ECOLE POLYTECHNIQUE OF MONTREAL

DEPARTMENT OF MECHANICAL ENGINEERING

Research proposal

Adaptive Fuzzy Control of Nitriding Furnace

Presented by: Kiarash Aminollahi

Submitted for Ph.D. candidacy

August 2006

TABLE OF CONTENTS

TABLE OF CONTENTS ..............................................................................................................................1

INTRODUCTION .........................................................................................................................................2

LITERATURE REVIEW .............................................................................................................................3

TEMPERATURE CONTROL IN HEAT TREATMENT FURNACES ..........................................................................3 ADAPTIVE FUZZY CONTROL......................................................................................................................14

Adaptation of Scaling Factors .............................................................................................................14 Adaptation of FIS Parameters .............................................................................................................15 Adaptation of Rules..............................................................................................................................15 Direct and Indirect Adaptive Fuzzy Model Based Control ..................................................................16

FUZZY ADAPTIVE MODEL PREDICTIVE CONTROL .....................................................................................16 THE SUGENO FUZZY MODEL .....................................................................................................................18 GENETIC FUZZY SYSTEMS (GFS) ..............................................................................................................19 SUMMARY OF LITERATURE REVIEW...........................................................................................................21

RESEARCH METHODOLOGY...............................................................................................................23

PROBLEM DEFINITION................................................................................................................................23 SUGGESTED METHODOLOGY......................................................................................................................25

Furnace Predictive Fuzzy model..........................................................................................................26 Validation.............................................................................................................................................31 Rule generation....................................................................................................................................31 Parameter optimization........................................................................................................................31

CONCLUSION .............................................................................................................................................31 Contribution.........................................................................................................................................33 Time chart ............................................................................................................................................33

REFERENCES ............................................................................................................................................34

1

Introduction

NITREX is a leading company in modern surface treatment of metal and an equipment

manufacturer. NITREX Metal specializes in providing solutions to whose product

manufacturing process involves heat treating of ferrous or non-ferrous materials.

A fuzzy logic controller is taking over the task of temperature control for furnaces in

NITREX.

In NITREX, the task of temperature control in furnace is dealing with three different

problems:

The first problem is to track the desired temperature rise and also preventing overshoot.

The second problem originated in use of different loads for nitriding process, which

changes the characteristics of the furnace and its response to input power.

The third problem is the variety of furnaces. Since there are different models of furnaces

with different characteristic therefore the knowledge base has not the same effect on all

the furnaces, which means each furnace individually needs the modification on

knowledge base.

Hence designing a new structure for the control system as an adaptive controller is

intended to overcome mentioned problems.

2

Literature review

Temperature control in heat treatment furnaces

Temperature control of heat treatment furnaces have been the subject of many studies and

received special attention during the past decades.

A comprehensive review on this matter show that the most of work done deal with

influence of temperature control on chemical or metallurgical process as well as hardware

control systems (i.e., sensors, digital controllers), system identification and modeling

method, efficiency, environment and energy saving and temperature control system.

A review on temperature control system indicates that very less attention has been paid to

“temperature control in nitriding furnaces”.

In general, temperature control systems consist of:

• Improvement on existing classical controllers, such as PID and using soft

computing techniques for tuning [1-11].

• Defining new strategies for controllers, such as hierarchical structures, multi-

sectional thermal system [12-20].

• Model-Based Control, i.e., predictive/adaptive control, on-line modeling [21-33].

• Soft computing and intelligent control, i.e., Fuzzy control, Genetic Algorithm,

Neural Networks and Expert System [34-53].

In general, non-linear control systems are robust, adaptive and predictive controls,

discrete event and artificial intelligent control. The latter consists of expert systems,

neural networks and fuzzy control. Although most industrial applications of fuzzy control

have been based on rule-based control, in which controllers have been designed on the

basis of operator experience or knowledge of control engineer. There is a growing

interest in model-based fuzzy designs. Fuzzy models and control methods for temperature

control systems are found in the literature [35-40,43,48,49].

Temperature control for most kind of furnaces, such as heat-treatment furnaces deal with

presence of non-linearity with unknown structure, multivariable, time-varying behaviour

of the process, large delays in dynamic channels as well as interaction between the

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different variables, i.e., cross relationship between control parameters. Non-linearity in

heat treatment furnaces is a consequence of convection and radiation heat-transfer

[35,41,42,45,46,49,53].

The task of control system is to maintain the reference rate of temperature change (i.e.,

temperature slope) and attain the temperature reference without overshooting. In this

manner, the initial sets of fuzzy rules have been compiled by compromising between fast

attaining of the desired temperature and avoiding its overshoot.

Loading furnace with different type of loads changes its characteristics and makes it more

sluggish and it could lead to the changes of the temperature response in the closed loop

with the fuzzy controller [42,45].

In continuous, reheating, refineries and open fire furnaces with burning process,

temperature measurement is very difficult or even impossible and also long time delay is

a challenging factor, therefore a large portion of researches in this area is about modeling

a furnace by different system identification methods, model-based control methods,

predictive control and tuning parameters of the existing PID controllers

[7,10,15,22,27,35,39-45,49].

The problems with PID controller applications originate from the object non-linearity,

resulting in mismatches of the real responses and the projected ones.

Apart from non-linearity, there is a problem of furnace characteristics alteration. The

feasible solution is an application of gain-scheduling methods, used in the manner that

the parameters are determined from the set of previously performed measurements or

measurements during the real-time regulated process [2,7,10].

In most applications, a linear model has been used to represent the dynamic behaviour of

the process, namely impulse/step response function, transfer function and state space

model. However, because of severe non-linearities, a fixed linear model for predictive

control might not really result the required performance. On the other hand, its tuning by

using numerical simulations cannot be precisely performed due to the difficulties in

precise modeling of the controlled object [19,27,29,31,37].

