Multyiple Model Indutrial Tubular Het Exchanger System

8/3/2019 Multyiple Model Indutrial Tubular Het Exchanger System

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Appl Intell (2011) 34: 127140

DOI 10.1007/s10489-009-0185-8

An intelligent multiple models based predictive control schemewith its application to industrial tubular heat exchanger system

A.H. Mazinan N. Sadati

Published online: 16 June 2009

Springer Science+Business Media, LLC 2009

Abstract The purpose of this paper is to deal with a novel

intelligent predictive control scheme using the multiple

models strategy with its application to an industrial tubu-

lar heat exchanger system. The main idea of the strategy

proposed here is to represent the operating environments of

the system, which have a wide range of variation in the span

of time by several local explicit linear models. In line with

this strategy, the well-known linear generalized predictive

control (LGPC) schemes are initially designed correspond-

ing to each one of the linear models of the system. After

that, the best model of the system and the LGPC control

action are precisely identified, at each instant of time, by an

intelligent decision maker scheme (IDMS), which is playing

the so important role in realizing the finalized control action

for the system. In such a case, as soon as each model could

be identified as the best model, the adaptive algorithm is

implemented on the both chosen model and the correspond-

ing predictive control schemes. In conclusion, for having a

good tracking performance, the predictive control action is

instantly updated and is also applied to the system, at each

instant of time. In order to demonstrate the effectiveness of

A.H. Mazinan ()

Islamic Azad University (IAU), South Tehran Branch, Tehran,

Iran

e-mail: [email protected]

N. Sadati

Electrical and Computer Engineering Department, University

of British Columbia, Vancouver, Canada


N. Sadati

Electrical Engineering Department, Sharif University

of Technology, Tehran, Iran


the proposed approach, simulations are carried out and the

results are compared with those obtained using a nonlinearGPC (NLGPC) scheme as a benchmark approach realized

based on the Wiener model of the system. In agreement with

these results, the validity of the proposed control scheme can

tangibly be verified.

Keywords Fuzzy adaptive predictive control scheme

Nonlinear generalized predictive control scheme Multiple

models strategy Intelligent decision maker scheme

Tubular heat exchanger system

1 Introduction

The linear model based predictive control (LMBPC) scheme

has been extensively used in many control areas and acad-

emic centers, since it has a good performance, as long as

we are using an explicit linear model of the system. In most

applications of the LMBPC family, such as linear model al-

gorithmic control (LMAC), linear dynamic matrix control

(LDMC), linear generalized predictive control (LGPC) and

other related techniques, the process is represented over its

operating environment by using an explicit linear model [1

10]. In this paper, the LGPC scheme is used for controlling

an industrial tubular heat exchanger system. This controlleris realized based on the explicit use of process model to pre-

dict the controlled variables over a specified range of time

horizon. In this scheme, an optimal control is obtained by

optimizing an objective function that minimizes the con-

trol effort and the error between the predicted output and

the set point, during the prediction and control horizon. As

we know, the LGPC method is realized based on a single

fixed linear model or slowly adaptive model of the system.

Here, it assumes that the operating environment is either
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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128 A.H. Mazinan, N. Sadati

time invariant or slowly time variant in the span of time.

In this case, the LGPC method based on the linear mod-

els are well behaved for the linear processes, but when the

operating environment region is extended, the nonlinearity

of the process cannot be ignored. In practical applications

such as the tubular heat exchanger system, due to the co-

efficients variation, the system needs to operate in multiple

operating environments, which may change abruptly from

one to another [11]. An appropriate strategy to improve the

LGPC scheme, while we are having a nonlinear system is

to use the multiple models control strategy, if the models

are approximately available for different operating environ-

ments. In fact, the main idea of multiple models control ap-

proach is to determine the best model, so to activate the cor-

responding controller. The multiple models control strategy

has been mentioned by several researchers such as Madani,

Guerci, Ning, Wang, Gang and others [1226]. In the con-

trol strategy proposed, the best model identification mecha-

nism and the finalized control action generation are realized

by a new intelligent decision maker scheme (IDMS), where

the identification mechanism presented is realized in associ-

ation with the both fuzzy-based adaptive Kalman filter and

fuzzy-based weight generation approaches and also the fi-

nalized control action generation is realized based on the

soft switching technique. In line with this strategy, as soon

as the best model of the system is quite identified by the

proposed IDSM, the adaptive algorithm is implemented on

the chosen model and the corresponding LGPC controller.

Hereinafter, for having a good tracking performance, both

in desired set point variation and in system coefficients vari-

ation, the finalized LGPC control action is applied to the

system, at each instant of time. In fact, the system with wide

and rapid variation in coefficients could easily be controlled

in the strategy proposed. The remainder of this paper is or-

ganized as follows. The tubular heat exchanger system mod-

eling is presented in Sect. 2. The proposed multiple models

control strategy and the nonlinear GPC approach are pre-

sented in Sects. 3 and 4, respectively. The simulation results

and the concluding remarks are finally given in Sects. 5 and

6, respectively.

2 Tubular heat exchanger system modeling

The heat exchanger system is a process that is used tochange the temperature distribution of two materials, when

they are in direct or indirect contacts [2732]. It has both the

inner and the shell tubes with concurrent reactions. The fluid

flows through the inner tube and its temperature is varied by

another fluid which flows concurrently around it. The tem-

perature and the flow rate of the fluid not only change with

respect to time but also change along the axial direction, as

shown in Fig. 1. In order to model the heat exchanger sys-

tem, the following parameters are now defined : section

Fig. 1 Diagram of a tubular heat exchanger system

area of the tube (m2), : fluid density (kg/m3), v: fluid ve-

locity (m/s), x: incremental element in tube (m), Tx : tem-

perature of x (K), d: internal diameter of the tube (m), U:

overall heat transfer coefficient (W/m2 K), Cp : specific heat

capacity (J/kgK).

The dynamics of the heat exchanger system is described

by the partial differential equations (PDEs). Thus, it is truly

used as an infinite dimensional system. In this case, the tem-

perature distribution of an incremental element x, along x,

based on the principle of conservation of energy, at the time

t, could be given as

CpxT

t= Cpv(Tx Tx+x) + UdxT (2.1)

where CpxTt

denotes the accumulation of energy in

x, CpvTx denotes the convection flow of the energy

into x, CpvTx+x also denotes the convection flow of

the energy out ofx and finally UdxT represents the

heat transfer to x. It should be assumed that for modeling

the tubular heat exchanger system, the fluid velocity varia-

tion should be negligible, i.e., to be independent of x. Also

the fluid temperature of the shell tube should be constant.

