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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia

Design of a MIMO Controller for a Multimodul

Dc-Dc Converter Based on Particle Swarm Optimized

Neural Network

Ashkan M.Z.Jasour, Mostafa Khazraei, Abdolreza Rahmati

IRAN University of Science and Technology, TEHRAN, IRAN

amjasour@ee.iust.ac.ir, m.khazraei@ee.iust.ac.ir

Abstract— Different kinds of multi-module Dc-Dc converters

have been introduced to obviate demands for different level of

voltage and power in input and output. The suitable control

scheme for this type of converter necessitates equal voltage

sharing for series connected modules and equal current sharing

for the parallel connected modules for all operating conditions

even with existence of dissimilarity in devices and components

used in each module. Such a control scheme can be designed by

means of linear controllers. But in the case of large variations in

the parameters or considerable difference between modules of

converter, linear scheme cannot accomplish equal sharing

correctly. In this paper a MIMO controller scheme based on

artificial neural network (ANN) will be developed to solve this

problem in an input-series and output-parallel (ISOP) Dc-Dc

converter. The proposed MIMO controller is trained using

Particle Swarm Optimization (PSO). Using PSO to train the

ANN based controller, eliminates the need for a prior knowledge

of the system dynamics. The latter merit shows its significant

usefulness when the under study system is a large multi-module

system and consequently the derivation if its dynamic equations

is a tedious and time consuming work. To implement the

proposed controller for the ISOP converter MATLAB software

will be used in this paper.

I. INTRODUCTION

s a vigorous solution to meet power requirements, power

supplies for distributed power application Use

combinations of dc-dc converter modules. An ISOP connected

converter is one of these recently converters. The main control

issues in these modular converters are to equalize the output

current and input-voltage among modules [1]. The mismatch

in some components such as power transformer turns-ratio

and input capacitance of two modules leads to unequal input

voltage sharing and consequently it results in significant

deviation of currents of two parallel modules from each other.

It means that the ISOP type converters are more prone to

unequal output current sharing of modules than any other type

of converter. A new control scheme consists of a simple

current sharing for converter connected in series at the input

side and in parallel at the output side has been proposed in [1].

This proposed scheme ensures sharing of output currents and

input voltage among modules. This scheme has three linear

controllers used in three control loops. But due to the use of

linear controllers, in the case of large variations in unit

parameters, the unequal voltage and current sharing puts

excessive stress on some of the modules and elevate their rate

of failure [2, 3]. Moreover, for large disturbances in input

voltage and load current, linear small-signal models are no

longer valid. On the other hand, to design linear controllers for

the converter, we need to derive small signal equivalent circuit

model. But sometimes the small signal equivalent circuit

model is unknown or in the case of large systems such as a

multi-module converter the mathematical manipulation may

become inconvenient for the circuit designer.

Obviously, because of the above mentioned demerits, in the

case of multi-module converters the linear controller may not

yield satisfactory results. To solve this problem different

nonlinear control systems can be used. But the design and

implementation of nonlinear controllers especially in the case

of multi-module converters is very complicated. Among

nonlinear controllers the fuzzy controllers because of the

easier implementation have been proposed in literature to

control multi-module converters. Control systems consisting

of both linear and fuzzy (fuzzy-linear) controllers have been

proposed in [4,5,6] to improve the large signal performance of

converters with multi-module structures in the case of large

variations in the parameters or considerable difference

between modules of converter. Although in this case the

closed loop system can work at a wider operating point due to

the use of a fuzzy controller, the remained linear controllers

limit the closed loop system to work at considerable wide

operating point. Substituting fuzzy controllers with all the

linear controllers in the control system of multi-module

converter seems to be an alternative. But implementing a

control system consisting of several fuzzy controllers is an

expensive solution. Moreover, due to the digital

implementation of fuzzy controllers, by using such controllers

the speed of closed loop system will be reduced significantly.