In predictive control approach, a model is used to predict output for each action and then

decision maker selects the most favourable action. Afterward the selected control action

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will be applied to the process and subsequently the whole procedure repeats itself at each

control interval [22,24-27,33,49].

The rules of the traditional fuzzy control strategy are stationary and difficult to adapt to

different operating modes, whereas in adaptive rule method, rules are changed responding

to different situations by the weight factors of the input parameters and make the system

adapt to the changing conditions automatically.

For automatic adaptation of fuzzy logic, genetic algorithm (GA) and neural network (NN)

techniques are used to fix the adaptive parameters in the fuzzy control system

[34,37,38,40,43].

Fang [34] studied neural-fuzzy regulator to control temperature of resistance furnace. For

raising learning speed, an improved back propagation algorithm is proposed. The result

of practical operation shows that the system with the neural-fuzzy regulator has a better

static and dynamic characteristic than similar models.

Wang [35] investigated application of fuzzy inference compound method to resistance

furnace temperature control system. According to the characteristics of the resistance

furnace temperature control, i.e. one way temperature rise, large time delay and time

varying parameters, the fuzzy inference compound method was employed to build fuzzy

model and design fuzzy controller. The basic procedure to build fuzzy model and the

table of inquisition were presented. A fuzzy variable was introduced to enhance further

accuracy of fuzzy control and the fuzzy control system with parameters online self-

adjustment was constructed. The simulation result shows that the fuzzy control system

with parameters self-adjustment removes small amplitude oscillation in the system

without parameters self-adjustment and improves steady precision.

Hu [36] developed a fuzzy-neural network intelligent temperature control system of

quench furnace. The weight values of neural networks, parameters of fuzzy membership

functions and inference rules can be automatically adjusted by combined genetic

algorithm with back-propagation algorithm, which results the optimal control of

temperature. The results show that this control system can run effectively with satisfied

temperature precision; in temperature uprising stage, overshoot of temperature is under

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4˚C; in stable stage, the scope of temperature change is controlled within +2˚C, which

meets the need of control veracity of temperature.

Kayama [37] investigated adjusting neural networks for accurate control model tuning in

reheating furnace plants. He proposed adjusting neural networks (AJNNs), which are

extended model of conventional multi-layered neural networks (CNNs), for accurate

model tuning with small tuning numbers. The AJNN consists of two multi-layered neural

networks, namely, a CNN and an error calculation neural network (ECNN) which is

added in parallel to the CNN. The ECNN calculates the output error of the CNN and

subtracts it from the output of the CNN, to obtain accurate tuning values. A training

method for the AJNN is also proposed, where the modified back-propagation developed

for reducing the error of the AJNN and the conventional back-propagation for decreasing

the output of the ECNN, are applied to the AJNN alternately. The AJNN is evaluated

with model tuning of temperature control for reheating furnace plants and is

demonstrated to be effective to improve the accuracy of tuning and decrease tuning

numbers.

Liu [38] presented a high-order-fuzzy CMAC adaptive control, using the fuzzy subset to

partition input state spaces, employing the multi-layer quantification to quantify input

states and utilizing the algebraic product and algebraic sum to integrate the result of

multi-layer quantification. In general, cerebellar model articulation controller (CMAC) is

a linear combination of overlapped basis function. It is a type of local neural network,

which means only a local set of neurons, is activated by a particular input. The high-

order-fuzzy CMAC adaptive controller has better capability of generalization than the

ordinary CMAC. Due to the use of multi-layer quantification, the controller has better

control performance than that simply based on the generalized basic function fuzzy

CMAC. Temperature control experiments on an industrial furnace prove the effectiveness

of the proposed method.

Wang [39] conducted a research on soft sensor model for slab temperature in reheating

furnace. In his work a slab temperature neural network soft sensor model based on fuzzy

clustering has been studied. The approach consists of two components: an FCM (Fuzzy

C-Means) clustering, which classifies training objects into a couple of clusters, and a

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distributed Radial Basis Function (RBF) network, which is used to train each cluster. In

the online stage, the values of membership are computed using an adaptive fuzzy

clustering algorithm for the new object. The proposed approach has been applied to the

slab temperature estimation in an actual reheating furnace. Simulations show that the

approach is effective.

Ma [40] investigated genetic-based fuzzy bed temperature control system of circulating

fluidized bed boiler. A kernel problem in fuzzy control system design is generating the

control rules library. Genetic algorithm is a global optimization algorithm based on

evolutionism. GA can be used to designing fuzzy controller, but the convergence process

usually takes a great deal of time, especially when the standard GA is used to generate the

control rules of MIMO system. It is due to the huge multivariable search space. To

overcome this disadvantage, an improved GA is proposed in which excellent patterns in

chromosome are defined and the genetic operations in GA are regulated by the excellent

patterns, as a result, the convergence of search process is evidently accelerated. Bed

temperature, which determines the operation security and continuance of circulating

fluidized bed boiler, is a very important parameter of CFB. A new regulation strategy of

bed temperature is put forward according to the working characters of CFB, and a fuzzy

bed temperature controller is designed using the improved GA. In the new designing

method, the genetic operations are guided with human experience and heuristic

information. Consequently, fuzzy control rules are created with higher speed. The

simulation results indicate the proposed scheme has good efficiency. It can keep the

stabilization of main steam pressure and bed temperature and meet the need of load.