Now, by assuming x x , the obtained PDEs describing

the system could be written as

CpT

t= Cpv

T

x+ UdT (2.2)

In such a case, by using Tt and Ts as the temperature para-

meters in the inner tube and the shell tube, respectively, we

can have the following

Ttt

= vtTtx

+ atTs atTt; at =U d

ttCpt( 1

sec.)

Tst

= vsTsx

+ as Tt as Ts ; as =U d

s s Cps( 1

sec.)

(2.3)

Also by defining Tt and Ts as the outlet and the inlet of thesystem and assuming s =

t, we can deduce the following

Tt(x,s)

x+

s + at

vtTt(x,s) =

at

vtTs (x,s) (2.4)

Hence, the outlet temperatures in terms of the inlet temper-

atures and the x, could be deduced as

Tt(x,s) = exp

x

vt(s + at)

+

at

s + atTs (x,s) (2.5)


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An intelligent multiple models based predictive control scheme with its application to industrial tubular heat 129

The system modeling results should uniformly be divided

into small incremental elements, while the boundary condi-

tions are given at x = kN; k = 0, 1, 2, . . . , n. Therefore, the

system temperature could be represented as

Tt k = Tt(kN, s), T sk = Ts (kN,s) (2.6)

where Ttk and Tsk are given as the temperatures at the

kth point of the inner tube and the shell tube, respectively.Hence, using (2.5) and (2.6), the outlet temperature at kth

point of the inner tube could now be given as

Tt k = exp

kN

vt(s + at)

+

at

s + atTsk (2.7)

Now, the system transfer function could also be written as

Ttk

Tsk=

at

s + at

1 exp

kN

vt(s + at)

(2.8)

Moreover, the obtained results could be expressed in terms

of the valve pressure, i.e., TtkPv

, by using

KvPv U d

kN0

(Tsk Ttk )dx = CsTsk

t(2.9)

Also by using (2.8) at x = kN, we could deduce the follow-

ing

Tsk Ttk

= Tsk

s

s + at+

at

s + atexp

x

vt(s + at)

(2.10)

Here, Tsk is defined as constant temperature with respect to

x, i.e.,

Ts0 = Ts1 = = Tsk = ct e (2.11)

Hereinafter, by using (2.9), (2.10) and (2.11), we could have

the following

Tsk

U d

kN s

s + at+

atvt

(s + at)2

1 exp

kN

vt(s + at)

+ sCs

= KvPv

(2.12)

As a consequence, the tubular heat exchanger modeling

could be resulted using (2.8) and (2.12) as

Tt k

Pv=

k1(s)

aa1t s2 + (a + kN a1t )s +

vts+at

(s)(2.13)

where Kv, ,P v and Cs are the valve gain, the compressed

steam temperature of the shell tube, the valve pressure and

finally the shell tube capacitance, respectively. Also (s), k1and a are given as 1 exp( kN

vt(s + at)),

kvU d

and CsU d

,

respectively.

3 The proposed multiple models strategy

The multiple models control strategy presented here is an

approach for controlling the complex systems, where the

system parameters may abruptly change in the span of a

specified variation, at each instant of time. In fact, the con-

trol strategy operates in multiple operating environments,

which may change from one to another. Here, the system

behavior is either nonlinear or linear time variant, and a lin-

ear fixed model may not really lead to the expected perfor-

mance. In accordance with Fig. 2, a good approach for de-

signing the linear controllers to deal with the complex sys-

tems is to use multiple models control strategy. To realize

the strategy presented, some models which cover the differ-

ent operating environments of the system must first be iden-

tified and an appropriate controller must also be designed

for each one of them.

It should be noted that the multiple models strategy pre-

sented is described to define some models corresponding to

different operating environments of the system, to design thelocal controllers corresponding to each one of the predefined

models, to identify the best model of the system, to select the

appropriate control action and finally to generate the final-

ized control action for the system, at each interval of time.

To introduce the achieved specification of the proposed mul-

tiple model control strategy, we can say that the wide range

of system coefficients variation could be covered. In this

way, the weight generation mechanism is realized based on

the novel fuzzy-based approach to generate accurate weights

Fig. 2 The scheme of the proposed multiple models strategy


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Realizing the best model identification mechanism, us-

ing the fuzzy-based adaptive Kalman filter and the fuzzy-

based weight generator approaches.

Selecting the models and the corresponding controllers

status in the fixed or the adaptive situations.

Generating the finalized control action, using the soft

switching technique.

stabling the system performance under both the system

coefficients and the desired set point variations.

As it can be seen from the proposed multiple models con-

trol strategy, the IDMS has the several inputs and outputs,

where the desired set point, the finalized control action; u,

cmp and finally ccp; p = 1, 2, . . . , r are used as the output

signals of the IDMS. Also ymp and ucp; p = 1, 2, . . . , r are

used as the input signals of the IDMS in association with

the proposed control strategy. Based on these input-output

signals, all the mentioned tasks must appropriately be im-

plemented through the IDMS, where the details of them are

now given in the best model identification mechanism and

the finalized control action generation sections as follows.

3.2 The best model identification mechanism

The best model identification mechanism is realized to iden-

tify the best model of the system, at each instant of time,

when we are suddenly encountered with both the system co-

efficients and the desired set point variations. In fact, the

main idea of the proposed mechanism is to identify both

the best model of the system (BM) and the deviated models

from the best model of the system (DFBM), as long as the

wide range of variation in the system coefficients and in the

desired set point could be taken place. The mechanism pro-

posed here, as a subsystem of the intelligent decision maker

scheme (IDMS), has the so important role in this control

strategy. The closed loop stability of the strategy may un-

acceptably be changed with system coefficients variations,

provided that the best model identification mechanism can-

not work correctly with respect to time. Meanwhile, as long

as these parameters are rapidly changed in a wide range of

variation, the applicability of the best model identification

mechanism may actually be deteriorated. It means that the

closed loop stability cannot truly be accepted, in such a case.

