Industrial Boiler Modeling and Control Based on Adaptive Neuro Fuzzy Inference

System and Implementation in S7-400H PLC

Javad Shoorabeh1, Feridoon Shabaninia2, Iman Karimi3 1Shiraz University, Department of E-learning in Instrumentation and Automation Engineering, Iran

2Shiraz University, Department of Electrical and Electronic Engineering 3Bou Ali Sina Petrochemical Company, Department of Instrumentation, Mahshahr, Iran

Abstract

In this paper, a data driven method is employed to model a boiler. The method uses ANFIS as a fuzzy system

which its parameters calculated by a neural network training algorithm. The main advantage of ANFIS is that it

doesn’t need complicated tuning of fuzzy system parameters and it just needs a good training dataset. Training

dataset is obtained from a simulated mathematical model. However, this structure still needs PID and a good

tuning of that because of the required good dataset. The proposed ANFIS shows good responses and mimic the

boiler plant in acceptable manner. Furthermore, another ANFIS is designed to do a control job in boiler as a PID

and it shows even better responses than a normal PID controller in some ranges. In addition, designed ANFIS is

implemented in a S7 PLC to show the practical value of the method and it can be employed in industrial plant

for further development and researches.

Keywords: Boiler, Data driven modelling, ANFIS, PID, PLC

Corresponding Author 1ANN: Artificial Neural Network

Research Paper Research Paper International Journal of Review in Life Sciences ISSN: 2231-2935

Volume 5 (2015), Issue 3 (Jul-Sep), Pages 40-48 www.ijrls.com

Introduction

Modelling and simulation has a main role in

industry and process developments. Generally

speaking, There are two methods of modelling.

One of them is based on dynamic behaviour and

relation of variables and states in physical

equations and consequent differential equations

from the real system (Mathematical Modelling).

The other method is based on input-output data and

experience or knowledge of the system (Empirical

Modelling) (Boyatt et al., 2006). Mathematical

modelling of chemical plant or power plant

requires detailed calculation to obtain dynamics

and thermodynamics equations of the system which

is time consuming and tough task. In addition, in

large scale plants with many complex and MIMO

systems, modelling procedure becomes a

nightmare. On the other side, empirical modelling

is a straightforward way and just need a suitable

and sufficient data set, however, the precision of

this type is not as same as mathematical type and it

has some deficiencies from this point of view. In

addition, infrastructure of data gathering and

communication is prerequisite for empirical

modelling (Angell et al., 2008).

In recent decays, rapid development of computers

causes many industrial plants to use the benefits of

computers and apply DCS and similar

computerized and digital control system. As a

consequence, data collection and storage is

installed in many industrial plants. As a result, data

driven modelling like ANN1 modelling, Fuzzy

modelling and other empirical modelling which are

easier in comparison to mathematical modelling,

attracts many interest. In addition, empirical

modelling is easier to implement and to configure

for further development and changes (Rusinowski

and Stanek, 2007). Fuzzy systems and neural

networks are applied in many wide range of

application. A lot of publication in scientific

journals and conferences shows the popularity of

them. In spite of this, they have their own cons and

complexity. For example, in fuzzy systems need

enough experience from the system to adjust the

fuzzy parameters and procedure of adjustment is

time consuming. Neural network training process

needs enough and suitable data set and need

enough knowledge to manipulate the network. To

improve this issue a combination system of

Artificial Neural Networks and Fuzzy Inference

System were introduced by Jang (1993) to cover

the cons of these two popular structures. The

proposed structure was ANFIS which stands for

Adaptive NeuroFuzzy Inference System. ANFIS

has a wide range of application from fault detection

(Karimi and Salahshoor, 2012), to modelling

(Neshat et al., 2011), and control. It has a simple

structure and easy to configure.

In this paper, ANFIS uses as an empirical model to

mimic the behaviour of a boiler which has a

significant role in power plants. Training dataset is

build by a boiler model that simulated in MATLAB

SIMULINK. Furthermore, another ANFIS is

developed to control the boiler and becomes an

alternative of a PID controller. Finally, the trained

ANFIS which is used as a boiler model is

implemented in a S7 PLC and the procedure is

explained clearly. This part is done as a pre-process

of implementation ANFIS in real world for future

studies.