Fuzzy control of a multiple hearth furnace has been studied by Ramirez [41]. The

schematic of a multiple hearth furnace has been shown in Fig. 1. The system is divided

into different local domains; each one is described by its own rule base. Meta-rules of

classical non-fuzzy inference provide dynamical switching of the most suitable sub-base

among the whole set of sub-bases. The program has two kinds of user interfaces: the

developer’s interface and the operator’s interface. The developer’s interface contains

information that is needed for tuning the fuzzy control system, where controller’s

parameters (e.g., scaling factors, knowledge bases, etc.) are accessible for changes. In the

7

operator’s interface only basic information is presented. Operators can switch the control

system on or off, and change the settings (e.g., set point, limit values of technological

restrictions, etc.) [41]. The objective of process control in a reduction furnace is to

optimize nickel recovery, while minimising fuel consumption and environmental

contamination. This entails the exact control of temperature and gas composition in the

furnace. Controlling the temperature of a multiple hearth furnace is a difficult task. Fast

and extensive changes in operating conditions occur, complicated by non-linear and time-

varying behaviour of the process and interaction between the different variables. Failing

to solve the control problem with a normal PID controller led to development of a

knowledge-based fuzzy controller, which keeps the temperature as close to the set profile

as possible. Such controller is endowed with a set of 60 rule bases, which are dynamically

switched depending on technological constraints and/or operating regions. The algorithm

used for the resulting MIMO controller has a Mamdani-type inference system.

Figure 1: Proposed structure of the installed fuzzy supervisory control system for a multiple hearth furnace [41]

Abilov [42] investigated fuzzy temperature control of industrial refineries furnaces

through combined feedforward/feedback multivariable cascade systems. The proposed

structure has been depicted in Fig. 2.

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Figure 2: Fuzzy adaptive-model based control in industrial refineries furnaces proposed by Abilov

In this work, the application of the multivariable cascade fuzzy advanced control

structure for an industrial AVT furnace is investigated. The feedforward controller takes

care of the large and frequent measurable disturbances. The feedback controller takes

care of any errors that come through the process because of inaccuracies in the

feedforward controller or other unmeasured disturbances. In addition, the feedforward

controller has no effect on the closed loop stability of the system for linear systems. The

denominators of the closed loop transfer functions are unchanged. In a nonlinear system,

the addition of a feedforward fuzzy controller often permits tighter tuning of the feedback

controller because the magnitude of the disturbances is reduced [42]. The purpose was to

improve and apply a multivariable advanced control structure on the basis of fuzzy logic

technique for two flow tubular furnace having widespread applications in petroleum

refinery industries. After analyzing the dynamic properties of furnaces, it has been

concluded that these furnaces are the MIMO processes which have two inputs and two

outputs. There are a lot of reciprocal interactions between input and output variables. For

this reason, equivalent system methods were used to develop advanced control structures

for these furnaces. According to this method, symmetric MIMO system was divided into

two equivalent separate systems.

An adaptive fuzzy approach for the incineration temperature control process has been

studied by Shen [43]. The fuzzy logic strategy with the adaptive factors is used to

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improve the incineration temperature control system and a new correction model is

adopted to determine the proper adaptive factors. There are many factors affecting the

combustion process in incinerators; one of them is how to control the temperature of the

incineration and reduce the emissions. In his work, a second-order model of the adaptive

fuzzy control strategy is adopted to stabilize the combustion temperature and the results

demonstrate that the adaptive control strategy with the adaptive factors is a good method

to achieve the goal of incineration temperature control. The fundamental configuration of

adaptive fuzzy controller for the incineration temperature control process is shown

in Fig. 3.

Figure 3: Fuzzy self-adaptive control proposed by Shen

Application of temperature fuzzy controller in an indirect resistance furnace has been

investigated by Radakovic [44]. The application results of a fuzzy controller of

temperature and its rate of change in indirect resistance chamber furnaces have been

presented. Controller basic structure in an indirect resistance furnace is shown in Fig. 4.

The method of an initial controller tuning based on the computer simulations is described,

where the modelling of the furnace appears as a special problem. Further controller

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tuning was done based on tests performed on the real furnace. The quality of the finally-

adopted controller on the real furnace is assessed by its tracking of the desired response,

regulation robustness with respect to the presence of load in the furnace as well as by a

comparison with the ideal implementation of the Dahlin algorithm for classic PID

control. The experimental part of the work is made using a 5 kW indirect resistance

chamber furnace.

Figure 4: Duty-separated Fuzzy control proposed by Radakovic

In the domain far from the commanded temperature, the control task is to maintain the

temperature slope (maximum or commanded). In the domain close to the commanded

temperature, the slope must not be tracked in order to avoid temperature overshoot, i.e. it

is primary to obtain a convenient approach to the commanded temperature. As a

consequence of separated scopes of duty, control can be implemented via two separate

fuzzy controllers [44].

Gao [45] studied a stable self-tuning fuzzy logic control system for industrial temperature

regulation. A closed-loop control system incorporating fuzzy logic has been developed

for a class of industrial temperature control problems. A unique fuzzy logic controller

(FLC) structure with an efficient realization and a small rule base that can be easily

implemented in existing industrial controllers was proposed. The potential of FLC in both

software simulation and hardware test in an industrial setting was demonstrated. This

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includes compensating for thermo mass changes in the system, dealing with unknown and

variable delays, operating at very different temperature set points without retuning, etc. It

is achieved by implementing, in the FLC, a classical control strategy and an adaptation

mechanism to compensate for the dynamic changes in the system. The proposed FLC was

applied to two different temperature processes and performance and robustness

improvements were observed in both cases. Furthermore, the stability of the FLC is

investigated and a safeguard is established.

An intelligent ladle furnace (ILF) control system has been presented by Sun [46]. The

main functions and system structure has been introduced. The system applied combined

artificial intelligent technology for ladle furnace heat balance calculation and steel

temperature prediction, dynamic energy input optimization and intelligent electrode

control. The application results achieved are given to demonstrate the capability of this

intelligent control system.

The design of functional module of the intelligent fuzzy micro controller based on

80C196 for heat treatment furnace was introduced by Zhu [47]. The rule self-seeking-

optimization fuzzy control algorithm has been studied, simulated and applied to heat

treatment furnace. The running results indicate that the system has reasonable control

scheme, high reliability, advanced control algorithm, self-learning capability, good

tracking property, high static accuracy, small overshoot, friendly man-machine interface

and easy operation.