In the mechanism presented, the controller weight parame-ters; wp,k , p = 1, 2, . . . , r , k = 1, 2, . . . , should accu-

rately be varied to appropriate value, i.e., weight parameters

must be adapted to the ones, as soon as the corresponding

model state estimation error; ep,k , is close to the acceptable

minimum values. Hereinafter, as soon as each one of the

models of the system could be identified as the best cho-

sen model, the corresponding output of the selector system,

i.e., cmp ; p = 1, 2, . . . , r can cause to change the chosen

model from fixed to adaptive parameters. In addition, c cp;

p = 1, 2, . . . , r can cause to change the corresponding con-

troller from fixed to adaptive parameters.

To demonstrate the proposed mechanism in details, the

fuzzy-based adaptive Kalman filter (FAKF) and also fuzzy-

based weight generators (FWG) must first be organized.

In this way, FAKF#p ; p = 1, 2, . . . , r is used to obtain the

model states estimation error; ep,k , p = 1, 2, . . . , r , where

FWG is also used to generate the appropriate controller

weight signals of the corresponding ep,k . In fact, to realize

the proposed approach, the FAKF and the FWG must ap-

propriately be realized, when the statistical behavior of the

system inputs and outputs could exactly be known. Now,

the best model identification mechanism can briefly be de-

scribed as follows

ep,k Min wp,k 1; i.e.,

F /A Model#p BM(adaptive model).

ep,k Max wp,k 0; i.e.,

F /A Model#p DFBM (fixed model).

(3.6)

Realization of the best model identification mechanism

based on the FAKF and the FWG is now described in the

proceeding sections.

3.2.1 The fuzzy-based adaptive Kalman filter approach

The fuzzy-based adaptive Kalman filter; FAKF, has been

used to estimate the model states, as long as the linear model

state spaces, i.e., Ap, Bp and Cp; p = 1, 2, . . . , r could be

given. In association with this matter, the linear single input-

single output model of the system can be described as

xk+1 = Ak+1,kxk + Bkuk + wkyk = Ckxk + vk

(3.7)

where xk is given as the system state vector, yk is given as

the scalar measurement, Ak+1,k is given as the system state

matrix, Ck is given as the measurement vector, wk (o,Q)

is given as the process Gaussian white noise, vk (o,R) is

also given as the measurement Gaussian white noise and fi-

nally R and Q are given as the scalar measurement noise

covariance and the system noise covariance matrix, respec-

tively. Now, the adaptive Kalman filter approach could be

described as

xk = xk,k1 + Kkek

Pk,k1 = Ak,k1Pk1ATk,k1 + Qk

Kk = Pk,k1CTk (CkPk,k1C

Tk + Rk)

1

Pk = (I KkCk)Pk,k1

(3.8)

To realize the approach presented, at the kth instant of time,

the posterior covariance matrix; Pk,k1, and the prior co-

variance matrix; Pk , must instantly be obtained. In fact, the


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system states as the output of the approach should be esti-

mated using the Kalman gain; Kk , and the following model

states estimation error

ek = yk yk (3.9)

where Qk and Rk must be adapted using a fuzzy-based sys-

tem. The parameters mentioned could accurately be varied

to the appropriate values, so that the state estimation errors

could be close to the desired values. To realize the FAKF,

the fuzzy-based system presented determines the value of,

where Qk and Rk must be followed as

Rk = R2(k+1), Qk = Q

2(k+1) (3.10)

In this way, Q and R are given as the constant matrices

and also must be chosen either equal or greater than one.

Now, for having high accuracy in the fuzzy-based system,

the fuzzy set parameters are initially obtained from the GA

algorithm [4855]. The obtained fuzzy sets are also shown

in Fig. 3, where Z, S, M and L denote the zero, the small, the

medium and finally the large fuzzy sets, respectively. Also

the rules of the fuzzy-based Kalman filter is tabulated in Ta-

ble 1.

Fig. 3 The fuzzy sets of FAKF scheme

Table 1 The fuzzy rule based of Kalman filter

Pe

Me

Z S L

Z S Z Z

S Z L M

L L M Z

In the same way, the error estimation covariance matrix;

Pe , and the error estimation mean value; Me , could be de-

fined asPe = CkPk,k1C

Tk + Rk

Me =1

Ne

ki=kNe+1

ei eTi

(3.11)

where Ne denotes the size of the mean value window.

3.2.2 The fuzzy-based weight generator approach

The fuzzy-based weight generator (FWG) approach pre-

sented here is used to generate the appropriate weight sig-

nals; wp,k , p = 1, 2, . . . , r , as long as we are encountered

with variation in the system coefficients and also in the de-

sired set point, abruptly. Based on this approach, the FWG

must be positioned in sequence with the FAKF. It means

that the FWG is realized based on the their input data;

ep,k , p = 1, 2, . . . , r , that are generated of FAKF. To pre-

vent the random weight variation, the stability of the pro-

posed FGW could relatively be guaranteed by using the fol-

lowing performance index

Jp,k = e2p,k(t ) +

kj =0

exp((k j))e2p,j ;

0; , > 0 (3.12)

Here, ep,k denotes the pth model state estimation error, at

the kth instant of time. The above performance index aims

to use the model states estimation errors, using the past to

the present time. In other words, while disturbance takes

place abruptly in the system, the performance index could

reject the noisy data from ep,k , where the past data are used

in this approach. In such a case, the performance index pa-

rameters are given as; , and , where and are the

weighting factors on the instantaneous measures and the

long term accuracy, respectively. In addition, is a forget-

ting factor, which assures the boundedness of the criterion

for the bounded ep,k . Also in order to prevent the rapid un-

wanted changes in the mechanism presented, it is better to

apply the achieved weights in the minimum time delay to

the control strategy. Also an effective way to increase the

weight generation accuracy is to apply the weights average

in periods of time to this control strategy. In such a case,

the unwanted changes have no effect on the system perfor-

mance. Now, the approach presented here is realized based

on a novel fuzzy-based algorithm, given by

Defining the some performance indexes, i.e., Jp,k ; p =

1, 2, . . . , r, k = 1, 2, . . . , .

Determining the minimum value of performance indexes

and also the maximum acceptable value of performance

indexes, i.e., Jmin and Jmax , respectively.


