Download Proceedings of the 15th IEEE International Symposium

Proceedings of the 15th IEEE International Symposium
on Intelligent Control (ISIC 2000)
Rio, Patras, GREECE
17-19 July, 2000
AN APPLICATION OF A NEURAL PREDICTIVE CONTROLLER IN
BOOST CONVERTER INPUT CURRENT CONTROL
IVAN PETROVIƆ, MIROSLAV BARIƆ, ANTE MAGZAN‡, NEDJELJKO PERIƆ
†University of Zagreb, Faculty of Electrical Engineering and Computing, Department of
Automatic Control and Computer Engineering in Automation, Unska 3, Zagreb, CROATIA,
[email protected], [email protected], [email protected]
‡ Polytechnics College of Zagreb, College of Electrical Engineering, Konavoska 2, Zagreb,
CROATIA, [email protected]
Abstract. An application of a non-linear predictive controller in the cascade control
structure of an boost converter is investigated. The neuro-predictive controller is realized
as a non-linear optimizer, using Levenberg-Marquardt unconstrained optimization
procedure. For the prediction of future process response two MLP neural networks are
used. One network is used for modeling the converter dynamics and the other one for an
on-line estimation of the converter’s input voltage. This structure ensures good
performance in all operating regions and inherent compensation of ripples in converter’s
input current, caused by variations of the input voltage. Advantages of the proposed
control structure are demonstrated through the experimental comparison to a linear GPC
with manually adjusted feed forward compensator.
Key Words. boost converter, input current ripples compensation, MLP neural networks,
predictive control.
1.INTRODUCTION
Converters used for supplying consumers with
changeable voltage and frequency represent a load
for the supply network (ac or dc) with current
harmonics, which produce undesired electromagnetic disturbances and additional parasitic
effects. Electromagnetic disturbances are particularly
undesired in a supply network that is in conductive
connection or near devices sensible to disturbances,
such as telecommunication and/or signaling safety
devices. The typical supply network with high
demands on the permitted level of generated
disturbances is the railway electric supply network.
This is the reason why the International Railways
Union regulations (UIC) require that high level
requirements should be imposed on converters by
means of which the allowed disturbance levels in this
supply network are determined [1]. The European
railway supply network is specific due to two types
(ac and dc) and four levels of supply voltage and has
specific additional requirements on converters. One
of the important requirements when converter
operates on a dc network (1500 V dc; 3000 V dc) is
that the input impedance has to be higher than the
impedance permitted by UIC regulations in the
frequency range from 50 Hz to 100 kHz. The other
requirement relating to the case when the converter
operates on an ac network (25 kV ac, 50 Hz; 15 kV
ac, 16 2/3 Hz) is the power factor greater than 0.95 in
the input voltage range between 80 % and 120 % of
the rated value. Boost converter is commonly used
converter structure in these applications. It serves as
an active filter at the input of the four-system
converter [2, 3]. To meet above stated highdemanding requirements special attention should be
paid to the converter control system.
The
conventional solution is to use a PI controller. PI
controller doesn’t give satisfactory performances in
all operating regions, due to the non-linear
characteristic of the boost converter. Better results
could be achieved if the Generalized Predictive
Controller (GPC) is applied, because of its robustness
to process parameter variations [5]. Neither PI nor
GPC can provide satisfactory reduction of the
converter input current ripples (causing electromagnetic disturbances) unless and additional feed
forward compensator is applied [4,5]. The design of
this compensator is not an easy task and should be
done carefully. It requires quite a lot of manual
adjustments, because any amplitude and/or phase
shift between the compensation signal and the actual
current ripples causes additional ripples.
With the purpose to increase the performances of the
input current control loop and to avoid the difficulties
of controller and compensator adjustments, we have
been investigated the usage of the neural networks in
the design of the input current predictive controller.
The paper is organized as follows. Section 2
gives more detailed description of boost converter
control structure. Implementation of the NPC in the
control of converter’s input current is described in
Section 3. Experimental results are given is Section 4,
where the developed controller is compared to a
linear GPC.
2. CONTROL SYSTEM STRUCTURE
Generally accepted structure of the control system is
one of the cascade type, with converter input current
control loop as the inner loop and converter output
voltage loop as the outer, superimposed control loop
(Fig. 1) [4]. The control of input current is realized
by means of an input current controller Rii, which
provides input voltage to the high frequency pulse
width modulator (PWM) that controls the states of
the power electronic switch V1 (Isolated Gate
Bipolar Transistor, IGBT). Since it is necessary to
stabilize the output voltage of the boost converter at a
constant value, while varying load or input voltage,
the output voltage controller Ruo is superimposed to
the input current controller Rii, providing the
reference value for the input current controller.