Balazinski [48] developed fuzzy logic control of industrial heat treatment furnaces. The

application of fuzzy logic to the control system for industrial heat treatment furnaces has

been presented. A modified fuzzy decision support system has been developed to control

the temperature in an industrial nitriding furnace. The results obtained using the fuzzy

logic controller are very good and the system is fully automatic and maintains a very

stable temperature control.

Zou [49] studied fuzzy predictive functional control strategy for decomposing furnace

temperature system of cement rotary kiln. A new fuzzy predictive control method has

been proposed for the decomposing furnace in cement rotary kiln system.

A Takagi-Sugeno fuzzy model for the decomposing furnace is established, which merges

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several linear models together with fuzzy logic. The parameters of fuzzy model can be

modified, depending on the flow of raw material. Based on the dynamic fuzzy model,

incremental predictive functional control arithmetic has been developed to control the

decomposing furnace temperature, improving the robustness of the control system

without adding computational load. Real time control software of this arithmetic has been

developed on the platform of Plantscape discrete control system of Honeywell

Corporation. Application results exhibit the superiority of the proposed method over

conventional ones even on the condition of existing large delay and time-varying

parameter. The cement decomposing rate is improved from 81.5% to 89.1%, and the

control precision of the decomposing furnace temperature is ensured.

A multivariable fuzzy decoupling control system has been developed and applied to

temperature control of hydrogen sintering furnace by Li [50]. The authors learn from

experienced operators of hydrogen sintering furnace and abstract with them from their

observation a number of rules of decoupling control. Then the fuzzy mathematics is used

to make a table whose tabulated values are compensating values for fuzzy decoupling

values. Through using compensating values, control values can be computed and so much

coupling can be eliminated as to make the control of each variable practically

independent.

Wang [51] developed a hybrid intelligent control (HIC) by using the techniques of expert

control and fuzzy neural network for industrial rotary kiln plant. The HIC consists of a

knowledge base, information pre - processor, and intelligent coordinator in a hierarchical

structure. The basic idea is to give an effective control strategy to complex controlled

plant using knowledge - based coordinator so as to achieve the desired performance. The

results of simulation as well as temperature control for industrial rotary kiln furnace were

performed to demonstrate the feasibility and effectiveness of the proposed scheme.

A new developed and designed real-time expert intelligent control system (REICS) for

industrial process control has been introduced by Cai [52]. The global architectures of the

hardware and software of the system have been proposed. A multi-level method of

knowledge representation based on the combination of frame, production rules and real-

time procedures has been discussed, and used to represent the control knowledge and

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algorithms of the control system. Meanwhile, the reasoning mechanism, control strategy

and its flow chart have been presented. The simulation and the practical application of an

industrial rotary kiln furnace for the proposed tool and method have been described.

Zheng [53] studied a real-time fuzzy control for a kind of multivariable object. This paper

describes the application of fuzzy control to a complex object, that of temperature control

for furnace, and develops a three-dimensional fuzzy control table. Electrical furnace with

multiple temperature zones (EFMTZ) is a typical kind of multivariable control object. It

has some characteristics which are harmful to control such as strong coupling,

nonlinearity, time-variant parameters, and so on. For this kind of object, the control

strategy will be divided into two steps. At first, it employs a decoupling strategy based on

feedforward compensation to reduce the coupling between adjacent temperature zones.

Then it applies the fuzzy control strategy to each temperature zone after compensation,

and a three-dimensional fuzzy control table-E, EC, T is specially presented. The results of

practical run show that the control strategy is encouraging.

Adaptive Fuzzy Control

Anderson [54] indicates that adaptive fuzzy controllers are fuzzy controllers with a

mechanism for changing their own characteristics during operation. According to

Driankov [55], adaptive fuzzy controllers may be classified according to which

parameters are adjusted. This classification method results in three major groups:

Adaptation of Scaling Factors

To design a temperature controller for a chemical reactor, Yamashita et al. [56] have

found that different controller gains are required for different stages of operation. To

allow this, an adaptation mechanism was added to the system. This mechanism monitored

the performance of the system and consequently altered the scaling factor on this basis by

using an additional set of fuzzy rules. The alteration of the scaling factors effected a

change in the controller gains and it was found that this approach improved overall

performance significantly. Schemes which adapt the scaling factors on the basis of the

parameters of an adaptive linear process model are given in [57,58].

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Adaptation of FIS Parameters

Some significant publications that describe methods of adapting the FIS parameters are:

which apart from presenting the Fuzzy Model-Reference Learning Control (FMRLC)

method, provides a useful overview of other similar methods [59]; which aims to improve

FMRLC by implementing three methods of focusing the attention of the learning

paradigm [60]; which presents a method identical in concept to the neural feedback-error

learning architecture described in [54] section 3.1.12 [61]; and which defines a set of

heuristic adaptation actions selected by a set of rules based on a series of performance

criteria [62].

Ordonez [63] presents an excellent comparison of indirect and direct adaptive fuzzy

control (IAFC and DAFC respectively) paradigms. In particular, this work compares

these methodologies with each other and with more traditional control methods. It is

found that direct and indirect adaptive fuzzy control methods yield comparable

performance in the case of rotational inverted pendulum and ball-and-beam balancing

problems, and that both methods outperform their non-fuzzy counterparts.

Adaptation of Rules

The first adaptive fuzzy controller was designed by Mamdani and et al. in 1975; it is

called the Self-Organizing Controller (SOC) [55,64-66]. Instead of changing the

characteristics of the existing FIS, the SOC automatically replaces poorly performing

rules with better ones. This is achieved by utilizing a performance monitor and an

adaptation mechanism. The purpose of the performance monitor is to indicate how much

the plant output needs to be changed in order to achieve good performance. The

adaptation mechanism then translates this desired change in the plant output into a

required change in the control signal using a plant model, and generates a new rule which

will effect this change.