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Defining the acceptable, the conditionally acceptable and

the unacceptable fuzzy sets, i.e., AFS, CAFS and UAFS,

respectively, for each one of the performance indexes.

If the performance indexes, i.e., Jp,k is obtained in the

AFS, the corresponding model; F /A Model#p, p =

1, 2, . . . , r , should now be identified as the best chosen

model of the system and the algorithm stopped, otherwise

the rest of the algorithm must be followed.

Defining the some decision maker parameters; (p) =

Jp,k Jmin; p = 1, 2, . . . , r .

Defining the fuzzy sets corresponding to the acceptable

decision and the unacceptable decision; ADFS, UDFS, re-

spectively, for each one of the decision maker parameters;

(p).

Identifying the best predefined model of the system;

F /AModel#p; p = 1, 2, . . . , r in the following fuzzy rule

based system

IF Jp,k is AFS THEN F /A Model#p BM

IF Jp,k is CAFS AND (p) is ADFS

THEN F /A Model#p BM

IF Jp,k is CAFS AND (p) is UDFS

THEN F /A Model#p DBFM

IF Jp,k is UAFS THEN F /A Model#p DFBM

Defining the fuzzy sets corresponding to low value and

high value; LVFS, HVFS, respectively, to generate the

controller weights parameters.

Calculating the controller weights parameters based on

the predefined models; F /A Model#p , in the followingfuzzy rule based system

IF F /A Model#1 BM AND F /A Model#2 DFBM

AND, .. . , AND

F /A Model#r DFBM

THEN w1,k is HVFS, w2,k is LVFS, .. . , wp,k is LVFS

IF F /A Model#1 DFBM AND F /A Model#2 BM

AND, .. . , AND

F /A Model#r DFBM

THEN w1,k is LVFS, w2,k is HVFS, .. . , wp,k is LVFS

...

IF F /A Model#1 DFBM AND F /A Model#2 DFBM

AND, .. . , AND

F /A Model#r BM

THEN w1,k is LVFS, w2,k is LVFS, .. . , wp,k is HVFS

where the fuzzy sets of the performance indexes; Jp,k , and

the decision maker parameters; (p), are given in Figs. 4 to

5, respectively.

Also the fuzzy sets of the controller weight parameters;

wp,k , are given in Fig. 6.

Regarding the proposed fuzzy-based weight generator

approach, the best model of the system could instantly be

identified for the system, as soon as the system coefficients

variation is abruptly implemented on the control strategy

proposed.

3.3 The finalized control action generation

The finalized control action generation is realized by the

IDSM scheme, in this proposed control strategy, as men-

tioned before. In reality, this subsystem is used to generate

an appropriate control action for the system. In this way,

as soon as the system coefficients are abruptly varied, the

control action must be adapted to the appropriate value. In

Fig. 4 The scheme of the fuzzy sets of the performance indexes

Fig. 5 The scheme of the fuzzy sets of the decision maker parameters

Fig. 6 The scheme of the fuzzy sets of the controller weight parame-

ters


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fact, the system coefficients variation must be compensated

by an appropriate control action, at each instant of time.

On the other hand, the success of the proposed strategy is

quite seen in proposed appropriate control action genera-

tion. As introduced in the multiple models strategy before,

the F /A Cont#p; p = 1, 2, . . . , r as the local controllers are

realized based on the concept of the LGPC scheme, in this

paper. Here, the controller designing is realized based on

the predefined explicit linear model of the system. In this

case, the finalized control action could be realized by a soft

switching technique, i.e., the linear combination of the local

controllers, given by

uk =

rp=1

wp,k ucp,k,

rp=1

wp,k = 1 (3.13)

where r is given as the number of appropriate local LGPC

controllers, wp,k is given as the appropriate weight of the

pth local LGPC controller, at the kth instant of time, that is

given by the best model identification mechanism, ucp,k isalso given as the pth local LGPC output and finally uk is

given as the finalized control action. Based on this strategy,

the control action is adapted to appropriate value and also is

applied to the system, at the kth instant of time.

4 Nonlinear GPC approach

In this section, a nonlinear GPC (NLGPC) approach for con-

trolling an industrial tubular heat exchanger system is pro-

posed [56, 57]. As we know, the LGPC approach is a well-

known control strategy used both in industrial and academicenvironments, for deriving the linear systems. So nonlinear

systems cannot appropriately be controlled by this approach.

Here, we need to modify the traditional LGPC approach in

its present form, where it could be used for controlling the

nonlinear systems as well. The strategy is shown in Fig. 7,

where u(k), yLm(k) and yNm (k) denote the control action, the

linear model output and the nonlinear model output, respec-

tively.

For realizing the NLGPC approach, we first need to ob-

tain linear and nonlinear parts of the Wiener model of the

system that is shown in Fig. 8. The main purpose of realizing

Fig. 7 The nonlinear GPC approach in controlling the heat exchanger

the Wiener model of the system is to remove the nonlinear-

ity of the system, when the inverse of the nonlinear function

of the Wiener model could be used in sequence with the sys-

tem, as shown in this strategy.

Based on this approach, the linear part of the Wiener

model could be used as the model of the system. Moreover,

for designing a control strategy, control engineers normally

need to have an initial model of the system, which would

give them a scope about the structure of the system under

investigation. This initial model allows them to use a sim-

ulation platform, where control strategy could be tested be-

fore being transferred into the real time environment. Hence

in most cases, the structure of the model including linearity

and nonlinearity could be known. It means the various struc-

tures lead to the same linearity and nonlinearity effect. In

this case, for realizing the Wiener model of the system, the

nonlinear model output; yNm (k), could be represented, when

the linear model output; yLm(k), is obtained. Here, by using

the recursive least square (RLS) identification algorithm, the

linear part of the Wiener model could be identified. In addi-tion, the nonlinear part of the Wiener model could also be

expressed as

yNm (k) = f (yLm(k))

= yNm (0) + 0 tanh(0 (yLm(k) y

Lm(0))) (4.1)

where 0 and 0 denote the nonlinear model coefficients. We

know that the LGPC approach must be used with linear sys-

tem and the NLGPC approach must also be used with non-

linear system, so we have to find the Wiener model of the

system that is shown, in this approach. Now, by having the

obtained results, the nonlinearity of the system could be re-

moved using the inverse of the nonlinear function; NLM1,

as shown in the proposed strategy. As we know, a sequence

of the future model outputs using the system modeling could

be obtained by the following j -step ahead predictor of the

LGPC algorithm

yLm(k + j ) = Hj (q1)u(k 1) + Gj (q

1)u(k + j 1)

