power Electronics,vol.18,pp.

679685,2003.

[5] R.Erickson and D.Maksimovic,Fundamentals of Power Electronics.Kluwer Aca-

demic Publishers,2001.

[6] E.V.Dijk,H.Spruijt,D.O'Sullivan,and J.Klaassens,PWM-switch modeling of

DC-DC converters, IEEE Trans.on Power Electronics,vol.16,pp.659665,Jan.

1995.

## Comments 0

Log in to post a comment