BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
Publicat de
Universitatea Tehnică „Gheorghe Asachi” din Iaşi
Tomul LV (LIX), Fasc. 4, 2009
Secţia
AUTOMATICĂ şi CALCULATOARE
APPLICATION OF NEURO-PREDICTIVE APPROACH FOR
DISTURBANCE REJECTION IN A STEAM DRUM BOILER
BY
CRISTINA BUDACIU
Abstract. In this paper a neuro-predictive method is proposed in order to control
the water level in the steam drum boiler system being in use at a Power Plant of Iaşi,
Romania. The steam boiler provides thermal and electrical power and it works under
complex technology in order to satisfy numerous technical, security and economical
requirements. A nonlinear dynamic simulator for the proposed steam drum boiler was
used in order to build up the neuro-predictive structure. Based on the data taken from the
simulator, the adopted strategy was tested and simulation results are given.
Key words: steam drum boiler, neural model, neuro-predictive strategy, drum level
control, steam flow disturbance.
2000 Mathematics Subject Classification: 93C10, 93C40, 93C83.
1. Introduction
Process control is an efficient expression of improving the operation of
a process, the productivity of a plant, and the quality of products. In Power
Plant systems, even a small improvement in the operation of a process can have
great economic and environmental influences. As there is no universal best
solution that would apply to all control problems, knowledge of different model
structures and alternative methods can be used to offer advice on the choice of
the most suitable technique for a specific application. According with this idea,
the paper proposes a solution for controlling the water level in a steam drum
boiler system. The drum boiler being a complex and dangerous component of
the power plant offers nonlinearities and non-minimum phase response and
therefore needs carefully choice of a control strategy. Although the power plant
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Cristina Budaciu
models are very complex and are suitable for simulators, they are of little
interest for different control strategies because of their complexity. Such
particularly models can be found in [1],…,[4]. The nonlinearity of a steam drum
boiler-turbine unit was analyzed in [5] and [6], using a nonlinear state space
reduced model and a multivariable controller designed via loop-shaping H∞
approach. An output tracking control system for improving the load-following
capability of boiler-turbine units has been developed in [7]. A suitable
multivariable model is derived in [8] for designing a life extending controller.
For a typical nonlinear drum boiler-turbine unit model in [9], the feedback
linearization theory is used to deduce a pseudo-linear system of the model for
implementing a two-degree of freedom control structure.
In the last decade many researchers concentrates their work towards
identification and adaptive control using neural networks due to the
computational ability and universality. Moreover, little knowledge about the
problems specifications is required. Therefore a very complex system model can
be replaced with a neural network model having a known structure, but
containing a number of unknown parameters such as weights and biases.
The use of neural networks for nonlinear drum boiler process modeling
and identification is justified by their capability to approximate unknown nonlinear systems. In [10], a recurrent neural network is used in the form of a
multistep-ahead predictor to model the drum level process dynamics. For the
drum level process, a NNARMAX (neural nonlinear ARMAX) model was
presented in [11] and employed to develop a neuro predictive tuner for
optimizing the drum level controller. Others neural based models are used for
modeling a drum boiler–turbine–generator unit using physical principles and
different control strategies for level control are found in [12],…,[15].
This paper proceeds from [11] and expands the neuro-predictive
method to the case when the nonlinear system – the steam drum boiler is
affected by steam flow disturbances. The controller design uses a neural
network to model the nonlinear steam drum boiler system. Based on the neural
model, the process output prediction will be achieved considering a set of
command and disturbance values which act on the process. The presence of the
load disturbance, assumed to be known, influences the process parameters,
these changing once disturbance modifies. Therefore, the controller should
compensate the variations of the process dynamics by adapting its parameters.
By the minimization of the predicted error calculated through the prediction
horizon the controller tuning parameters are obtained.
The paper is organized as follows: Section 2 presents the description of
the steam drum boiler system and the neural model obtained; in Section 3 the
proposed solution for drum level control based on neuro-predictive approach is
discussed in detail and some simulation results are performed, and Section 4
concludes the paper.
Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009
11
2. The Neural Model of the Steam Drum Boiler
The industrial process analyzed in this paper is a steam drum boiler
system which ensures the steam flow to the industrial consumers. Based on the
nonlinear mathematical model of the plant, the data set for neural network test
was achieved from the simulator designed in [10]. The data set for training the
neural network from the boiler simulator are utilized to estimate the neural
model of the steam boiler. The main objectives of the drum boiler system are to
produce steam and to ensure safety operational functionality. In order to
understand the steam boiler dynamics, some basic information about the process
description is given as follows.
In Fig. 1 it is illustrated a schematic structure for a steam generation
system, considering the main subsystems: the risers - downcomers, the steam
drum and the superheater. It is worth mentioning that the complete system is
more complicated than shown in Fig.1. A complete description of the system
and the suitable mathematical model which includes the main parts of the boiler
using the characteristics for risers, downcomers and for the superheater can be
found in [2], [10].
Qir
We, he
L
RisersDowncomers
Wd
Drum
Wr
Wv Superheater Ws
Pv
Fig. 1 − The Drum, Risers-Downcomers and the Superheater block diagram.
Fig. 1 shows the interconnections between the modules mentioned
above: the Drum, the Risers-Downcomers assembly and the Superheater
subsystem. The Risers-Downcomers module has a principal input variable, the
heat energy Qir provided from combustion conversion of fuel chemical energy
and some variables incoming from the Drum outputs. The Drum module has
some input variables, the feed water flow We with the feed water enthalpy he
and the variable incoming in the drum from the Risers - Downcomers
subsystem. Wr is the liquid - vapour mixture mass flow from the Risers Downcomers subsystem The main output variables are the drum water level L,
steam pressure in the drum Pv and the water flow through downcomers Wd. The
superheater assures the steam flow quantity Ws. to the consumer.
In order to implement the neuro-predictive strategy, the neural model of
the plant based on the real plant data must to be developed.
The model of the proposed steam drum boiler being in use being in use
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Cristina Budaciu
at the Power Plant of Iasi is obtained with a MLP neural network with two
neurons in the hidden layer and one neuron on the output layer. The artificial
neural network used in process identification is able to identify NARXNARMAX models. Therefore, the NARMAX model can be described by:
y N (k ) = f [ y (k − 1),..., y (k − n), u (k − d ),...u (k − d − m),
(1)
p (k ),K p (k − h)]
where f (.) is a nonlinear function. The inputs of the neural network are the
past values of the command input u ( k − d ), u ( k − d − 1),..., u (k − d − m) , the
disturbances p (k ), p (k − 1),..., p (k − h) and the output regresor vector
y (k − 1), y (k − 2),..., y (k − n) .
Steam flow
1
0
Drum water level
Feedwater flow
-1
0
100
200
300
400
500
600
700
100
200
300
400
500
600
700
100
200
300
400
500
600
700
1
0
-1
0
1
0
-1
0
Time [s]
Fig. 2 − The open loop data set for training the neural network.
In a first iteration, the off-line parametric identification around a
nominal point has been performed in order to find the number of past outputs,
past values of input and past values of disturbance, respectively. The data set
used for identification are the feedwater mass flow, the steam mass flow and the
level in the drum as is ilustrated in the Fig. 2. As is shown the input quantities
Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009
13
are represented in normal range [-1 1], the feedwater flow coming in the drum
and the steam flow disturbance signal to the consumer. The dynamic of the
drum level is influenced by the feed water flow changes at variation of heat
flow and in the presence of steam flow disturbance. The variation in feedwater
flow input is justified by the fact that the feed water flow is varying in order to
control manually, in open-loop, the drum water level around a nominal point,
otherwise the drum water level would increase outside the safe limit.
Steam flow
1
0
-1
0
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
50
100
150
200
250
Time [s]
300
350
400
450
Steam flow
1
0
Drum water level
-1
0
1
0
-1
0
Fig. 3 − The open loop data set from simulator for testing the neural network.
The neural network has been created using functions from Matlab
Neural Network toolbox. For the training and validation of the neural network
that models the process the data set illustrated in the Fig. 2 and Fig. 3 was used.