Boiler

The function of boiler is to deliver steam with a

predefined pressure and temperature to a turbine or

other process equipment. There are have several

types of boilers such as water tube and fire tube

(which is outdated), in this research water tube

boilers steam-drum with saturated zone is the

objective. The employed model proposed by

Aström and Bell (1999) and is shown in Fig.1. In

this figure, Q (Kj) is heat and causes boiling in the

risers, qf (Kg/s) is feed water flow and supplied to

the boiler, p(Kpa) is drum pressure, qs (Kg/s) is

steam flow and is taken from the drum to the super

heaters, turbine or any other equipment which

needs predefined quality of steam.

Fig. 1. The proposed Drum model

Although, in reality boiler system is much more

complicated than shown in fig.1 and there is many

down comer and riser tubes. But, the total

behaviour is well captured by global mass and

energy balances. Drum pressure is a very critical

and important variable in boiler and any changes in

the drum pressure cause the energy stored in steam

and water is released or absorbed very rapidly. The

rapid release of energy ensures that different parts

of the boiler change their temperature in the same

way.

As mentioned earlier, the operating zone in the

following model is saturated zone and in this

region relation of pressure and temperature is

extremely nonlinear. To overcome this issue a

lookup table was extracted from Engineering

Toolbox web site to produce the pressure variable.

The resulted pressure is processed in a set of

differential equation to make the other variables.

Much of the behaviour of the system is captured by

global mass and energy balances .Inputs to the

system are the heat flow rate to the risers ,Q and

the feed water mass flow rate, qf .Furthermore, let

the outputs of the system be drum pressure, p, and

the steam mass flow rate, qs. This way of

characterizing the system is convenient for

modelling. Additional notation is needed, then, let

V denotes volume, ρ denotes specific density, u

specific internal energy, h specific enthalpy ,T

temperature and qs mass flow rate. The total mass

of the metal tubes and the drum is m and the

specific heat of the metal is Cp. Furthermore, let

subscripts s, w, f and m refer to steam, water, feed

water, and metal, respectively. Sometimes, for

clarification, need a notation for the system

components. For this purpose would use double

subscripts where t denotes total system, d drum and

r risers. With the above definition, the state space

model is:

𝑒11𝑑𝑉𝑤𝑡

𝑑𝑡+ 𝑒12

𝑑𝑃

𝑑𝑡= 𝑞𝑓 − 𝑞𝑠

𝑒21𝑑𝑉𝑤𝑡

𝑑𝑡+ 𝑒22

𝑑𝑃

𝑑𝑡= 𝑄 + 𝑞𝑓ℎ𝑓 − 𝑞𝑠ℎ𝑠 (1)

which e11, e12, e21 and e22 are :

𝑒11 = 𝜌𝑤 − 𝜌𝑠 (2)

𝑒12 = 𝑉𝑠𝑡𝜕𝜌𝑠

𝜕𝑃+ 𝑉𝑤𝑡

𝜕𝜌𝑤

𝜕𝑃 (3)

𝑒21 = 𝜌𝑤ℎ𝑤 − 𝜌𝑠ℎ𝑠 (4)

𝑒22 = 𝑉𝑠𝑡 ℎ𝑠𝜕𝜌𝑠

𝜕𝑃+ 𝜌𝑠

𝜕ℎ𝑠

𝜕𝑃 + 𝑉𝑤𝑡 ℎ𝑤

𝜕𝜌𝑤

𝜕𝑃+

𝜌𝑤𝜕ℎ𝑤

𝜕𝑃 − 𝑉𝑡+ 𝑚𝑡𝐶𝑝

𝜕𝑡𝑠

𝜕𝑃 (5)

and the state variables are p and V. If only

discussion interested in drum pressure, use a

simplified model. If the drum level is controlled

well the variations in the steam volume are small.

Neglecting these variations extracts the following

approximate model:

𝑒1𝑑𝑃

𝑑𝑡= 𝑄 − 𝑞𝑓(ℎ𝑤 − ℎ𝑓) − 𝑞𝑠ℎ𝑐 (6)

which

𝑒1= 𝑉𝑠𝑡𝜕𝜌𝑠

𝜕𝑃+ 𝜌𝑠𝑉𝑠𝑡

𝜕ℎ𝑠

𝜕𝑃+ 𝜌𝑤𝑉𝑤𝑡

𝜕ℎ𝑤

𝜕𝑃+ 𝑚𝑡𝐶𝑝

𝜕𝑡𝑠

𝜕𝑃−

𝑉𝑡 (7)

Detailed information of the above equation is

presented in the Aström and Bell (1999) paper. The

equations are implemented in SIMULINK and

operating point and steady state values are

calculated by “operspec” command in MATLAB.