Considerable time delays may even lead to instability

conditions. In recent years experts have applied ANN as a

A

1-4244-2405-4/08/$20.00 ©2008 IEEE 224

2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia

faster controller for nonlinear controlling of simple converters

[7,8]. Here in this paper, to avoid mentioned difficulties when

nonlinear controllers such as fuzzy controllers are used, a

different design approach based on ANN is presented. Instead

of designing a control system consisting of several linear

controllers based on the dynamics of the converter, or

substituting the linear controllers with several slow and

expensive nonlinear controllers, an ANN as a MIMO

controller will be designed to control the converter. Such an

ANN controller because of its inherent nonlinear performance

will improve the large signal performance of the ISOP

converter in the case of large variations in the parameters or

considerable dissimilarity between modules of converter

comparing to linear controllers. Moreover, by using PSO for

determining the unknown variables of ANN, there is no need

for dynamic equations of converter. Such a merit shows its

significant usefulness when system is a large multi-module

system and derivation if its dynamic equations are a tedious

and time consuming works. Finally, because of the less

number of calculations and the paralleled structure of

calculations in the ANN control system, the time delay which

is imposed by processor speed limitation will be reduced

comparing to a control system consisting of several nonlinear

controllers (e.g. fuzzy controller).

II. LINEAR CONTROL OF THE ISOP CONNECTED CONVERTER

Fig.1 shows the ISOP connection of two identical Dc-Dc

converters. There are three control loops for each module of

the converter: an individual inner current loop, a common

output voltage loop and an individual input voltage loop. Fig.2

shows the complete control block diagram of the converter.

The three loops in each module should be designed in order

to ensure equal sharing of output load currents and input

voltages. The reference current is produced by output voltage

loop, based on the error in the output voltage. The reference

for input voltage loop is equal to total input voltage divided by

number of modules (here the number of modules is two) [1].

The output signal of input voltage loop is equal to the

difference between the actual input voltage across the

respective converter and mentioned reference voltage. Sum of

the signals from above two loops generate a reference for

inner current loop. Output of inner current loop in each

module of converter is individual duty ratio which makes

output current of each converter track the respective reference.

To design a control loop with linear controllers in

conventional method we need some transfer functions in the

power stage.

To design Gi1,i2 we need bode and phase plot of i^

L1/ d

^

1

(or i^

L2/ d

^

2). The desired transfer function to design output

voltage loop is v^

o/ i^

Lref 1 (or v^

o/ i^

Lref 2 ) and to design Gvin1,vin2

in the input voltage loop v^

in1/i^

Lref 1 (or v^

in2/i^

Lref 2 ) is needed.

Because the control scheme is current mode, the simple type

ΙΙ controller is convenient for both voltage and current loop

compensation. By assuming a crossover frequency of 5 kHz

and a phase margin of 60o the current compensator transfer

function is [9]:

2in

C

2in

R2in

L

1o

L

2o

L

1in

C

1in

R1in

L

1o

C

1

esr

R

2

esr

R

Load

R

in

V

2o

C

2:1 nn

2:1 nn

Fig.1 ISOP connected converter

TABLE I

CONVERTER PARAMETERS

Parameter Value

Output Inductor Lo1, Lo2 100uH

Output capacitance Co1,Co2 300uF

Load Resistance R 1Ώ

Capacitance Resistance Resr1, Resr2 .06 Ώ

Transformers turns ratio(N2/N1) 1

Input series Resistance Rin1,Rin2 .04 Ώ

Input series Inductor Lin1,Lin2 40uH

Input Capacitance Cin1,Cin2 300uF

Switching frequency fs 50kHz

Input Voltage Vin 48 Volt

Output voltage Vo 12 Volt

Fig. 2 Complete control block diagram of the converter

(1)

In order to achieve a crossover frequency of 2 kHz and

a phase margin of 600,Gvois designed as follows:

)

107000

1(

)

8480

1(1149

s

s

s

Gvo

+

+

= (2)

1, 2

1149(1 )

8480

(1 )

107000

ii

s

Gs

s

+

=

+

Gvin1

Gi2

Gvo

Gi1 Module1

Module2

oref

v

2L

i−

1Lref

i

2Lref

i

o

v−

1L

i−

inref

v−

1in

v

inref

v−

2in

vGvin2

225

2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia

To design Gvin1,vin2, controllers in the input voltage loop,

usually considering an integrator with a suitable gain at high

frequencies is enough to guarantee the error correction in the

loop. The transfer function of such compensator can be

written as:

2,1 vinvin

G=s

k (3)

Selection of K for this compensator is a compromise

between correction pace of input voltages deviation and

momentarily amount of switch current of each module in the

case of dissimilarity in components of the converter. That is, a

larger K yields faster correction of input voltage deviation

while it results in momentarily larger switch current of each

module. In fact, the actual choice of depends on the expected

tolerances in the input capacitor values, the characteristic

impedance of the input LC filter and the magnitude of

disturbance expected in the total input voltage [10]. Here in

this work the value 15020 was selected for K. This value was

found to be relatively suitable in order to make the control

scheme correct the deviation of input voltages of each module

as fast as possible while both switches in both modules bear a

reasonable amount of current.