15

Direct and Indirect Adaptive Fuzzy Model Based Control

Conceptually, there are two distinct approaches that have been formulated in the design

of a fuzzy adaptive control system: direct and indirect schemes. In the direct method, a

fuzzy system is used to describe the control action and the parameters of the fuzzy system

are adjusted directly to meet the required control objective [67-73]. In contrast with the

direct adaptive scheme, the indirect adaptive approach uses fuzzy systems to estimate the

plant dynamics and then synthesizes a control law based on these estimates [67-71,73-

77]. The indirect fuzzy adaptive controller for SISO uncertain nonlinear systems has been

developed in many investigations [68,71,75,76]. The multi-input multi-output (MIMO)

nonlinear systems are investigated in several articles [67,69,70,74,77].

Fuzzy Adaptive Model Predictive Control

Model Predictive Control (MPC) has recently become one of effective control methods

for handling multivariable control problems. The simplest MPC system uses a linear plant

model. For a highly nonlinear process the linear assumption may lead to unsatisfactory

performance. For better performance and also for nonlinear compensation the adaptive

MPC systems have been recently developed [78-80]. The adaptation is usually achieved

by using the Recursive Least Squares (RLS) parameter estimation technique. However,

adaptation of a single process model over wider operational range may result in a

transient error [81]. Alternatively, fuzzy logic can be used for modeling a non-linear

process system where different rules can be conveniently allocated to represent different

local models of the process [81]. Although there are many representations in fuzzy

systems, Takagi-Sugeno (TS) type fuzzy systems [82] have been widely used in modeling

nonlinear process systems [83]. The TS fuzzy model allows a high dimensional nonlinear

modeling problem to be decomposed into a set of simpler linear local models and the

fuzzy inference interpolates the fuzzy outputs of the local models in a smooth fashion.

Therefore, TS type fuzzy model based MPC strategy recently generated considerable

interests among the researchers [81,83-86]. In many cases [81,83,85] the parameters of

the linear model extracted from the nonlinear fuzzy model are used for linear MPC

formulation at every sampling instant. In other cases,[86] a Nonlinear MPC (NMPC)

16

problem is solved at every step with the nonlinear fuzzy model [84,86]. When the process

is time variant the predefined linear local models will become applicable only for a small

operating region. Introducing more local models may increase the accuracy but at the cost

of heavy computation.

Roy et al. [87] present design of a rule-adaptive fuzzy Model Predictive Control (MPC)

algorithm for controlling temperatures of a multivariable soil-heating process system. The

system uses Takagi-Sugeno (TS) type fuzzy model structure. The control objective is to

track a desired temperature profile at three locations in the soil sample using three heat

sources located at the outer surface of the soil cell. The system recognizes the active

fuzzy rules which are recursively adapted for handling the time-variant behavior of the

process. In order to show the effectiveness, the performance of the proposed scheme is

compared against the non-adaptive fuzzy model based MPC scheme. A classical non-

adaptive MPC is also developed to confirm the superiority of the fuzzy model based

MPC controllers.

Takagi [82] introduced a novel fuzzy logic-based modeling methodology, where a

nonlinear system is divided into a number of linear or nearly linear subsystems. A quasi-

linear empirical model is then developed by means of fuzzy logic for each subsystem.

The model is a rule-based fuzzy implication (FI). The whole process behavior is

characterized by a weighted sum of the outputs from all quasi-linear FIs. The

methodology facilitates the development of a nonlinear model that is essentially a

collection of a number of quasi-linear models regulated by fuzzy logic. It also provides an

opportunity to simplify the design of model predictive controllers. More recently, Huang

et al. [88] have introduced a fuzzy model predictive control (FMPC) approach to design a

control system for a highly nonlinear process system. The approach utilizes the Takagi–

Sugeno modeling methodology to generate a fuzzy convolution model. With this model,

a novel hierarchical control design approach is described.

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The Sugeno Fuzzy Model

Jang [89] proposed an adaptive-network-based fuzzy inference system, which is a fuzzy

inference system implemented in the frame work of adaptive networks. By using a hybrid

learning procedure, the proposed fuzzy system could construct an input-output mapping

based on both human knowledge and stipulated input-output data pairs and could be used

to identify nonlinear components on-line in a control system.

Sugeno fuzzy model proposed by Takagi, Sugeno and Kang [90] is an effort to develop a

systematic approach to generating fuzzy rules from a given input output data set.

Roubos [91] indicates that Takagi Sugeno-fuzzy models are suitable to model a large

class of nonlinear systems [84,92,93]. Fuzzy modeling and identification from measured

data are effective tools for the approximation of uncertain nonlinear systems. So far, most

attention has been devoted to single-input, single-output (SISO) or multi-input, single-

output (MISO) systems. Recently, also methods have been proposed to deal with multi-

input, multi-output (MIMO) systems [94-96]. Most articles deal with various aspects of

multivariable relational models, such as the decomposition of fuzzy relations,

simplification of the models to avoid memory overload, etc. Relatively little attention has

been devoted to the identification of MIMO fuzzy models from input-output data.

Babuška, R. et al. [97] developed a MIMO identification algorithm which uses input-

output data. This algorithm is used to obtain MIMO Takagi-Sugeno models which can be

used for control purposes.

Abonyi [98] presents an adaptation method for Sugeno fuzzy inference systems that

maintain the readability and interpretability of the fuzzy model during and after the

learning process. This approach can be used for the modeling of dynamical systems and

for building adaptive model-based control algorithms for chemical processes. The

gradient-descent based learning algorithm can be used on-line to form an adaptive fuzzy

controller. This ability allows these controllers to be used in applications where the

knowledge to control the process does not exist or the process is subject to changes in its

dynamic characteristics. The proposed approach was applied in an internal model (IMC)

fuzzy control structure based on the inversion of the fuzzy model. The adaptive fuzzy

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controller was applied in the control of a non-linear plant and is shown to be capable of

providing good overall system performance.

