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Design of a MIMO Controller for a Multimodul Dc-Dc Converter Based on Particle Swarm Optimized Neural Network

Authors:

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.
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
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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
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
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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
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
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
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
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)
NN controlle
Linear controller
Output voltages (Volt)
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
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
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2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
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This paper studies the open problem of reduced- and fixed-order Hα synthesis. Often, this non-convex constraint is tackled with iterative convex optimisation procedure over LMI constraints. In this paper, an evolutionary approach is proposed such that the trial and error approach involved in LMI techniques might be overcome. The order of the controller is optimised as a multiobjective problem over a set of controller structures, Hα, and time-domain specifications. Numerical results are presented with its counterpart the LMI procedure design, that show the advantage of investigating the Pareto optimal set resulting from the design procedure proposed.
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Genetic Algorithms (GAs) are used in a set of covariance based optimum input signal algorithms using a proposed architecture suitable for on-line system identification. The optimal signals are computed recursively using a predictive filter. The relationships among these algorithms are investigated and compared based on a set of simulations. In addition, a nested GA is proposed for intelligent LQR controller design. The GAs are used to find the minimum distance to uncontrollability of a given system and to maximize that minimum distance by finding the optimal coefficients in the weighting matrices of the LQR controller. Copyright © 2005 IFAC
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This paper studies the open problem of reduced- and fixed-order H∞ synthesis. Often, this non-convex constraint is tackled with iterative convex optimisation procedure over LMI constraints. In this paper, an evolutionary approach is proposed such that the trial and error approach involved in LMI techniques might be overcome. The order of the controller is optimised as a multiobjective problem over a set of controller structures, H∞, and time-domain specifications. Numerical results are presented with its counterpart the LMI procedure design, that show the advantage of investigating the Pareto optimal set resulting from the design procedure proposed. Copyright © 2005 IFAC
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