The result of simulated model is illustrated in fig.2,

which pressure and temperature of the drum has

been shown. As it can be seen, the changing

direction and amplitude of temperature and

pressure are similar that shows a validation of

model.

Fig.2. Drum pressure and Temperature response to

input energy (Heat)

The result shows that the model is suitable for

making data set in our training procedure in

ANFIS.

ANFIS

ANFIS is a Sugeno-Type fuzzy inference whose

free parameters in membership functions (MFs) are

adjusted via the learning methods being employed

in Neural Networks. Sugeno FIS was first

introduced in 1985 by Sugeno. This type of fuzzy

inference is similar to the Mamdani method in

many aspects. The main difference between

Mamdani and Sugeno is that the output MFs is only

linear or constant for Sugeno fuzzy inference. In

fuzzy systems, adjusting the parameters of MFs is

time consuming and need enough experience. In

addition, for generating rules adequate previous

knowledge of the system is needed. However, Jang

(1993) proposed ANFIS to solve the problem. In

fact, by performing training algorithms like BP

0 5 10 15

x 104

1000

1500

2000DrumPressure(Kpa)

0 5 10 15

x 104

180

200

220Temperature(DegC)

0 5 10 15

x 104

2.4

2.6

2.8x 10

5 Heat(KJ)

time(s)

(Back Propagation) on input/output data set, the

characteristics of data has been extracted and

transformed to the rules and parameters of FIS for

the best mapping from input to output.

Elaborated information on ANFIS structure and its

behaviours can be found in literature. In this paper,

just addressed some parts of it. Each rule in ANFIS

is like:

If x is A1 and y is B1 Then f1=p1x+q1y+r1 (9)

If x is A2 and y is B2 Then f2=p2x+q2y+r2 (10)

Which x and y are inputs, A1, A2, B1and B2 are

input MF and f is output that can be linear or

constant. p, q and r are the consequent parameters.

Since, would have chosen linear output with one

input then f=px+r. A simple structure of ANFIS

with two inputs and two membership functions on

each input is illustrated in Fig.3. First layer is input

layer and it has membership functions. In second

layer, multiplying function of each membership

function with each other is done to make the fire

strength weight of each rule. Third layer just makes

a normalization of weights in each rule. In fourth

layer, the output of Takagi-Sugeno (f) is made with

combination of consequent parameters (p, q and r)

with inputs (x and y). Finally in fifth layer, final

output of the network is made by adding the

outputs of fourth layer.

Fig.3. A simple structure of ANFIS

There are two types of parameters in ANFIS, one is

premise parameters and the other one is consequent

parameters. Premise parameters are related to the

membership function, as used triangle shape

membership function, in this study they are a, b

and c in the following equations.(8)

0,

,

( ; , , )

,

0,

x a

x aa x b

x bf x a b c

c xb x c

c b

c x

(8)

Tuning of premise parameters affects the shape of

membership function directly. Consequent

parameters are related to fourth layer and make the

output of Takagi-Sugeno and they are p, q and r.

In this work, main input and output are heat, Q, and

drum pressure, p. Then, ANFIS has just one input

and the best and minimum number of membership

function is 4. So the number of rules would be 4.

The resulted structure of ANFIS is presented in

fig.4.

Fig.4. The structure of the proposed ANFIS

Training data set is obtained from the simulated

model which is presented in section 2. The ANFIS

is trained with hybrid algorithm which contains

back propagation and least square method. The

obtained result is satisfactory and illustrated in

fig.5. In the figure, red line is related to

mathematical model which is presented in section 2

and the blue line is related to ANFIS.

It is obvious that trained ANFIS follow the

mathematical model in a good manner.

Input of this incitation is presented in fig.6. The

trained data was in a medium load range. The

designed ANFIS shows good responses in medium

load range even with other shape of input, i.e. the

direction of increasing or decreasing.

However, the ANFIS just shows good responses in

medium load range and in other range which are

not included in training data set, the quality of the

response decreases gradually. In spite of this, the

proposed ANFIS structure is also employed in

control application (not modelling) and it shows

good responses in comparison to PID. In next

session, this comparison has been made.