Genetic Fuzzy Systems (GFS)

A genetic algorithm (GA) is a parallel, global search technique that emulates operators

[99]. Because, it simultaneously evaluates many points in the search space, it is more

likely to converge toward the global solution. A GA applies operators inspired by the

mechanics of natural selection to a population of binary string encoding the parameter

space at each generation; it explores different areas of the parameter space, and then

directs the search to regions where there is a high probability of finding improved

performance. By working with a population of solutions, the algorithm can effectively

seek many local minima, thereby increasing the likelihood of finding the global

minimum.

A GFS is basically a fuzzy system augmented by a learning process based on a genetic

algorithm (GA). GAs are search algorithms, based on natural genetics, that provide robust

search capabilities in complex spaces, and thereby offer a valid approach to problems

requiring efficient and effective search processes [100-102]. Genetic learning processes

cover different levels of complexity according to the structural changes produced by the

algorithm [103], from the simplest case of parameter optimization to the highest level of

complexity of learning the rule set of a rule based system. Parameter optimization has

been the approach utilized to adapt a wide range of different fuzzy systems, as in genetic

fuzzy clustering or genetic neuro-fuzzy systems [104].

Analysis of the literature shows that the most prominent types of GFSs are genetic fuzzy

rule-based systems (GFRBSs) [105], whose genetic process learns or tunes different

components of a fuzzy rule-based system (FRBS). Fig. 5 shows this conception of a

system where genetic design and fuzzy processing are the two fundamental constituents

[104]. Inside GFRBSs it is possible to distinguish between either parameter optimization

or rule generation processes, that is, adaptation and learning.

19

Figure 5: Genetic fuzzy rule-based systems (GFRBSs)

Belarbi [106] indicates that GA have been used diversely for FLC design either off-line

or on-line although in the latter case computation time is sometimes prohibitive. Off-line

learning is carried through closed loop simulation using a simplified model of the plant

for fitness computation. The search is carried out either in the set of the parameters of the

membership functions and/or the set of rules. Thrift [107], Nishiyama et al. [108], Lee

and Tagaki [109], and Tagaki and Lee [110] used GA through off-line learning to find an

optimal rule base. Karr [111,112] applied GA with binary coding to find good parameters

for the membership functions. The problem is to locate support points for the

membership functions. Since there is an underlying ordering of the fuzzy sets to be

maintained, each point is constrained to lie between a lower and an upper bound.

GA has been used to optimize the parameters of the membership functions as well as the

rule base. Differences between the approaches lie mainly in the type of coding and the

way the membership functions are optimized. Homaifar and Maccormick [113] used

nonbinary integer coding to optimize the rule base and membership function parameters

of the input variables. The summit of the triangular membership functions is kept

constant and only the width of basis is allowed to vary during the search process. While

the particular coding reduces the length of the string it implies additional computation in

the decoding process and during defuzzification. Moreover, extensive testing [114] has

shown that the position of the summit of the triangular fuzzy set of the output variable is

20

more influential than the width of the basis. Linkens and Nyongesa [115] give more

flexibility to the variation of the parameters in particular the summit and the two support

points of the triangular fuzzy sets are allowed to vary at the cost of extra computation and

longer string. Kim and Ziegler [116] propose a global, hierarchical search that includes

the shape and number of fuzzy sets.

Summary of literature review

A research was conducted on the subject within 1995-2005 in Compendex (Search

strategy: heat treatment furnace, temperature control) and 384 articles were found. A

quick review on these articles showed that most of them deal with influence of

temperature control on chemical/metallurgical process and behaviour.

The rest of the articles (≈ 150 articles) could be separated in four following categories:

Hardware control systems

System identification and modeling methods

Efficiency and energy saving

Temperature control systems

A review on “Temperature control systems” shows that during the past 10 years, no

research results have been published in the area of “temperature control in nitriding

furnaces”, except the work done by Balazinski et al. [48], in which the fuzzy controller

has been used in NITREX.

Literature review in temperature control of furnaces leads us to the following results:

Temperature control for most kind of furnaces, such as heat-treatment furnaces deals with

the presence of non-linearity, multivariable and time-varying behaviour of the process.

Non-linear control systems that used to deal with these problems are mostly adaptive,

predictive and fuzzy control.

Apart from non-linearity, there is a problem of furnace characteristics alteration. The

feasible solution is an application of gain-scheduling methods and adaptive control, used

in the manner that the parameters are determined from the set of previously performed

measurements or measurements during the real-time regulated process.

21

The rules of the traditional fuzzy control strategy are stationary and difficult to adapt to

different operating modes, whereas in adaptive rule method, rules are changed responding

to different situations by the weight factors of the input parameters and make the system

adapt to the changing conditions automatically.

For automatic adaptation of fuzzy logic, genetic algorithm (GA) and neural network (NN)

techniques are used to fix the adaptive parameters in the fuzzy control system.

In most applications, a linear model has been used to represent the dynamic behaviour of

the process, however, because of severe non-linearities, a fixed linear model for

predictive control might not really result the required performance. On the other hand, its

tuning by using numerical simulations cannot be precisely performed due to the

difficulties in precise modeling of the controlled object.

There is a growing interest in model-based fuzzy designs in most industrial applications

of fuzzy control.

A large portion of researches in this area is about modeling a furnace by different system

identification methods, model-based control methods, predictive control and tuning

parameters of the existing PID controllers.

The problems with PID controller applications originate from the object non-linearity,

resulting in mismatches of the real responses and the projected ones.

Occurring fast and extensive changes in operating conditions, complicated by non-linear

and time-varying behaviour of the process and interaction between the different variables,

will resulted normal PID controller fail to solve the control problem and led to

development of a knowledge-based fuzzy controller, which keeps the temperature as

close to the set profile as possible.

The mentioned statements lead the review to the aspects of fuzzy adaptive control, fuzzy

model based control and applications of genetic algorithms in fuzzy control. Finally the

results of investigated articles showed that:

22

• The adaptive fuzzy control system with use of a fuzzy model removes small

amplitude oscillation and improves steady precision.

