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Volume 5, Issue 1 2010 Article 6

Chemical Product and Process

Modeling

Simulation and Control of a Commercial

Double Effect Evaporator: Tomato Juice

Praveen Yadav, Indian Institute of Technology, Kharagpur

Amiya K. Jana, Indian Institute of Technology, Kharagpur

Recommended Citation:

Yadav, Praveen and Jana, Amiya K. (2010) "Simulation and Control of a Commercial Double

Effect Evaporator: Tomato Juice," Chemical Product and Process Modeling : Vol. 5: Iss. 1,

Article 6.

DOI: 10.2202/1934-2659.1443

Brought to you by | Universiti Teknologi Malaysia

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Simulation and Control of a Commercial

Double Effect Evaporator: Tomato Juice

Praveen Yadav and Amiya K. Jana

Abstract

This work aims to present a detailed study on a commercial double-effect tomato paste

evaporation system. The modeling equations formulated for process simulation belong to

backward feeding arrangement. Open-loop process dynamics has been studied by rigorous

simulation of the model structure. In the next, three multi-loop control schemes, namelyconventional proportional integral (PI), gain-scheduled PI (GSPI) and nonlinear PI (NLPI), have

been synthesized for the sample process. Finally, several simulation experiments have been

conducted to investigate the comparative closed-loop performance based on set point tracking and

disturbance rejection.

KEYWORDS: evaporator, double-effect, tomato paste, modeling, dynamics, control


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1 INTRODUCTION

An evaporator is commonly used to concentrate a solution by removing a part of

the solvent in the form of vapor. It has various areas of application. In most of theindustrial and commercial applications, the multiple effect evaporator is used due

to its advantages over the single effect system. The first and most importantadvantage is the economy. Multiple effect scheme evaporates more water per kg

of steam fed to the unit by reusing the vapor from one effect as the heating

medium for the next. Secondly, the heat transfer gets improved due to the viscous

effects of the products as they become more concentrated. The invention of themultiple effect evaporators is the result of the demand of sugar industry. A

revolution in the sector of sugar industry was brought by Norbert Rillieux by the

development of multiple pan evaporation system for use in sugar refinery.Literature reviews revealed that in the beginning, the study on the multi-

effect evaporators was based on steady state analysis. Subsequently, the researchattention was paid to develop the dynamic model of the evaporation system. In the1960s, the mathematical model for a single effect evaporator was proposed by

Andersen et al. (1961) and the simulation was carried out after reduction and

linearization of that model to study the closed-loop control performance using an

analog computer. An empirical input-output model of a single concentrationevaporator with PID control application was described by Kropholler and Spikins

(1965). Andre and Ritter (1968) formulated the nonlinear model of a double-

effect evaporator.During 1970s, it was realized through the development of several process

models that the important behaviors of the evaporator system can easily be

described by its dynamic nature. Linear and nonlinear models of a genericevaporator were discussed in detail by Newell and Fisher (1972). The simulation

study became easier with the development of a computer code which is capable ofsimulating the steady state condition of a multiple effect evaporator. This

computing technique was brought by Bolmstedt and Jernquist (1976) which was

further supported by their publication in 1977 showing a dynamic simulatorthrough blocks which is capable of simulating more complex plants.

A mathematical model with a wide variety of its extension for plants of

different configurations, including the death-time arising due to circulation in

each effect and through the pipe within effects, was developed by Tonelli (1987).In the past, the mathematical models were constructed for open-loop simulations

and for application of conventional control laws. But in the last decade, the statespace models suitable for designing the multivariable controllers and stateestimations (Newell and Lee, 1989) were reported. Cadet et al. (1999) formulated

a detailed evaporator model based on energy and mass balance with considering

semi-empirical equilibrium functions. This model was implemented in a sugar

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Yadav and Jana: Simulation and Control of an Evaporator


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plant and showed satisfactory results. Recently, a phenomenological, stationary

and dynamic model of a multi-effect evaporator was presented by Miranda and

Simpson (2005) for simulation and control purposes.