After several simulations was seen that a neural network with only 1 hidden
layer with 2 neurons and one neuron on the output layer is sufficient to describe
the dynamics of the system. Therefore the neural network output, with the
number of neurons on the hidden layer ns = 2, can be expressed as:
ns
u
T
p
T
y
T
(2) y pred (k ) = ∑ w j tansig(w j u(k − d − 1) + w j p(k − h) + w j y (k − 1) + b j ) + b,
j =1
where:
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Cristina Budaciu
u(k − d − 1) = [u ( k − d ) u (k − d − 1) K u ( k − d − m)] ,
p(k ) = [ p (k ) p ( k − 1)K p ( k − h)]
y (k − 1) = [ y ( k − 1) y (k − 2)K y (k − n)]
- w uj is the weights vector associated with u(k-d-1) inputs in connection with
jth neuron on the hidden layer.
- w pj is the weights vector associated with p(k) disturbance in connection with
jth neuron on the hidden layer
y
- w j is the weights vector associated with the past values of the output.
- bj represents the biases for jth node on the hidden layer and b represents the
bias for the output neuron.
Open loop data set for training
1
Drum level
0.5
0
-0.5
-1
0
50
100
150
200
250
300
350
400
300
350
400
Simulator data set for testing
1
Drum level
0.5
0
-0.5
-1
0
50
100
150
200
250
Time [sec]
Fig. 4 − The simulation results for neural network validation.
The hyperbolic tangent function is used as the activation function in the
artificial neural network for hidden layer. During the Backpropagation stage of
the neural network training, the output layer of neurons is adjusted, to make the
Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009
15
output closer to the desired output.
In order to test the neural network, the Fig. 3 illustrates the data set
taken from the steam drum boiler simulator developed in [10].
In the Fig. 4 are plotted comparatively the responses of the neural
network with circle and the data set used with solid line. The simulation results
from Fig. 4 indicate a good agreement, between neural network response and
the desired output.
3. The Neuro-Predictive Structure for Drum Level Control
The neuro-predictive structure that permits the on line design of the
controller parameter is illustrated in Fig. 5. The figure shows an existing
controller with tunable gains in a closed-loop configuration which has a known
parametric structure. Its parameters will be modified at each sample time as a
result of an optimization method. This strategy presented in [11] proposes the
existing of two feedback loops, the real time control loop with the real process
and the controller, and the prediction control loop with the predictor and the
gain adaptation law with the simulated controller.
upred(k+i|k)
epred(k+i|k)
r(k+i|k)
+
Controller
p(k+i|k)
Neural model
ypred(k+i|k)
Neuro-predictive control loop
q
Cost function
Constraints
Optimization block
qopt
e(k)
r(k) +
p(k)
y(k)
u(k)
Controller
Process
Real-time control loop
Fig. 5 − The Neuro-Predictive strategy for drum level control.
The neuro-predictive control loop is used to make a prediction, at each
sample time, over a certain horizon, of the future behavior of the real time
control loop. The future response of neural model of the process and the
predicted error are obtained at each time instant of the prediction horizon.
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Cristina Budaciu
The future control u pred ( k + i | k ) is calculated at each time instant in
predictive control loop considering a smaller sampling time than the one from
the real-time control loop. Therefore, the predicted output ypred(k+i|k) is
determined over a finite horizon, with i = N1 , N 2 , N1 and N2 being the
prediction horizons.
The neural model design in Section 2 for the steam drum boiler is used
in predictive control loop, so that at each time instant k, the predicted behavior
of the process is obtained by the form:
(3)
y pred = [ y ( k + N1 | k ) y ( k + N1 + 1| k ) ... y ( k + N 2 | k )]T .
The predicted disturbance p(k+i/k) meaning the steam mass flow is
assumed to be known so that the predicted output can be calculated.
The controller used in the both loops is of PI type and the control law is
given by
(4)
u (k ) = u (k − 1) + q0 e(k ) + q1e(k − 1)
The vector q = [ q0 q1 ] contains the controller parameters and are
obtained at each sample time, using numeric minimization of a cost function,
over prediction horizon N2. The cost function is considered the mean squared
prediction error over a prediction horizon:
(5)
J=
1 N2 2
∑ e pred (k + i | k ),
2 i = N1
where
(6)
e pred (k + i | k ) = y pred (k + i | k ) − r (k + i | k ) , i = N1 , N 2
is the prediction error over prediction horizon N2 between the predicted output
and the reference. In the optimization block the optimal tuning parameters qopt
are obtained, taking into account the process predictable dynamics variations.