In the functional block diagram of boost
converter control (Fig. 1.) the dc-ac switch marks the
control structure change when the converter works on
a dc network or an ac network. The measured
instantaneous value of the input voltage uim serves for
the compensation of input voltage ripple influence on
input current (switch on dc) when boost converter
operates on a dc network. Moreover, it serves for
generation of input current reference value (switch on
ac) when boost converter operates on an ac network.
In the presented control structure the measured
filtered input voltage performs function of input
current feed forward control when the converter
operated on both a dc and an ac supply network.
More detail description is given in [5].
Li
ui
V1
C0
ii
uO
-- --PWM
up
Rii
uim
dc
ac
ui +
comp.
+
Input
current
controller
iim
-
+i
ir
x
Ruo
Output
voltage
controller
iimax
+
uom
Filter
uor
Filter
CONTROL COMPUTER
Fig. 1. Functional block diagram of boost converter
control. ( Ruo - output voltage controller; uor output voltage reference value; uom - output voltage
measured value; Rii - input current controller; iimax input current maximum value; iir - input current
reference value; iim - input current measured value;
uim - input voltage measured value; up – input
voltage to the PWM block).
In order to control the converter-input impedance,
when the converter operates on a dc supply network
or the input power factor when converter operates on
an ac supply network, it is necessary to realize a fast
input current control loop. In research of boost
converter input current control algorithms
conventional and modern algorithms have been
analyzed [4].
When the converter operates on a dc network
the boost converter input voltage contains a high
alternating component. The frequency of this
alternating component is proportional to the
frequency of an ac voltage from that is dc voltage
obtained using a power electronic rectifier. Variations
of the input voltage cause the high ripples in input
current that should be eliminated or reduced to the
smallest amount possible.
As
mentioned
in
the
introduction,
conventional control structures (PI) and more
advanced ones (GPC) require additional feed forward
compensator in order to successfully reduce ripples
of the input current. This compensator usually
requires a lot of manual adjustment that must be
carried out every time when the frequency or the
amplitude of the input voltage is changed. To avoid
this and to achieve good controller performance in all
operating regions an advanced control strategy based
on neuro-predictive controller is investigated.
3. DESIGN OF THE NEURO-PREDICTIVE
CONTROLLER
The structure of the proposed neuro-predictive
controller is given in Figure 2.
NN1
uim(k)
Input
voltage
In each sample k a sequence of future control
signals up is obtained by the minimization of the
criterion function:
û im
iˆi ( k  N 1 ),, iˆi ( k  N 2 )
N2
NN2
( k )   Q(i ) yr ( k  i )  ii ( k  i ) 
2
i  N1
Nc
Input
current
reference
iir
Optimization
procedure
up'(k)
upmax
up(k)
upmin
Boost
converter
p
( k  i  1)  u p ( k  i  2)
(2)
i 1
Fig. 2. Neuro-predictive controller for input current
control
The developed controller consists of two multi-layer
perceptron (MLP) neural networks and of the
nonlinear optimizer.
Neural network NN1 (Fig. 2) works as an online estimator of the converter’s input voltage and it
is used for the prediction of its future values needed
by the neural network NN2. As an adaptation
algorithm
recursive
back-propagation
with
momentum is used.
Neural network NN2 is used for modeling and
prediction of the non-linear dynamics of the boost
converter. Input signals to the process are input
voltage to the PWM block up (control signal) and
measured value of the input voltage uim, while the
output signal is measured value of the input current
iim (Fig. 2). The process is modeled by the following
nonlinear discrete-time difference equation:
iim ( k  1)  f [iim ( k ),, iim ( k  n1  1);
u p ( k ),, u p ( k  n2  1); ,
 R(i ) u
iim(k)
,
2
(1)
uim ( k ),, uim ( k  n3  1)]
where: k - is discrete time step; f - nonlinear map; n1,
n2, n3 – number of past values of the corresponding
variables.
The output of the NN2 is used in the calculation of
the control signal. By introducing measured and
predicted values of the converter’s input voltage in
the prediction of the input current, future input
current ripples caused by the input voltage variations
can also be anticipated. In this way the compensation
of the disturbances is included in the control action,
i.e. the compensator and the input current controller
are joined.