In the recent years, energy conservation is a big issue for the research andindustrial organizations. Thus the latest research efforts by the scientists and

engineers working in industrial organizations are towards more efficient use ofenergy. Balkan et al. (2005) did the performance evaluation of a triple-effect

evaporator with forward feeding using exergy analysis. Kaya and Sarac (2007)

developed a model for a multiple effect evaporator and performed energy

analysis. There are several types of feeding patterns for the evaporator systemssuch as forward feeding, backward feeding, mixed feeding and parallel feeding.

Each operation was investigated by the authors with and without pre-heating

arrangements. The effect of pre-heating on evaporation process was investigatedfrom the point of energy economy. Mohanty and Khanam (2007) developed a

simplified model based on the principles of process integration for the analysis ofmultiple effect evaporator systems taking into account the variation in physico-thermal properties as well as boiling point rise. It included new concepts of stream

analysis, temperature path and internal heat exchange for the formulation of the

model equations.

Modeling and online control is very relevant for food concentrates, mainly because of its influence on product quality and also on energy consumption

(Cadet et al., 1999). Although, a significant progress has been made on modeling,

there are limited papers dealt with the control of multi-effect evaporation systems(e.g., Runyon et al., 1991; Kam and Tadé, 2000). It is with this intention that the

present work has been undertaken.

In this paper, a systematic study is conducted on a commercial double-effect tomato paste evaporator. The dynamic process model, consisting of mass

balance, energy balance and empirical correlations, is presented by thedifferential-algebraic equations. The simulation of the model structure is

performed for open-loop process dynamics. For closed-loop study, three multi-

loop control strategies, namely conventional proportional integral (PI), gain-scheduled PI (GSPI) and nonlinear PI (NLPI), have been synthesized. Finally, a

comparative control performance is addressed on the sample process. The

contribution of this paper is the comparison of the three control schemes.

2 THE PROCESS

The example process as shown in Figure 1 is a double-effect evaporator with backward feeding arrangement used for tomato concentrate. The two effects are

numbered from left to right as Tank1 and Tank2, respectively. The raw juice

having flow rate F , concentration X f and temperature T f enters Tank2, and the

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Chemical Product and Process Modeling, Vol. 5 [2010], Iss. 1, Art. 6

DOI: 10.2202/1934-2659.1443


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steam with flow rate S and temperature T S enters Tank1. The mass holdup in the

two tanks are defined as M 1 and M 2 . V 1 and V 2 are the vapor flow rates from

the overhead of two tanks with temperature T 1 and T 2 , respectively. P 1 and P 2 are the product flow rates from the two effects with product concentration X p

and X 2 , and temperature T 1 and T 2 , respectively. The steady state and parameter

values are listed in Table 1 (Runyon et al., 1991).

Figure 1 Schematic of a double-effect evaporator.

Process model

The dynamic model for the sample process is derived for tomato concentrate based on the study of Runyon et al. (1991), and Miranda and Simpson (2005).

This model is also validated (Runyon et al., 1991) for a different set of design and

parametric variables. An evaporation process involves mass and heat transfer. Thetomato juice is assumed as a binary solution of water and soluble solids, both

considered inert in a chemical sense. The macroscopical evaporator model

consisted of a set of differential-algebraic equations (DAEs) has been constructed

based on conservative laws and empirical relationships. It should be noted that

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only the juice phase is considered for modeling. The assumptions involved in the

formulation of model are listed below.

● Negligible heat losses to the surroundings● Homogeneous composition and temperature inside each evaporator

● Variable liquid holdup and negligible vapor holdup

● Overhead vapors considered as pure steam

● Latent heat of vaporization or condensation varied with temperature

● No boiling point elevation of the solution

Table 1 Steady state and parameter values.