III. DESIGN OF MIMO CONTROLLER BASED ON PARTICLE

SWARM OPTIMIZED NEURAL NETWORK

In this section a neural network controller with six inputs

and two outputs using PSO will be designed to regulate the

output voltage and to ensure the equal sharing of output

currents and input voltages among modules. Fig.3 and Fig.4.

respectively show the block diagram and the structure of the

proposed neural network controller for the ISOP converter.

Where in Fig.3,

refoutVo VVe −= (4)

21 outoutI IIe out −= (5)

21 ininV VVe in −= (6)

And Iout1,Vin1 and Iout2,Vin2 are respectively the output

currents and input voltages of the first and the second module.

Also, ce represents the change of each mentioned error. The

developed neural network controller consists of three layers,

with six neuron in the input layer. As inputs, the actual and

change of errors are fed into the network. The hidden layer

consists of 10 neurons, while the output layer consists of 2

neurons which the output of each of these neurons is the

desired control signal. Here in this work, the desired control

signal for each module is the needed duty cycle of each

module that guarantees the equal sharing of input voltages and

output currents between modules and provides a good

regulation for output voltage. The outputs of the network are

obtained as follows:

)(

10

1

0

∑

=

+=

j

kjkjkk ZyZfO (7)

)(

6

1

0

∑

=

+=

i

jijijj WxWfy (8)

Where Ok for k=1,2 is the output of net, yj for j=1,…,10 is

the output of hidden neurons, for is the input of network,

Wji is the weight between ith and jth neuron in the input layer

and hidden layer respectively, Zkj is the weight between j

th

and kth neuron in the hidden layer and output layer

respectively. W0j is bias of jth neuron in hidden layer and Z0k

is bias of kth neuron in output layer. fj and fk are the transfer

function of jth and kth neuron in hidden layer and output layer

respectively. The transfer functions of hidden layer and output

layer respectively are tansig and saturation.

out

I

e

o

V

e

o

V

ce

out

I

ce

in

V

e

in

V

ce

1d

2d

Fig.3 Block diagram of the proposed neural network

controller for the ISOP converter

Fig.4 The structure of ANN controller for the ISOP converter

To design a suitable controller the values for weights and

biases in ANN must be computed in order to minimize the

cost function J which can be described as follows:

∑

=

=

++=

sim

inouto

Tt

t

VIV eMeMeMJ

0

2

3

2

2

2

1})()()({ (9)

Parameters M1, M2 and M3 are weighting factors that can be

defined due to the specification of design. For example, if the

5

x

2

x

3

x

4

x

6

x

1

x

2

O

1

O

226

switches and other components of the converter do not have

high voltage and current rate and as a result, fast convergence

of input voltages and inductor currents are needed, the

designer should choose high value for M2 and M3 in order to

navigate the optimization of controller's parameters, toward

obtaining better convergence in input voltages and output

currents. According to the number of layers and neurons in

ANN, the number of weight and bias variables that must be

determined is 92.

Usually the back-propagation (BP) algorithm which applies

the gradient descent method is used for training the ANN. But

by using the gradient descent method, the neural network is

easily trapped to local optimum, which leads to descent of

global performance. On the other hand, the gradient descent

method needs dynamic equations which represent the system

model to train the ANN. But when the under study system is a

large multi-module system for example the ISOP converter

which is studied in this paper, the derivation of dynamic

equations needs complicated calculations and is a tedious and

time consuming work. As an alternative for the gradient

descent method, famous optimization techniques can be used

to optimize the parameters of the ANN controller (including

the weights and biases) such as genetic algorithm (GA) or

particle Swarm Optimization technique. Such optimization

techniques do not need the prior knowledge of the system

dynamics to train the ANN based controller [11,12]. On

account of the fact that the PSO has a higher velocity of

convergence, this algorithm is used in this paper in order to

expedite the simulation process.