For the next time instant, k+1, the tuning parameters qopt are transferred to real
time control loop and the simulated control loop. At each sample time, the
controller parameters must respect the relations that characterizes the discrete PI
controller:
Bul. Inst. Polit. Iaşi, t. LV (LIX), f. 4, 2009
17
q0 > 0
(7)
q1 < −q0
The neuro-predictive method for controller parameters tuning is
advantageous because it allows on line adjustment of parameters to change the
dynamics of the process, thereby avoiding the off line identification stage. The
performances depend of the data set and the accuracy of results obtained from
minimizing criterion function depends on the quality of the model obtained.
4. Simulation Results
Feedwater
and steam flow
Drum level [0-100]%
The neuro-predictive approach presented in Section 3 was applied to the
steam drum boiler system in order to obtain better performances for level
control subject to steam flow disturbances. The steam boiler provides thermal
and electrical power and it works under complex technology in order to satisfy
numerous technical, security and economical requirements. The simulation
results are shown in the Fig. 6, considering a step variation in level reference
values subject to a step variation of 10% in steam demand.
40
20
0
100
Drum level
Reference
150
200
250
300
350
400
100 Feedwater flow
50
Steam flow
0
100
150
200
250
300
350
400
200
250
Time [s]
300
350
400
PI Parameters
20
10
0
qo
q1
-10
100
150
Fig. 6 − Simulation results and PI controller parameters for the
adaptive discrete PI controller.
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Cristina Budaciu
As it is shown in the Fig. 6, at t = 200 , the reference of the level is
increase from 10% to 25% , so that the control action of the level controller will
force the closing of the feed water valve. At moment t = 300 the steam flow is
suddenly increased in the drum. A decreased of the feed water flow is
accompanied by an increase of the drum level as was expected because due to
the drop in the pressure, more steam bubbles will appear making the steamwater mixture to swell.
The steam disturbance is rejected by the PI controller with adapted
parameters, proving its capacity to keep the level at desired values. The PI
controller parameters are adjusted according to the change in the process
dynamics, thus compensating for variations that occur in both set point change
and an increase in steam consumption.
5. Conclusions
This paper reports an application of a neuro-predictive method for a
nonlinear physical model with a high complexity - the steam drum boiler system
being in use at the Power Plant from Iasi area. It is well known that in Power
Plant systems, even a small improvement in the operation of a process can have
great economic and environmental influences. This approach for self-tuning
controllers demonstrates a good performance for processes having predictable
dynamics variations. The method was applied to a 420t/h steam drum boiler
system in order to obtain better performances for level control subject to steam
flow disturbances.
Received: August 5, 2009
“Gheorghe Asachi” Technical University of Iaşi,
Department of Automatic Control
and Applied Informatics
e-mails: chalauca@ac.tuiasi.ro
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STRUCTURĂ NEURO-PREDICTIVĂ PENTRU REJECŢIA PERTURBAŢIILOR
DE SARCINA ÎN TAMBURUL UNUI BOILER DE ABUR
(Rezumat)
În această lucrare a fost testată o structură neuro-predictivă de acordare a
parametrilor unui regulator PI discret. Metoda permite adaptarea on-line a parametrilor
regulatorului atât la modificarea dinamicii procesului cât şi la apariţia unei perturbaţii
de sarcină. Metoda de reglare neuro-predictivă propusă pentru reglarea nivelului în
tamburul unui boiler în prezenţa unui consum de abur a fost testată prin simulare,
considerând seturi de date preluate din functionarea în timp real a procesului existent la
CET 1 S. A. Iasi. Pentru implementarea structurii de reglare adaptive s-a determinat un
model neuronal care să modeleze dinamica procesului neliniar. Setul de date folosit
20
Cristina Budaciu
pentru antrenarea reţelei neuronale a fost preluat din funcţionarea reală a unui boiler de
abur industrial, iar setul de date de testare a fost preluat dintr-un simulator proiectat
pentru tamburul boilerului considerat. Rezultatele experimentale au demonstrat că
schimbările în dinamica procesului sunt compensate prin variaţii ale parametrilor
regulatorului discret PI. Rezultatele prezentate subliniază avantajele folosirii acestei
tehnici de acordare pentru a controla procese neliniare în toata zona de operare a
acestora precum şi capacitatea de a rejecta perturbaţiile de sarcină în comparaţie cu
alegerea unui regulator cu parametri ficşi determinaţi în jurul unui punct de operare.