Both neural networks (NN1 and NN2) are
initially trained off-line as NARX models [9]. NARX
model predicts the future value of the input current
one step ahead and is used during the initial training
of networks. When operating, networks are used in
the so-called NOE configuration [9] that enables
multiple step ahead predictions.
NN1 and NN2 are realized as two-layered
MLPs with tansig activation function in the hidden
layer. An efficient Newton-type algorithm with
implicit regularization is employed to initially adjust
network weights [7].
N1 and N2 denote the first and the second prediction
horizon, and Nc the control horizon, Q and R are
sequences of the weighting factors, ii is a sequence of
model outputs for the current control sequence up, yr
denotes the desired, referent response – the, so called,
reference trajectory, defined as:
yr ( k  i )    iir  (1   )  yr ( k  i  1) ,
(3)
where   [0,1].
By minimizing (2) an optimal control sequence
up=[up(k),...,up(k+N2-N1+1)] is obtained, from which
the first element is used as a process input. At the
next time step, ii , yr, and up are shifted by one step
and the complete procedure is repeated. This strategy
is the well-known “receding horizon” control strategy
[9], [10].
The first term in (2) is a measure of the
distance between the predicted process output y and
the reference trajectory yr. A non-linear model,
represented by a neural network, is used for
predicting outputs of the process. If the model is
accurate, minimization of (2) makes the process track
the reference trajectory. The second term in (2)
penalizes excessive changes of the controller output.
At the same time, minimizing this part of the criterion
function slows the response of the closed-loop system
down and increases the tracking error. A trade-off
between these two objectives must be found by
properly choosing the weighting factors Q and R.
The core of the non-linear predictive controller is the
optimization algorithm used for the minimization of
the criterion function (2). In this paper LevenbergMarquardt unconstrained optimization algorithm is
used to obtain the controller output. Since the boost
converter control signal has its minimum and
maximum value that should not be exceeded, a
modification of the predictive controller structure is
made (see Fig. 2).
The process is considered to have a limiter in
the form of a continuous differentiable function at its
input, which transforms the unlimited controller
output
u'p to the process input up within the specified
limits, up[upmin, upmax]. We used the sigmoid
function:
,
(4)
up 
F
1  expG
Hu
up max  up min
F
G
H
u
 up min
g
 u'p  p max

u
2
p max
p min
IJIJ u
KK
p min
where g is the coefficient that determines the slope of
the limiter. The same limiter is attached to the model
input, as shown in Fig. 2. No constraints on the
variable u p exist and its optimal value can be
obtained by using an unconstrained optimization
algorithm, giving at the same time optimal value of
the actual control variable up within the specified
limits. The detailed description of the algorithm is
given in [9].
4. EXPERIMENTAL RESULTS
Experimental investigations of the performances of
the neuro-predictive controller were done on a
laboratory model of the boost converter (power 2.5
kW) with IGBT switch (Fig. 3). The control system
has
been
implemented
using
MATLAB/SIMULINK® program package and its
Real-Time Workshop. The experiments were
conducted separately for dc and for ac supply
networks.
varied
manually in random fashion via
autotransformer. 2N values of up and iim had been
collected during the experiment. Then the neural
network NN2 (Fig. 2) was trained on the first half of
data, while the second half of data were used for the
regularization and validation purposes [8]. The MLP
network with one hidden layer with 10 neurons
(tansig activation functions) was used. Input vector to
the neural network NN2 was [iim(k), iim(k-1), uim(k),
uim(k), up(k)]. Network NN1 was initially trained to
approximate full wave rectified sinusoidal input
10 pt
voltage. A two-layered MLP network with 5 tansig
neurons in the input layer is used. During the
operation of the controller, the network continues to
adapt itself using simple recursive back-propagation
algorithm in order to catch possible amplitude and/or
frequency changes of the input voltage signal.
A comparison to the linear Generalized
Predictive Controller is made. The results obtained
from the laboratory model of the boost converter are
given in Figures 4-6.
Fig. 4. The response to set point changes of the GPC
without feed forward compensator
Fig. 3. Laboratory model of the boost converter.
a) Boost converter supplied from the dc network
The analysis of input current control loop, when the
converter operates on a dc network has been carried
out on a boost converter physical model with Li=84
mH input inductor inductance and C0=3.75 mF output
condenser capacitance. The boost converter is
supplied by variable voltage ui obtained from
autotransformer connected to single-phase network of
220 V, 50 Hz. With regard to full wave rectified
network voltage, the boost converter input voltage
contains a high alternating component with a
frequency of 100 Hz. The neuro-predictive controller
is designed on the basis of identification experiments.