+ Fj (q1)yLm(k); j = N1, . . . , N 2 (4.2)

where Fj (q1), Hj (q

1) and Gj (q1) are all given as

Fj (q

1) = [FN1 (q1) , . . . , F N2 (q

1)]T

Hj (q1) = [HN1 (q

1) , . . . , H N2 (q1)]T

Gj (q1) = [GN1 (q

1) , . . . , GN2 (q1)]T

(4.3)

Fig. 8 The Wiener model scheme of the heat exchanger


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Here, the gji (q

1)s are denoted as the coefficients of

Gj (q1) matrix polynomials, which correspond to the sys-

tem step response values, given by

Gj (q1)

=

gjN1

(q1) gjN11

(q1) . . . 0

gj

N1+1(q1) g

jN1

(q1) . . . 0

......

......

gjN2

(q1) gj

N21(q1) . . . g

j

N2Nu+1(q1)

(4.4)

Meanwhile, N2 N1 + 1 and Nu are given as the predic-

tion horizon and the control horizon, respectively. After-

ward, Fj (q1), Hj (q

1) and Gj (q1) could be obtained

using the following Diophantine equation, i.e.,

1 = Ej (q1)A(q1)(q1) + qj Fj (q

1) (4.5)

where we could have

Ej (q1)B(q1) = Gj (q

1) + qj Hj (q1) (4.6)

Here, A(q1) and B(q 1) could be obtained using the RLS

identification algorithm, as the CARIMA model of the sys-

tem, and are adapted, at each instant of time. Hereinafter, by

using the obtained results, we could calculate a sequence,

i.e., j = N1, . . . , N 2, of future nonlinear part of the Wiener

model output as

yNm (k + j ) = f (yLm(k + j ))

=

yN

m (0) + 0 tanh(0 (

yL

m(k + j )

yL

m(0)))(4.7)

Afterward, the manipulated variable; u(k), could be ob-

tained by optimizing the following cost function

JNLGPC =

N2j =N1

( yNm (k + j ) r(k + j ))2

Nuj =1

u2(k + j 1) (4.8)

where r(k) and denote the desired set point and controlweight coefficients, respectively. In this strategy, the NL-

GPC control action; u(k), is finally obtained by using the

following discrete filter

Hf(q1) =

u(k)

u(k)=

1

1 q1(4.9)

where q1 denotes the delay term. As a consequence,

according to Fig. 7, realization of the proposed NLGPC

scheme could be summarized as

Calculating a sequence of future nonlinear model outputs

based on the proposed nonlinear function, using (4.1).

Identifying the linear part of the Wiener model of the sys-

tem based on the RLS identification algorithm and also

calculating a sequence of future linear model by the GPC

algorithm, using (4.2).

Obtaining the NLGPC manipulated variables by optimiz-

ing the proposed cost function, using (4.8).

Obtaining the NLGPC control action based on the dis-

crete filter, using (4.9).

5 Simulation results

To consider the applicability of the proposed approach, a

tubular heat exchanger system, which has the many in-

dustrial environments such as food processing, automotive,

aerospace, metallurgy, pulp and paper, fertilizers, chemicals-

petrochemicals and cement is considered for simulation. As

it can be seen, the fluid of the inner tube at x = Ln = 2.5 m,

t = 0.15 m2 and vt = 0.1 m/s has a wide variation in the

span of time, as long as the water, steam, engine oil, min-

eral oil, palm oil, white oil, vegetable oil, dry air, milk, liq-

uid metal, petroleum jelly, petroleum resin and other related

liquids could be used as the fluid of the inner tube. More-

over, the steam is used as the fluid of the shell tube, in this

simulation. In such a case, the inner tube fluid is used as

an outlet of the system and the shell tube fluid is also used

as an inlet of the system. Here, the inner tube temperature

should be adjusted by commanded valve pressure; Pv , on the

shell tube. Here, the tracking performance of the proposed

scheme, called by the authors as an intelligent multiple mod-

els based adaptive predictive control scheme (IMMBAPC),

using both the desired set points between 0C and 44C and

the following parameters variation, is considered [58].

t(k) = t + t(k), Cpt(k) = C

pt

+ Cpt (k),

Ut(k) = Ut + Ut(k)

t t(k) t, Cpt Cpt (k) Cpt ,

Ut Ut(k) Ut

t = 711 kg/m3, Cpt = 0.14 kJ/kg K,

Ut = 7.90 W/m2 K

(5.1)

To overcome the system coefficients variation, we need to

define several system operating environments and to iden-

tify the corresponding models. For the number of models in

the multiple models control strategy presented, it is better

to define the least operating environments, while the sys-

tem performance is not ignored. Here, due to the results

obtained from experiments, the optimal number of models

was obtained to be three (p = 3) for these simulations. By

using this result, the system operating environments, i.e.,


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EV#p; p = 1, 2, 3, will cover the whole of the system co-

efficients variation, given below:

EV#1, i.e., M#1 :

t(k) = t = 0

Cpt (k) = Cpt = 0

Ut(k) = Ut = 0

(5.2)

EV#2, i.e., M#2 :

t(k) =

t+t2 = 208

Cpt (k) =Cpt +Cpt

2= 2.02

Ut(k) =Ut+Ut

2= 2000

(5.3)

EV#3, i.e., M#3 :

t(k) = t = 416

Cpt (k) = Cpt = 4.04

Ut(k) = Ut = 4000

(5.4)

where t, Cpt and Ut are given in 0C and t, Cpt and

Ut are also given in 100C, respectively. Now, using the

RLS identification method, the following CARIMA models

of the system corresponding to different system operating

environments; EVs, could be obtained, where the results of

the identification process are now tabulated by Table 2.

Ai (q1)yi (k) = Bi (q1)u(k 1) + e(k)(q1)

; i = 1, 2, 3

Ai (q1) = 1 + ai1q1 + + aipq

p; p = 4

Bi (q1) = bi0 + bi1q

1 + + bipqm; q = 4

(5.5)

Here, yi

(k), u(k) and e(k) denote the ith model outputvariable, the control action variable and finally the random

sequence number, respectively. Also (q1) is taken as

1 q1.