Term Abbreviation (unit) Value

Tank1 mass holdup M 10 (kg) 2268

Tank2 mass holdup M 20 (kg) 2268

Input feed flow rate F 0 (kg/hr) 26103

Input steam flow rate S 0 (kg/hr) 11023

Tank1 liquid product flow rate P 10 (kg/hr) 5006

Tank2 liquid product flow rate P 20 (kg/hr) 14887

Vapor flow rate from Tank1 V 10 (kg/hr) 9932

Vapor flow rate from Tank2 V 20 (kg/hr) 11165

Feed composition X f0 (kg/kg) 0.05

Tank1 composition X p0 (kg/kg) 0.2607 Tank2 composition X 20 (kg/kg) 0.0874

Steam temperature T s0 (0C) 115.7

Feed temperature T f0 (0C) 85.0

Temperature in Tank1 T 10 (0C) 74.7

Temperature in Tank2 T 20 (0C) 52.0

Heat transfer area of Tank1 A1 (m2) 102

Heat transfer area of Tank2 A2 (m2) 412

Overall heat transfer coefficient for Tank1 U 1 (kJ/hr.m

2.0C) 5826

Overall heat transfer coefficient for Tank2 U 2 (kJ/hr.m2.0C) 2453

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Total mass balance

First effect: V P P dt

dM 112

1

−−= (1)

Second effect: V P F dt

dM 22

2 −−= (2)

Component (solids) mass balance

First effect: X P X P dt

X M d p

p

122

1 )(−= (3)

⇒ X P X P dt

dM X

dt

dX M p p

p

1221

1 −=+ (4)

⇒ dt

dM X X P X P

dt

dX M p p

p 11221 −−= (5)

Substituting equation (1),

)( 1121221 V P P X X P X P dt

dX M p p

p−−−−= (6)

⇒ V X P X P X X P X P dt

dX M p p p p

p

1121221 ++−−= (7)

⇒ M

V X X X P

dt

dX p p p

1

122 )( +−= (8)

Second effect: X P X F dt

X M d f 22

22 )( −= (9)

Simplifying and rearranging, finally we get

M

V X X X F

dt

dX f

2

2222 )( +−= (10)

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Energy balance

The steam flow rate to the first effect is obtained through energy balance on the

first effect heat exchanger as:

)()( 111 T T AU T S S S −=λ (11)

where, λ is the latent heat. That means,

)(

)( 111

T

T T AU S

S

S

λ

−= (12)

Similarly, the vapor flow rate to the second effect is derived from the energy

balance on the second effect heat exchanger as:

)()( 212211 T T AU T V −=λ (13)

⇒ )(

)(

1

21221

T

T T AU V

λ

−= (14)

In the following, the energy balance equations are derived.

First effect: )(),()(),()],([

1111222

11

T H V X T h P T S X T h P dt

X T h M d pS

p−−+= λ (15)

⇒ (16) )(),(

)(),(),(),(

1111

2221

1

1

1

T H V X T h P

T S X T h P dt

dM X T h

dt

X T dh M

p

S P

p

−

−+=+ λ

⇒(17) ),()(

),()(),(),(

1111

11222

1

1

dt

dM X T hT H V

X T h P T S X T h P

dt

X T dh M

p

pS

p

−

−−+= λ

Substituting equation (1),

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)],()([)()],(),([

),(1111222

1

1 X T hT H V T S X T h X T h P dt

X T dh

M pS p p

−−+−= λ (18)

Using equation (11),

)],()([)()],(),([),(

1111111222

1

1 X T hT H V T T AU X T h X T h P dt

X T dh M pS p

p −−−+−=

------------(19)

This gives,

M

X T hT H V T T AU X T h X T h P dt

X T dh pS p p

1

11111112221 )],()([)()],(),([),( −−−+−=

-----------(20)

Second effect:

)(),()(),()],([

22222112 22

T H V X T h P T V X T Fhdt

X T h M d f f −−+= λ (21)

Simplifying and rearranging, finally we have

M

X T hT H V T T AU X T h X T h F

dt

X T dh f f

2

22222122222 2)],()([)()],(),([),( −−−+−

=

-----------(22)

Empirical correlations

The enthalpy of the product (tomato juice) is represented as (Heldman and Singh,

1981):

T X X T h )506.2177.4(),( −= (23)

The pure solvent vapor (steam) enthalpy is obtained using a polynomialregression equation of values from the steam tables as:

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T T T H 002128.0958.10.2495)(2−+= (24)

For the condensate streams, the pure solvent liquid enthalpy is also found from

the steam tables as:

T T h 177.4)( = (25)

The latent heat of vaporization can be computed as:

T T T hT H T 2002128.0219.20.2495)()()( −−=−=λ (26)

Using the above correlations, the energy balance equations ((20) and (22)) have

the following final forms:

)506.2177.4(

)()())(506.2177.4(

1

111212212221

X M

T T AU T T AU T T X P

dt

dT

p

S

−

−+−−−−= (27)

)506.2177.4(

)](177.4[)())(506.2177.4(

22

222212222

X M

T H T V T T AU T T X F

dt

dT f f

−

−+−+−−= (28)

Therefore, the final form of the model includes equations (1), (2), (8), (10), (12),

(14) and (25)-(28).

3 APPLICATION OF CONTROL THEORY

3.1 Control objectives

The control objectives for an evaporation system are selected taking into account

the product specifications, operational constraints and cost considerations. For theconcerned process, the primary objective is to maintain the product solids

concentration (or product viscosity) at its desired value. In order to achieve the

desired product quality in presence of disturbance and uncertainty, severaladditional control schemes, as mentioned below, need to employ with the

evaporator.

● To prevent the overflow or drying out of evaporator tubes, liquid mass holdupshould be controlled.

● To avoid the product degradation or damage, temperature must bemaintained at the desired value.

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● To reduce the steam consumption, steam economy should be maximized.

3.2 Degrees of freedom analysis

The evaporator model presented earlier includes fifteen independent variables

X X V V S T T T T M M P P F p f S f ,,,,,,,,, ,,,,[ 21212121 and ]2 X and eight

independent equations ((1), (2), (8), (10), (12), (14), (27) and (28)). Among these

variables, the inputs, namely f T , S T

, f X , S and F are specified by the external

world. Obviously, the degrees of freedom is seven. In order to have a completely

determined process, the number of its degrees of freedom should be zero. For this

purpose and to meet the control objectives, five control pairs have been selected

and two input variables, f X and f T , can be treated as known disturbances.

3.3 Selection of control pairs

For the example tomato paste evaporator, the followings are selected as controlled

variables: (i) final product concentration ( X p ), (ii) temperature of the inlet steam

( S T ), (iii) temperature of the second effect (T 2 ), (iv) liquid mass holdup in first

effect ( 1 M ), and (v) liquid mass holdup in second effect ( 2 M ). In order to

regulate the process variables, the corresponding manipulated variables are

chosen as the product flow rate from first effect ( P 1 ), the steam flow rate ( S ), the

vapor flow rate from second effect (V 2 ), the product flow rate from second effect

( P 2 ), and the feed flow rate ( F ). Figure 1 as well as Table 2 includes all these

control configurations.

Table 2 Control pairings and controllers used.

Controlled variable Manipulated variable Controller type

X p P 1 PI, NLPI and GSPI

S T S PI, NLPI and GSPI

T 2 V 2 PI, NLPI and GSPI

1 M P 2 P-only

2 M F P-only

3.4 Control equations

In this paper, a comparative control study is presented. For this, three types of

multi-loop controllers, namely PI, NLPI and GSPI, have been designed in this

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section for the example evaporator. The ISE performance criterion has been used

in selecting the controller tuning parameter values and they are reported in Table

3.

3.4.1 Proportional integral (PI) controller

The general form of a single-loop PI control law is given by the following

expression:

])1

()[(0 ∫ −+−+= dt Y Y Y Y K U U sp spτ

(29)

Here, K is the proportional gain, τ the integral time constant, U 0 the bias signal

and Y sp the set point value of Y .

Table 3 Tuning parameters values.

Parameter P or PI NLPI GSPI

a = 3.0

K f 1000 hr-1

− −

K V2 , K V20 1250 kg/hr.0C 1250 kg/hr.

0C 1550 kg/hr.

0C

K S , K S0 15 kg/hr.0C 15 kg/hr.