Fig.5. Mathematical and ANFIS model output

Fig.6. Related input of fig.5

ANFIS vs. PID

One of the main controllers in industry which still

has a lot of application and is employed in many

plants is PID. It has a simple structure and

understandable perfectly to many operators.

However, it has some deficiencies which the worst

one is the tuning. Each PID controller needs a

comprehensive work for fine tuning and most of

the time it has been made by try and error. In

addition, by the time in each plant engineer should

retune the PID parameters due to the variable

nature of the system dynamic. Several methods

have been proposed to overcome the issues of PID

controllers. Many of them suggest an optimal way

to calculate the PID coefficients like fuzzy logic,

genetic algorithm and etc. The other methods are

based on designing a different control structure like

DMC, MPC, Fuzzy control and etc, explained by

Fleming and Purshouse (2012). In this paper,

ANFIS is employed as a controller instead of PID.

Training data is obtained from the PID with a

definite coefficient. After that trained ANFIS

works as single and independent controller in the

boiler to control the drum pressure. The obtained

result of two control structure is shown in fig.7.The

operation point of the system is around 901 Kpa

which is obtained from operspec command in

MATLAB. The operation point line is illustrated

with green line in Fig.7, in another word, it is the

desired point which PID and ANFIS should keep

the pressure of the boiler in this aria. ANFIS

structure shows perfect responses in comparison to

PID, particularly when there is a sudden change in

input energy (Heat, Q,). However, if the input

range is changed, responses will decrease in quality

because of the training data set. Since our training

data set is chosen in medium load, i.e. input heat is

around 200 to 230 Mj, ANFIS will show good

responses only in mentioned range. Medium load

of heat or input energy is illustrated in fig.8.

Nevertheless, this structure has a big deficiency, it

still needs PID as a source of producing data,

consequently, good tuning of PID is prerequisite of

having a good data set for training ANFIS as a

controller and complete remove of the PID

controller is not good.

Fig.7. ANFIS and PID output response

PLC implementation

Programmable Logic Controller (PLC) is a device

which is so popular and practical in different

industries. It does a pre-programmed logic with

respects to its digital and analogue inputs and

makes appropriate outputs. For the first time, PLCs

have been used as an alternative with relay-

contactors circuits which control task and

maintenance of the plants with those circuits was a

0 5 10 15

x 104

950

1000

1050

1100

1150

1200

1250

1300

time(s)

DrumPressure(Kpa)

Math Model

ANFIS

0 5 10 15

x 104

2

2.05

2.1

2.15

2.2

2.25

2.3

2.35

2.4x 10

5

time(s)

Heat (Kj)

0 0.5 1 1.5 2 2.5

x 104

880

885

890

895

900

905

910

915

920

time(s)

Drum

Pressure(K

pa)

Compare between ANFIS(Blue)and PID(Red)... Kp=10.0 Ki=0.5 Kd=0.0

PID

ANFIS

nightmare, specially in big plants with many

variables. At this stage, the PLCs were proposed to

overcome the issues of outdated and traditional

relay-contactors circuits. Gradually, they have been

employed in many factories, process plants, power

plants and even in houses.

Fig.8. Related input(Heat) of fig.7

They have many features and include many types

of functions and control blocks which make them

so practical. In this paper, the procedure of

implementation fuzzy logic is explained and the

ANFIS which is used as a model of boiler is

implemented in a S7 PLC from SIEMENS

company which is common in industrial plants.

Functions in programmable logic controllers

libraries are simple (bit operations, summations,

subtractions, multiplications, divisions, etc.) or

complex (sine, cosine, absolute value, vector

summations, PID, etc.) mathematical functions but

often without fuzzy systems, while PLC systems

are currently the most commonly used control

systems in industry. The aim of the proposed paper

is to present a universal fuzzy system’s design for

PLC and the principle of Matlab fuzzy system

conversion into PLC’s fuzzy structure.

Typically, these processes are still controllable by

using and applying the expert knowledge of

operators who have learned how the process

responds to various input conditions. The most

common industrial control systems are Distributed

Control System (DCS) and PLC’s. DCS (Fig.9.) is

a computerized control system used to control the

production lines in the industry as oil refining

plants, chemical plants, pharmaceutical

manufacturing, etc. where continues control (PID

loops) is dominating. PLC systems were typical for

discrete (event) control – automotive, electronics,

etc. Their primary goal was to replace the relay

technology. Nowadays they have wide instruction

libraries including function block for continues

control (well-designed PID, lead-lag blocks, etc.)

but there are missing libraries for intelligent control

(fuzzy systems and neural networks). The proposed

paper will summarize some existing fuzzy

toolboxes for PLC's and present a universal fuzzy

system for PLC with a methodology to convert

Matlab fuzzy system into PLC's fuzzy

structure (Körösi and Turcsek, 2011).