IV. PARTICLE SWARM OPTIMIZATION

The thought process behind the PSO was inspired by the

social behaviour of animals, such as bird flocking [13]. PSO

begins with a random population of solutions. Solutions for

optimization problem are called particles which for a D-

dimensional problem, each particle contains the D variable

values and denoted as Xi = [Xi1,Xi2,…,XiD]. Each particle

moves about the cost surface with a velocity (V). At each

iteration, the particles update their velocities and positions (X)

based on the local and global best solutions. Each particle

adjust its velocity using its previous best position (Xi

localbest)

and the best position of particles (Xglobalbest) and then the

velocity is used to compute the new position of particle. The

updates rules at iteration k are as follows:

(k))X -(X r

(k))X -(X r (k)V 1)(kV

i22

ii11ii

globalbest

localbest

××+

××+×=+

α

αω

(10)

1)k (V (k)X )1k(X ii i ++=+ (11)

Where i=1,..,N, N is the swarm size, r1, r2 are independent

uniform random numbers, α1,α2 are learning factors which are

assumed 1 and 3 respectively in this paper and

ω

= (max iteration – iteration) / ( iteration ) is inertia factor.

The optimization procedure which has been described in

Eq.(10) and Eq.(11) must be repeated until a sufficiently good

fitness considering equation Eq. (9) is achieved.

In the application of training the ANN controller for ISOP

converter, the dimension of each particle is 92 and contains

the weights and biases of ANN that must be determined.

The optimization procedure of ANN controller is done

using MATLAB software. To expedite the training of neural

network in SIMULINK the large signal average model of

ISOP converter is obtained by replacing the PWM switch of

each converter by its ideal transformer model, PWM1 and

PWM2. The turns ratios of these ideal transformers are

dynamically varying and are equal to the instantaneous duty

ratios, d1 and d2 respectively. During the training, conditions

of circuit are considered in both nominal and critical situation

in order to design the most possible robust controllers. To

obtain this situation for the ISOP connected converter circuit,

the turns ratio of transformer of modules are purposely chosen

to be very different. Moreover, in the interval simulation

[0,Tsim] where Tsim=.015s, sudden variations of input voltage

and load current are considered.

V. SIMULATION RESULTS AND DISCUSSION

To evaluate the validity of designed ANN controller the

ISOP converter in Fig.1 is simulated using MATLAB

SIMULINK. In this section the large signal performance of

the ISOP connected converter with both linear scheme

controllers and ANN controller are compared.

Fig. 5 shows respectively the steady state output voltage of

the ISOP converter with linear control method and ANN

control method for a sudden 14 volt decrease in the input

voltage at 7ms and a sudden 6A decrease in load current at

11ms. It is clear that linear control method because of its

inherent high speed performance rejects the line and load

disturbance faster than ANN control method. Moreover, the

linear control exhibit less steady state error as shown in Fig. 5.

But as it will be shown ANN control shows its high ability on

equalizing input voltages and output currents of modules in

spite of large differences among them. Clearly, because no

disparity was considered between modules in this step, input

voltage and output current sharing are maintained even during

transient condition and the input voltages and output currents

of two modules in both control method are completely

identical. For the second step other disparities are considered

for ISOP converter in Fig.1, as follows:

2.1)2(,1)1(,380,300 122121 ==== TNNTNNFCFC inin

μ

μ

(12)

Where N1/N2 (T1) and N2/N1 (T2) respectively represent the

turns ratio of transformers in the first and second module. Fig.

6 and Fig. 7, respectively show the input voltages of two

paralleled modules for two control methods for a sudden 14

volt decrease in the input voltage at 7ms and a sudden 6A

decrease in load current at 11ms. Fig. 8 and Fig. 9,

respectively show output currents of two paralleled modules

with the same load and line step. As seen, the convergence in

the input voltages and output currents of two paralleled

modules for ANN controller takes place sooner than the linear

one. Moreover, in the case of linear method during the

227

0 0.005 0.01 0.015

10

15

20

25

30

35

t (s)

Input voltages (Volt)

module1

module2

00.005 0.01 0.015

-15

-10

-5

0

5

10

15

20

25

30

t

(s)

Output Currents (Amp)

module1

module2

transient period the individual input voltages and output

currents deviate significantly from each other and respectively

one of the modules sustains considerable amount of voltage

and current that creates excessive stress on the module and

increases its rate of failure [4].