0C 15 kg/hr.

0C

K P1, K P10 30000 kg/hr 20000 kg/hr 20000 kg/hr

K P2 800 hr-1

− − 2V τ 0.03 hr 0.01 hr 0.01 hr

S τ 0.35 hr 0.52 hr 0.52 hr

1 P τ 0.05 hr 0.01 hr 0.01 hr

3.4.2 Nonlinear proportional integral (NLPI) controller

Different forms of nonlinear PI (and PID) controller are available in scientific

literature. It can be developed by adding higher-order terms of the error signal andintegral of the error to the control law. Also, there is a way to make the controller

parameters functions of the error (Cheung and Luyben, 1980) or parameterscheduling (Rugh, 1987) or both (Jutan, 1989). Actually, there is no particularcontrol scheme that has become standard in the literature.

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Here, the following nonlinear PI control scheme is applied on the

evaporator. The proportional gain of the NLPI is a function of the absolute value

of the error.

])1

()[(0 ∫ −+−+= dt Y Y Y Y K U U sp spτ

(29)

with )1(0 Y Y a K K sp −+= (30)

where, K 0 is the initial fixed gain. It is obvious that if there is no integral term,

the controller output is effectively proportional to the square of the error.

3.4.3 Gain-scheduled proportional integral (GSPI) controller

A gain-scheduled PI law (Bequette, 2003) has been designed for the

representative process. The GSPI has the following form:

])1

())[((0 ∫ −+−+= dt Y Y Y Y Y K U U sp spτ

(31)

The controller gain, K , is varied aiming to keep K K P constant, which then

keeps the stability margin constant. When the process gain is characterized as a

function of the scheduling variable, ( )Y K P , then the controller gain can be

scheduled as:

)(

)()()(

00

Y K

Y K Y K Y K

P

P = (32)

The gain of the GSPI scheme used has the following forms:

(i) When Y > 0Y ,

Y

Y K Y K

−

−=

1

1)( 00 (33)

where, Y Y K P −=1)( and 00)( K Y K = .

(ii) When Y < 0Y

0)( K Y K = (34)

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Here, Y 0 represents the nominal operating value of Y (=Y sp ). It is worthy to

mention that this is a one-way approach. Since the process gain increases with

lower purity, maintaining a constant controller gain speeds up the response when

the product is less pure.

4 RESULTS AND DISCUSSION

Matlab codes have been developed to generate simulation results. The 4th order

Runge-Kutta method is used to solve the differential equations contained in the

model. In the subsequent discussion, the open-loop followed by the closed-loopevaporator performance is presented.

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Figure 2 Effect of a pulse input change in Tank2 product flow rate (changed from14887 to 15200 kg/hr at time = 5 hr and then from 15200 to 14887 kg/hr at time

=10 hr).

4.1 Open-loop performance

Figure 2 illustrates the effect of Tank2 product flow rate on the main product

composition. Two consecutive step changes have been introduced in the product

flow rate (step increase: 14887→ 15200 kg/hr at time =5 hr; step decrease: 15200

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→ 14887 kg/hr at time =10 hr). As a consequence, the final product purity gets

disturbed and the process attains a new steady state against a change. This result

shows the interactive behavior of the process variables and it confirms that the

sample evaporator is open-loop stable.

4.2 Comparative closed-loop performance

4.2.1 Disturbance rejection

The comparative regulatory performances are depicted in Figures 3 and 4introducing a pulse input change in feed concentration (step increase: 0.05 →

0.0525 kg/kg at time = 5 hr; step decrease: 0.0525 → 0.05 kg/kg at time = 15 hr)

and feed temperature (step increase: 85 → 900C at time = 5 hr; step decrease: 90

→ 850C at time = 15 hr), respectively. Both the figures include the control

performance in terms of final product composition and liquid mass holdup inTank1. However, Tables 4 and 5 record the integral square error (ISE) for allcontrol loops. It is obvious from the simulation results that the NLPI and GSPI

provide better performance over the classical PI controller. Due to the moderate

nonlinearity of the process, the nonlinear controllers outperform the PI.