Table 2 The coefficients of the CARIMA models

k j akj bkj

1 1 0.9933 0.2506E03

1 2 0.4343 0.3519E03

1 3 0.0069 0.5283E03

1 4 0.4219 0.1830E03

2 1 0.9947 0.2469E03

2 2 0.4327 0.3426E03

2 3 0.0083 0.5208E03

2 4 0.4204 0.1738E03

3 1 0.9960 0.2434E03

3 2 0.4313 0.3336E03

3 3 0.0097 0.5135E03

3 4 0.4189 0.1637E03

Now, to validate the models, the ith model error; ei (k),

with respect to the system output; y(k), are expressed as

ei (k) = y(k) yi (k); i = 1, 2, 3 (5.6)

The results, as tabulated by Table 3 can verify the validity

of the chosen models. Also the LGPC prediction horizon

and the control horizon are given as; N2 N1 + 1 = 3 and

Nu = 3, respectively.These control parameters are obtained based on the sys-

tem performance with respect to the recursive computational

operation of the predictive controller. In this way, the sys-

tem performance could be improved, provided that these pa-

rameters are appropriately chosen. Here, Fig. 9 shows the

tracking performance of the proposed IMMBAPC, while

Fig. 10 represents the performance of the nonlinear GPC

(NLGPC). These results are obtained, when we are sud-

denly encountered with both the system operating environ-

ment and the desired set point variations, at several points of

time.

In these simulations, the system coefficients are abruptlyvaried at several points of time, i.e., at 9, 23, 38, 45, 60,

67, 76, 82, 90, 112, 126, 134 s and finally at 186 s, respec-

Table 3 The models validation

Model error M#1 M#2 M#3e2 (V ) 3.82E03 7.41E03 5.12E03|e| (V ) 5.14E02 9.89E02 6.46E02

Fig. 9 The scheme of IMMBAPC tracking performance

Fig. 10 The scheme of NLGPC tracking performance


11/14


tively, while the desired set point is varied at 0 and 112 s,

respectively. In accordance with Fig. 11, F /A Model#1,

F /A Model#2 and F /A Model#3 are identified as the best

chosen model several times, by the intelligent decision

maker scheme (IDSM) presented in this control strategy.

Here, the models behavior have the important roll in the

performance of the IDSM. Hereinafter, F /A Cont#p; p =

1, 2, 3 are used as the dominant adaptive predictive con-

troller, at the corresponding time, i.e., when the F /AModel#p;

p = 1, 2, 3 are identified as the best chosen model of the sys-

tem.

As it can be seen from Fig. 11, the F /A Model#p ;

p = 1, 2, 3 are identified as the best chosen model of the

system, as long as theses models could be relatively close to

system behavior that is abruptly influenced by variation in

the system coefficients and also in the desired set point. In

line with these results, F /A Model#1 is identified as the best

chosen model of the system from 1 to 2 s, from 24 to 27 s,

from 46 to 49 s, from 68 to 72 s, from 82 to 86 s, from 113

to 116 s, from 118 to 126 s, from 130 to 134 s, from 140 to118 s and finally from 192 to 200 s, respectively. In this case,

F /A Model#2 is also identified as the best chosen model of

the system from 6 to 7 s, from 10 to 11 s, at 40 s, from 62 to

Fig. 11 The scheme of IMMBAPC weight signals

63 s, at 77 s, at 92 s and finally at 127 s, respectively. In ad-

dition, F /A Model#3 is identified as the best chosen model

of the system from 3 to 5 s, at 9, at 39, at 61, at 76 and finally

at 90 s, respectively. In the IMMBAPC approach presented,

the local control actions are shown in Fig. 12, where these

signals are represented after multiplication of corresponding

weights. Furthermore, the finalized control action is shown

in Fig. 13, where this signal is obtained by proposed IDSM,

in this control strategy.

It should be noted that the proposed IDMS enable to gen-

erate the accurate weights and the accurate control action

Fig. 12 The scheme of IMMBAPC control action signals

Fig. 13 The scheme of IMMBAPC finalized control action signal


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signals, as long as the system coefficients are suddenly var-

ied, at each instant of time. Consequently, the simulation re-

sults are compared with those obtained using the nonlinear

LGPC (NLGPC) scheme, where for realizing this scheme

the linear and the nonlinear parts of the Wiener model of the

system are organized as

yLm(k) = yLm(0) +

np=1

ap(k)yLm(k p)

+

np=1

bp(k)u(k p)

yNm (k) = yNm (0) + 0 tanh(0 (y

Lm(k) y

Lm(0)))

(5.7)

Here, yLm(0), yNm (0), 0, 0 and n are given as 0.7, 0.5,

1.6, 0.5 and 4.0, respectively. In addition, both ap(k) and

bp(k) must be obtained using the RLS algorithm, at each in-

stant of time. By using both the IMMBAPC and the NLGPC

schemes in several simulations, with the same conditions,

the performance improvement of the IMMBAPC scheme is

easily observed. In these cases, the NLGPC scheme does not

perform well, when changes in the system coefficients and

in the desired set point are suddenly taken place. In fact, it

is shown that the IMMBAPC approach could track appropri-

ately the desired step points in the control strategy presented.

6 Conclusion

A novel multiple models strategy using the well-known lin-

ear generalized predictive control (LGPC) scheme is pro-

posed to control an industrial tubular heat exchanger system.

In the approach presented here, the best model identifica-

tion mechanism and also the finalized control action gener-

ation are realized by an intelligent decision maker scheme

(IDSM). In line with this strategy, the best model identifica-

tion mechanism is organized in agreement with the fuzzy-

based adaptive Kalman filter and the fuzzy-based weight

generator approaches. The applicability of the strategy pre-

sented is summarized in controlling the system with rapid

and wide range of variation in the coefficients and also in the

desired set point. Here, the control strategy is implemented

on the system and the results are compared with those ob-

tained using a nonlinear GPC (NLGPC) scheme realized

based on the Wiener model of the system. The achieved re-

sults can verify the validity of the proposed control strategy.

As it can be seen from these simulation results, the multiple

models control strategy presented outperforms the NLGPC

scheme in an satisfactory manner.