In the identification experiment the process
has been excited by the Band Limited White Noise
(BLWN) signal up while the input voltage ui has been
Fig. 5. The response to set point changes of the GPC
with feed forward compensator
The same neural controller was used as in the first
experiment when boost converter had been supplied
from the dc network. Fig. 7. and Fig. 8. show input
current step responses obtained on the laboratory
model of boost converter. It can be concluded that the
NPC provides good tracking performance of the
current loop, which implies high input power factor of
the converter.
20
Reference and measured value [A]
18
16
14
12
10
8
6
4
2
0
5. CONCLUSION
0
1
2
3
4
5
time [s]
Fig. 6. The response to set poin change of the boost
converter controlled by NPC
It can be seen that neuro-predictive controller
successfully compensates input current ripples. The
results obtained by the NPC are better than these
obtained by the GPC with feed forward compensator.
The feed forward compensator has been adjusted
manually for the specific operating range of the
converter and its performance decreases outside this
region due to its linearity.
b) Boost converter supplied from the ac network
In order to provide high power factor, it is necessary
to ensure higher active power, i.e. it is necessary to
ensure phase angle between input voltage and input
current as close to zero as possible for all voltage and
current harmonics starting from the fundamental one.
The use of neuro-predictive controllers for the control
of the input current of boost converter has been
investigated. The investigation of the control system
has been carried out for the cases when the converter
is supplied from a dc network and from an ac network.
The obtained results are very satisfactory in both
cases. Besides, it is much easier to adjust the neuropredictive controller than the PI controller or GPC
controller.
6. REFERENCES
[1]
[2]
3
Reference and measured value [A]
2.5
[3]
2
1.5
1
0.5
0
0.98
0.985
0.99
0.995
1
time [s]
1.005
1.01
1.015
1.02
[4]
Fig. 7. Response to positive step in the AC operating
mode
Reference and measured value [A]
3
[5]
2.5
2
1.5
1
[6]
0.5
0
1.485
1.49
1.495
1.5
time [s]
1.505
1.51
1.515
Fig. 8. Response to positive step in the AC operating
mode
[7]
UIC-Kodex, 550 VE (1995). Elektrische
Energieversorgungseinrichtungen für Wagen
der Reisezugwagenbauart, 9. Ausgabe vom
01.01.1995, Bureau Central de UIC, Paris,
1995.
Lai, J-S., Hurst, D., Key, T. (1991). SwitchMode Power Supply Power Factor
Improvement via Harmonic Elimination
Methods, Proceedings of PESC, pp. 415-422,
1991.
Magzan, A., Rajković B., Perić, N. (1998).
Research into possibilities to increase input
impedance of voltage and frequency converter
fed from DC network, Proceedings of 10th
International Conference on Electrical Drives
and Power Electronics, pp. 86-91, Dubrovnik,
Croatia.
Magzan, A. (1999). Algorithms and Structures
of Power Transistor Converters Control Fed
from Single Phase Network, Ph.D. thesis,
Faculty of Electrical Engineering and
Computing, Department of Control and
Computing Engineering in Automation,
Zagreb (in Croatian).
Magzan, A., Perić, N., Petrović, I. (1999).
Generalized Predictive Controller Applied in
Boost Converter Input Current Control, CDRom proceedings of the 8th European
Conference on Power Electronics and
Applications - EPE’99, Paper # 537,
Lausanne, Switzerland.
Kung, S. Y. (1993). Digital Neural Networks.
PTR Prentice Hall, Englewood Cliffs, New
Jersey.
Petrović, I., Baotić, M., Perić, N. (1998). An
Efficient Newton-type learning Algorithm for
MLP Neural Networks, Proceedings od the
International ICSC/IFAC Symposium on
[8]
[9]
[10]
Neural Computation – NC’98, pp. 551-557,
Vienna, Austria.
Petrović, I., Baotić, M., Perić, N.
Regularization and validation of neural
network models of nonlinear systems,
Elektrotechnik & Informationtechnik, 1/2000,
pp. 24-31, Springer-Verlag, Vienna, Austria.
I. Petrović et. al. (1999) A Neuro-Predicitve
Controller
for
Industrial
Processes,
Computational Intelligence for Modelling,
Control and Automation, IOS Press, 1999.
D.G.
Sbarbaro
Hofer,
Connectionist
Feedforward Networks for Control of
Nonlinear Systems, Ph.D. thesis, The Faculty
of Engineering of Glasgow University, 1992.