Table 4 ISE values corresponding to Figure 3.

Controller X p 1 M 2 M T 2 S T

PI 2.16x10-6 0.0052 7.23x10-4 5.76x10-7 0.2505

NLPI 4.93x10-7 − − 1.73x10-7 0.2030

GSPI 4.97x10-7

− − 6.89x10-8

0.0762



PI 7.25x10-8 2.11x10-4 0.0017 0.0011 0.0044

NLPI 1.65x10-8 − − 1.73x10-4 0.0026

GSPI 1.65x10-8 − − 2.33x10-4 0.0024

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Figure 3 Effect of a pulse input change in feed concentration (changed from 0.05to 0.0525 kg/kg at time = 5 hr and then from 0.0525 to 0.05 kg/kg at time = 15hr).

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Figure 4 Effect of a pulse input change in feed temperature (changed from 85 to90

0C at time = 5 hr and then from 90 to 85

0C at time = 15 hr).

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4.2.2 Set point tracking

Figure 5 displays a comparative servo performance between PI, NLPI and GSPI

control algorithms against a pulse change in set point value of the final productcomposition (step increase: 0.2607 → 0.27 kg/kg at time = 5 hr; step decrease:

0.27 → 0.2607 kg/kg at time = 15 hr). This simulation experiment confirms thatthe PI controller shows relatively poor performance compared to other two PIs.

The performance in terms of ISE values is analyzed in Table 6. Overall, the GSPI

showed best performance due to its ability of timely changing the gain.



PI 2.77x10-5 0.01917 0.0090 2.59x10-6 0.1866

NLPI 2.22x10-5

− − 2.09x10-6

0.1381GSPI 2.25x10-5 − − 1.03x10-6 0.0568

5 CONCLUSIONS

This article presents the open-loop as well as closed-loop operation of a

commercial double-effect tomato paste evaporation system. The model structure

developed based on backward feeding approach consists of differential algebraicequations. Open-loop simulation shows that the sample evaporator is a stable

process. Three multi-loop control strategies, namely traditional PI, NLPI and

GSPI, have been synthesized to investigate the comparative performance.Simulation experiments based on set point tracking and disturbance rejection

show that the classical PI controller provides relatively poor performance over the

NLPI and GSPI algorithms. The quantitative performance analysis has also beenincluded by computing ISE values.

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H(T) Enthalpy of pure vapor solvent (steam) at temperature T (kJ/kg)

K Proportional gain

M Mass holdup of liquid product (kg)

P Liquid product flow rate (kg/hr)S Steam flow rate (kg/hr)

t Time (hr)T Temperature (

0C)

U Overall heat transfer coefficient (kJ/hr.m2.0C) or manipulated variable

V Vapor flow rate (kg/hr)

X Mass fraction (kg solids/kg stream)

τ Integral time constant (hr)

Subscripts

f Feed p Final product

S Steam

sp Set point0 Steady state

1 First effect

2 Second effect

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Bolmstedt, U., Jernquist, A., “Simulation of the Steady-state and DynamicBehaviour of Multiple Effect Evaporator Plants”, American Institute of

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Behavior of Multiple Effect Evaporation Plants”, Computer Aided Design,

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Cadet, C., Toure, Y., Gilles, G., Chabriat, J.P. “Knowledge Modelling and Non-

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Cheung, T.F, Luyben, W.L., “Nonlinear and Nonconventional Liquid LevelControllers”, Industrial and Engineering Chemistry Fundamentals, Vol.

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Publishing Company, Westport, Connecticut (1981).

Jutan, A.A., “Nonlinear PI(D) Controller”, Canadian Journal of Chemical

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(2000).Kaya, D., Sarac, H. I., “Mathematical Modeling of Multiple-Effect Evaporators

and Energy Economy”, Energy, Vol. 32, 1536-1542 (2007).Kropholler, H., Spikins, D., “Principles of Control for Chemical Engineers. Part

3”, Chemical Process Engineering, 558-567 (1965).

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DOI: 10.2202/1934-2659.1443

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