Fig.9. Typical Architecture of a Distributed Process

Control System

SIMATIC S7 Fuzzy Control

The S7 Fuzzy Control software package consists of

two individual products: The product Fuzzy

Control mainly contains the control block (function

block - FB) and the data block (DB).The product

Configuration Fuzzy Control contains the tool for

configuring the control block.The FB is already

prepared in its full range of performance and with

all algorithms for configuration and assigning

parameters. A user-friendly tool is available for the

configuration and parameter assignment of this

function block (Fig.10). Fuzzy controllers are easy

to configure on the basis of Fuzzy Control because

their functionality is limited to the definition and

execution of core functions in fuzzy theory. An

instance data block in the CPU of the

programmable controller forms the interface

between the function block, the configuration tool,

and the user. It’s possible to download a number of

fuzzy applications to a CPU and run them there.

Each application is stored in a separate data block;

the number of the data block can be freely assigned

(Fig .11)

0 0.5 1 1.5 2 2.5

x 104

2

2.05

2.1

2.15

2.2

2.25

2.3x 10

5

time(s)

Heat(Kj)

Fig.10. Block diagram of the configuration tool sub

function

Fig.11. Structure of the block calls

There are three main parts of the designed fuzzy

structure: fuzzification, inference mechanism and

defuzzification. Fuzzification is the first step in the

fuzzy inferencing process. This involves a domain

transformation where crisp inputs are transformed

into fuzzy inputs. Crisp inputs are exact inputs

measured by sensors and passed into the control

system for processing, such as temperature,

pressure, rpm's, etc. Each crisp input that is to be

processed by the FIU has its own group of

membership functions or sets to which they are

transformed. This group of membership functions

exists within a universe of discourse that holds all

relevant values that the crisp input can possess

(Körösi and Turcsek, 2011).

Fig.12. PLC's integrated fuzzy tools

FuzzyControl++ :

The FuzzyControl++ configuration tool for the

automation of technical processes enables the

efficient development and configuration of Fuzzy

systems. Empirical process expertise and

verbalized knowledge by experience can directly

transformed into controllers, pattern identification

or logic decisions. Associated functions are also

easy to configure with the help of FuzzyControl++.

The rules are inputs either via a table or via a

matrix editor. Dynamic changes of the rules basis

identified immediately and, if no rule should be

applicable, a value previously prescribed for each

output will be use. The inference and

defuzzification method used by FuzzyControl++ is

the well-known Takagi-Sugeno method.

FuzzyControl++ can execute on SIMATIC S7

PLC's, the SIMATIC PCS7 process control system

and the WinCC SCADA system and provides

special function blocks. It is implemented in this

paper in Fig.14. that been shown Fuzzy Pressure

Controller made by only 4 Rules that been

produced by MATLAB's ANFIS editor, they are in

Fig.15 as 4 simple Rules was been built in

IF..THEN Box in Fig.14.

In Fig.16 about input Heat (Q), at Midrange of

Boiler's Operating Point, converted to Triangular

function in role of the Fuzzy Controller's input.

Fig.17 shows how is configuring Output of the

Fuzzy Controller and Fig.18 is showing Obviously

real output of PLC after download new fuzzy

program to S7-400H PLC and Set point Tracking

about Drum Pressure is clear .in Figure is obvious

that with increasing or decreasing of energy input

also Drum Pressure behaves same way and it is

correct because One of important factors in Drum

Pressure depends is Heat input (Körösi and

Turcsek, 2011).

Step 7:

STEP 7 is the standard software package used for

configuring and programming SIMATIC

programmable logic controllers. It is a part of the

SIMATIC Siemens industry software, Körösi and

Turcsek (2011) and Siemens (), that covers widely

usages such as:

Based on several types of programming: Flow

chart, Contact List, SCL, Grafcet, ...

Expandable with applications offered by the

software industry SIMATIC.

Calculation of functional modules and

communication modules.

Data transfer ordered by event using

communication blocks and function blocks.