Fig.5 Converter output voltage with sudden 14 volt decrease in input

voltage and sudden 6A decrease in load current for both linear

control and ANN control

Fig.6 Input voltages of modules with linear control for sudden 14

volt decrease in input voltage and sudden 6Adecrease in load

current considering the conditions in Eq. (12)

Fig.7 Input voltages of modules with ANN control for sudden 14 volt

decrease in input voltage and sudden 6A decrease in load current

considering the conditions in Eq. (12)

Fig.8 Output currents of modules with linear control for sudden 14

volt decrease in input voltage and sudden 6A decrease in

load current considering the conditions in Eq. (12)

Fig.9 Output currents of modules with ANN control for sudden 14

volt decrease in input voltage and sudden 6A decrease in

load current considering the conditions in Eq. (12)

Fig.10 Converter output voltage in transient for both linear control

and ANN control considering the conditions in Eq. (13)

0 0.005 0.01 0.015

10

15

20

25

30

35

t (s)

Input voltages (Volt)

module1

module2

5 6 7 8 9 10 11 12 13 14 15

x 10-3

10.5

11

11.5

12

12.5

13

13.5

t (s)

A

NN controlle

r

Linear controlle

r

Output Voltages (Volt)

00.005 0.01 0.015

-15

-10

-5

0

5

10

15

20

25

30

t (s)

Output Currents (Amp)

module1

module2

0 1 2 3 4 5 6 7 8 9

x 10-3

-5

0

5

10

15

20

25

t (s)

A

NN controlle

r

Linear controller

Output voltages (Volt)

228

Fig.11 Input voltages of modules in transient with linear control

considering the conditions in Eq. (13)

To check the statues of output voltage regulation in the case of

dissimilarity between modules, for the third step larger

disparities are considered for ISOP converter in Fig.1, as

follows:

2.1)2(,1)1(,100,160 122121 ==== TNNTNNFLFL outout

μ

μ

(13)

Fig.10, shows the output voltage transient response of ISOP

converter considering the conditions in Eq. (13). Although the

rise-time of response with linear controller is less, the

response of the converter with linear controller shows

instability and oscillation. While the output voltage of

converter with ANN controller is well regulated. Fig. 11, and

Fig. 12, respectively shows the input voltages of two

paralleled modules for both methods in transient. Fig. 13, and

Fig. 14, respectively shows output currents of two paralleled

modules in the same transient period. Because the considered

dissimilarity in the third step is more than the second step,

comparing the degree of convergence in the input voltages

and output currents of two paralleled modules for ANN

controller and linear controller in the third step can prove the

ability of ANN controller better.

Fig.12 Input voltages of modules in transient with ANN control

considering the conditions in Eq. (13)

Fig.13 Output currents of modules in transient with linear control

considering the conditions in (13)

Fig.14 Output currents of modules in transient with ANN control

considering the conditions in Eq. (13)

VI. CONCLUSION

A MIMO controller based on ANN was designed in this

paper to control an ISOP converter. PSO technique was used

to train the ANN controller. The simulation results proved the

validity of the MIMO controller performance. The merits of

using this new control method are the elimination of need for

tedious and time consuming small signal analysis of multi-

module converters for designing the linear control system and

improvement in large signal performance of ISOP converter in

the case of dissimilarity in parameters of each modules of the

converter. Moreover, using PSO instead of gradient descent

method for training the ANN, not only make us free from

derivation of dynamic equations but also by using PSO the

neural network no longer is trapped to local optimum points,

which leads to descent of global performance.

0 1 2 3 4 5 6 7 8 9

x 10 -3

-30

-20

-10

0

10

20

30

40

t (s)

Output currents (Amp)

module1

module2

0 1 2 3 4 5 6 7 8 9

x 10-3

-30

-20

-10

0

10

20

30

40

t (s)

Output currents (Amp)

module1

module2

229

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