References

1. Mazinan AH, Sadati N (2009) Fuzzy predictive control based mul-

tiple models strategy for a tubular heat exchanger. Appl Intell.

doi:10.1007/s10489-009-0163-1

2. Mazinan AH, Sadati N (2008) Fuzzy multiple models predictive

control of tubular heat exchanger. In: Proc of IEEE world congress

on computational intelligence, pp 18451852

3. Mazinan AH, Sadati N (2008) Multiple modeling and fuzzy pre-

dictive control of a tubular heat exchanger system. Trans Syst Con-trol 3:249258

4. Mazinan AH, Sadati N (2008) Fuzzy multiple modeling and fuzzy

predictive control of a tubular heat exchanger system. In: Interna-

tional conference on application of electrical engineering, pp 77

81

5. Mazinan AH, Sadati N (2008) Fuzzy multiple modeling and fuzzy

predictive control of a tubular heat exchanger system. In: Interna-

tional conference on robotics, control and manufacturing technol-

ogy, pp 9397

6. Hong X, Harris CJ (2002) A mixture of experts network struc-

ture construction algorithm for modelling and control. Appl Intell

16:5969

7. Flores A, Saez D, Araya J, Berenguel M, Cipriano A (2005) Fuzzy

predictive control of a solar power plant. IEEE Trans Fuzzy Syst

1:58688. Yager RR (1992) A general approach to rule aggregation in fuzzy

logic control. Appl Intell 2:333351

9. Sousa JMDC, Kaymak U (2001) Model prediction control using

fuzzy decision functions. IEEE Trans Syst Man Cybern, Part B,

Cybern 1:5465

10. Rashidi F, Mazinan AH (2004) Modeling and control of three

phase boost rectifiers via wavelet based neural network. Trans Syst

3:494497

11. Xia L, DeAbreu-Garcia JA, Hartley TT (1991) Modeling and sim-

ulation of a heat exchanger. In: Proc. of the IEEE international

conference on system engineering, pp 453456

12. Ho TB, Nguyen TD, Shimodaira H, Kimura M (2003) A knowl-

edge discovery system with support for model selection and visu-

alization. Appl Intell 19:125141

13. Thiaw L, Malti R, Madani K (2003) A multiple models approachfor nonlinear systems identification: Comparison between ANN

based and conventional implementation. In: Proceeding Book of

International Conference on Neural Networks and Artificial Intel-

ligence (ICNNAI 2003), Minsk, Byelorussia, pp 210214. ISBN

985-444-571-2

14. Madani K, Chebira A, Rybnik M (2003) Data driven multiple

neural network models generator based on a tree-like scheduler.

In: Mira J, Alvarez JR (eds) Computational methods in neural

modeling. Lecture notes in computer science, vol 2686. Springer,

Berlin, pp 382389. ISBN3-540-40210-1

15. Chebira A, Madani K, Rybnik M (2003) Non linear process iden-

tification using a neural network based multiple models generator.

In: Mira J, Alvarez JR (eds) Artificial neural nets problem solving

methods. Lecture notes in computer science, vol 2687. Springer,

Berlin, pp 647654. ISBN 3-540-40211-X16. Thiaw L, Rybnik M,Malti R, Chebira A, MadaniK (2004)A com-

parative study between a multi-models based approach and an ar-

tificial neural network based technique for nonlinear systems iden-

tification. Comput Int Sci J 3(1):6674. ISSN 1727-6209

17. Bouyoucef E, Chebira A, Rybnik M, Madani K (2005) Multi-

ple neural network model generator with complexity estimation

and self-organization abilities. Int Sci J Comput 4(3):2029. ISSN

1727-6209

18. Madani K, Thiaw L (2005) Multi-model based identification: ap-

plication to nonlinear dynamic behavior prediction. In: Saeed, K.,

Mosdorf, R., Pejas, J., Hilmola, O.-P., Sosnowski, Z., (ed) Image
http://dx.doi.org/10.1007/s10489-009-0163-1http://dx.doi.org/10.1007/s10489-009-0163-1


13/14


analysis, computer graphics, security systems and artificial intelli-

gence applications, pp 365375. ISBN 83-87256-86-2

19. Thiaw L, Madani K (2006) Self-organizing multi-model based

identification: Application to nonlinear dynamic systems be-

havior prediction. Image Process Commun J 10(2):6374. ISSN

1425-140X

20. Madani K, Thiaw L (2007) Self-organizing multi-modeling: A dif-

ferent way to design intelligent predictors. Neuro Comput 70(16

18):28362852. ISSN 0925-2312

21. Murray-Smith R, Johansen TA (1997) Multiple model approachesto modeling and control. Taylor & Francis, London. ISBN 0-7484-

0595-X

22. Guerci J, Feria E (1991) Multi-model predictive transform esti-

mation. In: Proc of aerospace and electronics conference, pp 119

125

23. Ning L, Shao-Yuan L, Yu-Geng X (2004) Multi-model predictive

control based on the Takagi-Sugeno fuzzy models: a case study.

In: Proc of IEEE conference on information science, pp 247263.

24. Wang N (2002) A fuzzy PID controller for multi-model plant. In:

Proc of IEEE conference on machine learning and cybernetics,

pp 14011406

25. Qi-Gang G, Dong-Feng W, Pu H, Bi-Hua L (2003) Multi-model

GPC for steam temperature system of circulating fluidized bed

boiler. In: Proc of IEEE international conference on machine

learning and cybernetics, vol 2, pp 90691126. Sadati N, Bagherpour M, Ghadami R (2005) Adaptive multi-

model CMAC-based supervisory control for uncertain MIMO sys-

tems. In: Proc of the 17th IEEE international conference on tools

with artificial intelligence, Hong Kong, China, Nov 2005, pp 457

461

27. Bakhshandeh R (1994) Multiple inputs-multiple outputs adaptive

predictive control of a tubular heat exchanger system. MSc Thesis,

Electrical Engineering Department, Sharif University of Technol-

ogy [in Persian]

28. Skrjanc I, Matko D (2000) Predictive functional control based on

fuzzy model for heat-exchanger pilot plant. IEEE Trans Fuzzy

Syst 8:705711

29. Matko D, Kavsek-Biasizzo K, Skrjanc I, Music G (2000) Gener-

alized predictive control of a thermal plant using fuzzy model. In:

Proc of the American control conference, vol 3, pp 2053205730. Abe N, Seki K, Kanoh H (1996) Two degree of freedom internal

model control for single tubular heat exchanger system. In: Proc of

the IEEE international symposium on industrial electronics, vol 1,

pp 260265

31. Fazlur Rahman MHR, Devanathan R (1994) Feedback linearisa-

tion of a heat exchanger. In: Proc of the 33rd IEEE international

conference on decision and control, vol 3, pp 29362937

32. Fazlur Rahman MHR, Devanathan R (1994) Modeling and dy-

namic feedback linearization of a heat exchanger. In: Proc of the

third IEEE international conference on control applications, vol 3,

pp 18011806

33. Sadati N, Talasaz A (2004) Robust fuzzy multimodel control using

variable structure system. In: Proc of IEEE conference on cyber-

netics and intelligent systems, vol 1, pp 497502

34. Sadati N, Ghadami R, Bagherpour M (2005) Adaptive neural net-work multiple models sliding mode control of robotic manipula-

tors using soft switching. In: Proc of the 17th IEEE international

conference on tools with artificial intelligence, pp 431438

35. Chang BR, Tsai H (2007) Composite of adaptive support vector

regression and nonlinear conditional heteroscedasticity tuned by

quantum minimization for forecasts. Appl Intell 27:277289

36. Liang K, Yao X, Newton CS (2001) Adapting self-adaptive para-

meters in evolutionary algorithms. Appl Intell 15:171180

37. Neri F, Toivanen J, Makinen RAE (2007) An adaptive evolution-

ary algorithm with intelligent mutation local searchers for design-

ing multidrug therapies for HIV. Appl Intell 27:219235

38. Saez D, Cipriano A (1997) Designof fuzzymodel based predictive

controller and its application to an inverted pendulum. In: Proc of

the sixth IEEE international conference on fuzzy systems, vol 2,

pp 915919

39. Hadjili ML, Wertz V, Scorletti G (1998) Fuzzy model-based pre-

dictive control. In: Proc of IEEE decision and control, vol 3, pp

29272929

40. Huang S, Tan KK, Lee TH (2002) Applied predictive control.

Springer, London

41. Clarke DW (1988) Application of generalized predictive control

to industrial processes. IEEE Control Syst Mag 4955

42. Sousa JM (2000) Optimization issues in predictive control with

fuzzy objective functions. Int J Intell Syst 15:879899

43. Zamarreno JM, Vega P (1999) Neural predictive control applica-

tion to a highly non-linear system. Eng Appl Artif Intell 12:149

158

44. Gadkar KG, Doyle FJ III, Crowley TJ, Varner JD (2003) Cyber-

netic model predictive control of a continuous bioreactor with cell

recycle. Biotechnol Prog 19:14871497

45. Saha P, Krishnan SH, Rao VSR, Patwardhan SC (2004) Modeling

and predictive control of MIMO nonlinear systems using Wiener-

Laguerre models. Chem Eng Commun 8:10831120

46. Franco E, Sacone S, Parisini T (2004) Practically stable nonlin-ear receding-horizon control of multi-model systems. In: Proc of

IEEE Conference on Decision and Control, 3, pp 32413246

47. Ding Z, Leung H, Chan K (2000) Model-set adaptation using a

fuzzy Kalman filter. In: Proc of the third international IEEE con-

ference on information fusion, vol 1, pp 29

48. Shiu SCK, Li Y, Zhang F (2004) A fuzzy integral based query dis-

patching model in collaborative case-based reasoning. Appl Intell

21:301310

49. Zhang Y, Chi Z, Liu X, Wang X (2007) A novel fuzzy compensa-

tion multi-class support vector machine. Appl Intell 27:2128

50. Chen S, Chen S (2005) A prioritized information fusion method

for handling fuzzy decision-making problems. Appl Intell 22:219

232

51. Li JH, LimMH, CaoQ (2005) Aqos-tunable scheme for ATM cellscheduling using evolutionary fuzzy system. Appl Intell 23:207

218

52. Sun S, Zhuge F, Rosenberg J, Steiner RM, Rubin GD, Napel S

(2007) Learning-enhanced simulated annealing: method, evalu-

ation, and application to lung nodule registration. Appl Intell

28:8399

53. Lee KK, Yoon WC, Baek DH (2006) A classification method us-

ing a hybrid genetic algorithm combined with an adaptive proce-

dure for the pool of ellipsoids. Appl Intell 25:293304

54. Karr CL, Wilson E (2003) A self-tuning evolutionary algorithm

applied to an inverse partial differential equation. Appl Intell

19:147155

55. Lee Z (2008) A robust learning algorithm based on support vec-

tor regression and robust fuzzy cerebellar model articulation con-

troller. Appl Intell 29:4755

56. Arefi MM, Montazeri A, Poshtan J, Jahed-Motlagh MR (2006)

Nonlinear model predictive control of chemical processes with a

Wiener identification approach. In: Proc of IEEE conference on

industrial technology, pp 17351740

57. Rueda A, Cristea S, Prada CD, Keyser RD (2005) Non-linear pre-

dictive control for a distillation column. In: Proc of 44th IEEE

conference on decision and control, pp 51565161

58. Cengel YA, Turner RH (2004) Fundamentals of thermal fluid sci-

ences, 2nd edn. McGraw-Hill, New York


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A.H. Mazinan was born on May 4,

1969, in Tehran, Iran. He received

the B.Sc. degree in Electronic Engi-

neering from the Islamic Azad Uni-

versity (IAU), Karaj Branch, Iran, in

1992, the M.Sc. degree in Control

Engineering from the IAU, South

Tehran Branch, Iran, in 1995 and

finally the Ph.D. degree in Control

Engineering from the IAU, Science

and Research Branch, Iran, in 2009,

respectively. He is now with Electri-

cal Engineering Department of the

IAU, South Tehran Branch as a fac-

ulty member, since 1996. His current research activities include pre-

dictive control, estimation theory, fuzzy logic, neural network, genetic

algorithm and their applications in multiple modeling and in hybrid

control systems.

N. Sadati http://ee.sharif.edu/~sadati/.
http://ee.sharif.edu/~sadati/http://ee.sharif.edu/~sadati/

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