• Fuzzy predictive control with Takagi-Sugeno fuzzy model results the better

performance over conventional ones even on the condition of existing large delay

and time-varying parameter and ensure the control precision of the furnace

temperature.

• Takagi Sugeno-fuzzy models are suitable to model a large class of uncertain

nonlinear systems.

• GAs offer a valid approach to problems requiring efficient and effective search

processes and thereby researchers use GAs to optimize both the parameters of the

membership functions and the rule base.

• Fuzzy control with genetic algorithm adjustment systems can run effectively with

satisfied temperature precision; in temperature uprising stage and in stable stage.

Research methodology

Problem definition

NITREX is a leading company in modern surface treatment of metal and an equipment

manufacturer. NITREX Metal specializes in providing solutions to whose product

manufacturing process involves heat treating of ferrous or non-ferrous materials.

A fuzzy logic controller is taking over the task of temperature control for furnaces in

NITREX. This controller is based on error and deviation of error between actual

temperature and required regime temperature. This controller was developed by

Balazinski in 1999 [48].

Figure 6 presents the simplified scheme of current controller in NITREX:

23

Figure 6: Idea of NITREX temperature control.

In NITREX, the task of temperature control in furnace is dealing with three different

problems:

The first problem is to track the desired temperature rise and also preventing overshoot.

Fig. 7 shows a sample of input (u1: power) and output (y1: furnace temperature) for

nitriding process.

Figure 7: Demonstration of input (u1: power) and output (y1: furnace temperature) during nitriding process

The second problem originated in use of different loads for nitriding process, which

changes the characteristics of the furnace and its response to input power.

24

The last problem is the variety of furnaces. Since there are different models of furnaces

with different characteristic therefore the knowledge base has not the same effect on all

the furnaces, which means each furnace individually needs the modification on

knowledge base.

In NITREX this modification is mostly applied by changing on database i.e. premises and

outputs whereas the rule base remains constant.

Hence designing a general control system is intended which could be used on the

different furnaces (or at least similar ones in the sense of physical characteristic).

Suggested methodology

Based on literature review and the experience of temperature control with classical

controllers and also fuzzy controllers, the suggestions are presented as follows:

Fuzzy Adaptive Model Predictive Control is an effective control method for handling

multivariable nonlinear control problems. Table 1 shows the advantage of this method.

Table 1: Advantages of fuzzy adaptive model predictive control

Control system Advantages Model predictive

control Accurate

Model predictive

control with fuzzy

model

Accurate nonlinear models

Model predictive

control with Takagi-

Sugeno fuzzy model

Accurate nonlinear models

Consist of different local

linear models which could

adapt separately

Figure 8 demonstrates the concept of Fuzzy adaptive model predictive control with

Takagi-Sugeno fuzzy model. In each step controller tries to generate different predicted

outputs and based on the least error with reference line, input with the best fitness would

be selected.

25

Figure 8: The idea of fuzzy adaptive model predictive controller

Furnace Predictive Fuzzy model

Takagi-Sugeno models divide fuzzy model to several linear models and have the ability

to switch smoothly between these local models. Hence, in contrast to global model

estimation, it can be guaranteed that the local models represent the local behavior of the

nonlinear system, and they do not suffer from the effects of compensation.

The idea of prediction is depicted in Fig. 9 based on the past and present temperatures,

the model could predict one or more step-ahead, herein we consider one step.

Figure 9: The idea of step-ahead prediction

Models built with 15 groups of actual data which gathered from nitriding process in a

certain furnace. For comparison 4 groups of data with different loads (not involved in

modeling) were used and the output temperature from model was compared in real time

to actual output of furnace F1. Table 2 shows the data which gathered and used for

modeling and comparison with related load for each process.

26

learning process LBS number of

pairs Training 100 696 Training 1294 1292 Training 640 982 Training 900 2006 Training 440 879 Training 230 1768 Training 308 838 Training 442 853 Training 250 1565 Checking 350 2598 Checking 1232 1189 Checking 656 1060 Testing 250 2837 Testing 440 863 Testing 990 1279

Validation 1194 1176 Validation 120 1681 Validation 550 1025 Validation 280 1890

Table 2: pair of data used for modeling and comparison

Considering dynamic characteristics of furnace, fuzzy models couldn’t map input/output

data based only on input power and output temperature. To overcome this problem, other

data should be used as complementary inputs, such as “current temperature”, “last

changes in temperature”, “last change in power” and the model output could be

considered as “change in the output”, which in each step of simulation, will be added to

the last output.

Also, Loading furnace with different type and amount of load change its characteristics

(i.e. makes it more sluggish) and it can lead to the changes of the temperature response,

therefore, load also could be considered as an input. On the other hand, all these models

could be used to predict one or more-step ahead of output.

For calculating rules in each model, suppose for power, 5 membership functions and for

the rest 3 will be used, then number of rules for different available models will be:

Model A using: load + output + Δ output + input for prediction with 135 Rules

Model B using: load + output + input for prediction with 45 Rules

27

Model C using: load + Δ output + input for prediction with 45 Rules

Model D using: load + input for prediction with 15 Rules

Model E using: output + Δ output + input for prediction with 45 Rules

Model F using: output + input for prediction with 15 Rules

Model G using: Δ output + input for prediction with 15 Rules

Model H using: input for prediction with 5 Rules

It should be noted that in these models input means “overall power” and output means

“overall temperature” and all the above data used as “input” to fuzzy model and the

“output” of fuzzy model is “change in the temperature”.

Considering time delay of the actual furnace, another criterion to choose was how many

step ahead prediction should be used for data samples and modeling, which has been

investigated as well.