Configuring Connections

Fig.13. FuzzyControl++ Drivers and Runtime

Module

Fig.14. Fuzzy Controller of the pressure created on

Fuzzycontrol++

Fig.15. The Fuzzy Rule Table

Fig.16. Fuzzy Controller's input

Fig.17. Output of the Fuzzy Controller

Fig.18. The fuzzy controller regulation’s curve

plotter

Fig.19. The fuzzy controller regulation’s surface

Conclusions

The influence of age and low education level on

motorcycle accidents resulting in death was

undeniably proved to be high in this study. In

addition, it was confirmed that men are more

exposed to such traumas. Although the frequency

of head and face injuries in individuals killed in

motorcycle accidents were significant, it decreased

from 2007 to 2011.

In this research, the ability of ANFIS in modelling

and control of a boiler is investigated. The strength

of ANFIS is related to its data driven nature which

it doesn’t need any mathematical equation to model

a system. It does just need an input/output dataset

of a system to make a model to mimic the exact

behaviour of the system. A mathematical model of

a boiler is addressed by Aström and Bell (1999).

This model produces required data for ANFIS in

training procedure and further qualification.

Designed ANFIS shows good responses to model

the real plant (in this work simulated model by

Aström and Bell (1999)). In addition, in section 4

another ANFIS was designed to mimic the

behaviour of a PID controller which was

predesigned in boiler model and again it shows

good responses in controlling the plant and it

became an alternative way to control the plant. This

paper presented a fuzzy system design for PLC

system and the automatic fuzzy structure

conversion from MATLAB into PLC. The fuzzy

toolbox has been verified on Real Training Package

and it’s suitable for modelling and control

nonlinear processes. The fuzzy system can be

designed directly in Matlab and after sets of

simulations the final fuzzy system can be

programmed into PLC. However, trained ANFIS

just has good result in a medium load range of

boiler which is used in training process. In high

range load ANFIS doesn’t show super behaviour

and still it needs PID controller to produced

training data and implementation ANFIS

controller. Fortunately, nowadays or in future with

improvement of technology that due to production

of high speed CPU's for PLC or DCS systems,

problems such as slow deffuzification progress

would be solved easily and could be used in many

of industrial Plants and factories , and using of new

methods such as this paper overcome some

problems that create with conventional classic

control methods.

References

Angell, C., Kind P.M., Henriksen, E. and

Guttersued, Q., 2008. An empirical-

mathematical modeling approach to upper

secondary physics. Phys. Educ., 43(3):

256-264.

Aström, K.J. and Bell, R.D., 1999. Drum-boiler

dynamics. Automatica, 36(3): 363-378.

Boyatt R., Harfield, A. and Beynon, M., 2006.

Learning about and through Empirical

modelling. ICALT, 662-666.

Fleming, P.J. and Purshouse, R.C., 2002.

Evolutionary algorithms in control

systems engineering: a survey. Control

Engineering Practice, 10(11): 1223-1241.

Jang, R., 1993. ANFIS: adaptive-network based

fuzzy inference system, IEEE Trans. Syst.

Man Cybern. B., 23(3): 665-685.

Karimi, I. and Salahshoor, K., 2012. A New Fault

Detection and Diagnosis Approach for a

Distillation Column based on a Combined

PCA and ANFIS Scheme. 24th Chinese

Control and Decision Conference

(CCDC), 3408-3413.

Körösi, L. and Turcsek, D., 2011. Fuzzy System

for PLC. Inproceedings of MATLAB

conference – 2012. Retrieved from:

http://dsp.vscht.cz/konference_matlab/MA

TLAB12/full_paper/040_Korosi.pdf.

Neshat, M., Adeli, A., Masoumi, A. and Sargolzae,

M., (2011). A Comparative Study on

ANFIS and Fuzzy Expert System Models

for Concerete Mix Design. IJCSI, 8(2):

196-210.

Rusinowski, H. and Stanek, W., 2007. Neural

modelling of steam boilers. Energ.

Convers. Manage., 48: 2802-2809.

Siemens, A.G., 2003. FuzzyControl++ User’s

Manual. Karlsruhe, Germany.

Siemens, A.G., 2006. SIMATIC Programming with

STEP 7, Manual.Siemens, pp. 1-1.

Siemens, A.G., 2009. SIMATIC. Process Control

System PCS 7. OS Process Control

(V7.1). Operating Instructions, Germany.