Fuzzy rule extraction

The underlying idea of an adaptive fuzzy network is to code the fuzzy if-then rules into a

neural network-like structure and then to use a learning algorithm to minimize the output

error using training data. The ANFIS approach which was implemented for modeling

uses triangular functions for fuzzy sets, zero order linear functions for the rule outputs,

and Sugeno's inference mechanism. The parameters of the network are the mean and

standard deviation of the membership functions (antecedent parameters) and the

coefficients of the output linear functions (consequent parameters). The ANFIS learning

algorithm is then used to obtain these parameters. This learning algorithm is a hybrid

algorithm consisting of the gradient descent and the least-squares estimate techniques.

Using this hybrid algorithm, the rule parameters are repeatedly updated until acceptable

error is reached. Each iteration involves a forward and a backward pass. In the forward

pass, the antecedent parameters are fixed and the consequent parameters are obtained

using the linear least-squares estimate. In the backward pass, the consequent parameters

are fixed and the output error is propagated back through the network and the antecedent

parameters are updated accordingly using the gradient descent method. 100 epochs used

for each learning process.

28

Fuzzy model optimization

After comparison between different models, Model E with 7 membership function for

input (overall power such as extreme low, very low, low, medium, high, very high,

extreme high), 3 membership functions for output (overall temperature such as low,

medium, high) and 3 membership functions for change in last output (change in overall

temperature as low rate, medium rate, high rate) with triangular shapes with weighted

average, defuzzification method and one step ahead of prediction were observed to have

the best mapping results (with 63 rules). Results of this comparison for all models were

presented in Table 3. Digit numbers which follow the model name are number of step-

ahead predictions. Table 3: Comparison between mean square errors of fuzzy models

A1 B1 C1 D1 E1 F1 G1 H1 model with one step ahead prediction -255.451 95.82266 85.83427 77.46621 86.2555 95.14666 87.43016 81.0757

A2 B2 C2 D2 E2 F2 G2 H2 model with two step ahead prediction 83.89512 94.92661 92.74462 78.33622 67.54981 95.08485 94.18364 82.74816

A3 B3 C3 D3 E3 F3 G3 H3 model with three step ahead prediction 95.58905 94.87282 92.54401 78.73823 50.69612 95.05 93.60554 83.12422

A4 B4 C4 D4 E4 F4 G4 H4 model with four step ahead prediction 95.6297 94.82405 91.63548 79.10944 78.36504 95.00928 93.01039 83.49109

333 335 336 337 355 535 555 model E1 with different

membership functions

93.80307 66.2487 93.23977 99.57447 89.37164 97.56796 92.20287

The selected fuzzy model has %99.57 fitness to actual output temperature and root mean

square error= 0.4º C. (validation with 4 loads which were not used for modeling)

Inputs for this model are: current power, current temperature and last change in

temperature and the output for this model are one step-ahead prediction of the change in

the temperature.

Fig. 10 demonstrates the idea of Takagi-Sugeno model with 3x3x7=63 rules.

29

Figure 10: Fuzzy model using: output (with 3 membership functions) + Δ output (with 3 membership

functions) + input (with 7 membership functions) for one step-ahead prediction

ANFIS (adaptive-network-based fuzzy inference system Fuzzy control) has the ability of

on-line and off-line adaptations. It should be considered that the data for modeling

gathered during a certain regime of process, this data is not sufficient to map completely

the plant. When performing on-line identification, the data distribution can usually not be

influenced. Therefore, two difficulties may arise: insufficient excitation in the frequency

and in the amplitude range.

The first problem of insufficient dynamic excitation is known from linear model

identification. Often, processes are operated at one set point for a long time, and it is

obvious that dynamic models cannot be estimated without dynamic excitation.

However, the second problem of insufficient static excitation arises exclusively for

nonlinear models. In many practical situations, the process will remain within one

operating regime for a long time. The challenge for nonlinear on-line identification is to

prevent all the parameters of the model from adapting to this single operation point, and

consequently unlearning all the previously trained nonlinear process behavior.

On the other hand, for the off-line identification a representative training data set can be

collected that covers a wide frequency and amplitude range. Measurements from many

operating conditions can be included, and badly exciting data can be excluded.

Therefore, we consider off-line adaptation for each furnace. Since that ANFIS networks

has the ability to adapt, we will provide a strategy to tune the model for each furnace

based on input-output data and these models will be implemented in fuzzy control system

for each different furnace.

30

The predictive controller has a feed forward structure. We will add a correction factor to

input parameters of plant within an adaptive fuzzy controller. This factor will be adapted

based on feedback signal from plant and takes over the task of robustness as well as

stability of the system since this controller will be considered as a supervisory controller.

Validation

A genetic algorithm (GA) is a parallel, global search technique that emulates operators.

Because it simultaneously evaluates many points in the search space, it is more likely to

converge toward the global solution. It explores different areas of the parameter space,

and then directs the search to regions where there is a high probability of finding

improved performance. By working with a population of solutions, the algorithm can

effectively seek many local minima, thereby increasing the likelihood of finding the

global minimum.

Genetic Algorithms could be used in two different aspects: rule generation and parameter

optimization.

Rule generation Genetic algorithms could be used to adjust membership functions and tuning fuzzy rules

of supervisory controller. Since this controller will implemented as a correction factor to

inputs, GA could generate appropriate fuzzy rules after gathering data of predictive

controller.

Parameter optimization

Genetic algorithm is an appropriate technique to find best matches on inputs to fuzzy

model in ach step, instead of searching whole possible inputs which results in time and

calculation consumption in each step. Based on the ability of Gas in global search, the

results are insured to be the best fit to reference line.

Conclusion

Fig. 11 shows the methodology for designing the control system.

31

Figure 11: methodology

32

Contribution

Our contribution in this research would be:

1. Define a strategy to model different nitriding furnaces based on Takagi-Sugeno

models.

2. Design a predictive fuzzy model based controller adaptive to predicted error.

3. Design an adaptive predictive controller with modified rule base, using Genetic

Algorithms to generate data for prediction.

Time chart

Finally time chart for this research is presented as follows:

33

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