Pp

MAa

b

c

1

Pntrlc

teeprmpapd

0h

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

j ourna l h omepage: www.elsev ier .com/ locate /cherd

erformance analysis of three advanced controllers forolymerization batch reactor: An experimental investigation

ohammad Anwar Hosena,∗, Mohd Azlan Hussainb, Farouq Sabri Mjalli c,bbas Khosravia, Douglas Creightona, Saeid Nahavandia

Centre for Intelligent Systems Research (CISR), Deakin University, Locked Bag 20000, Waurn Ponds, Geelong, VIC 3220, AustraliaChemical Engineering Department, University of Malaya, Kuala Lumpur, MalaysiaPetroleum and Chemical Engineering Department, Sultan Qaboos University, Muscat, Oman

a b s t r a c t

The performances of three advanced non-linear controllers are analyzed for the optimal set point tracking of styrene

free radical polymerization (FRP) in batch reactors. The three controllers are the artificial neural network-based MPC

(NN-MPC), the artificial fuzzy logic controller (FLC) as well as the generic model controller (GMC). A recently developed

hybrid model (Hosen et al., 2011a. Asia-Pac. J. Chem. Eng. 6(2), 274) is utilized in the control study to design and

tune the proposed controllers. The optimal minimum temperature profiles are determined using the Hamiltonian

maximum principle. Different types of disturbances are introduced and applied to examine the stability of controller

performance. The experimental studies revealed that the performance of the NN-MPC is superior to that of FLC and

GMC.

© 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Model based controller; NN-MPC; FLC; GMC; Hybrid model; Polystyrene

control of batch polymerization reactor temperature control

. Introduction

olymerization reactions are complex and exothermic inature, which leads to the nonlinear behavior of polymeriza-ion reactors (Hvala et al., 2011). Control of polymerizationeactors to obtain high quality polymer products is still a chal-enging task for researchers due to the reactor’s nonlinearharacter (Özkan et al., 2009).

The main problem in controlling the polymerization reac-ion variables are whether these variables can be measured,stimated, or can be measured with some time delay (Ghasemt al., 2007). One of the major difficulties encountered inolymerization reactor control is the lack of reliable onlineeal time analytical data. Reactor temperature as an inter-

ediate variable is relatively easier to measure than theolymer structure properties (Zeybek et al., 2006). Therefore,n optimal control policy is essential to infer the optimalrofile of intermediate variables (reactor temperature) to pro-

uce the desirable polymer structural properties such as the

∗ Corresponding author. Tel.: +61 3 5227 1352.E-mail addresses: a.hosen@research.deakin.edu.au, anwar.buet97@Received 10 June 2013; Received in revised form 29 July 2013; Accepted

263-8762/$ – see front matter © 2013 The Institution of Chemical Engittp://dx.doi.org/10.1016/j.cherd.2013.07.032

mechanical stress (molecular average molecular weight,number average molecular weight, and number averagechain length), melt viscosity, hardness and elastic modulus.(Kiparissides, 2006).

In recent years, nonlinear model-based controllers(Dougherty and Cooper, 2003) have become popular to controlthe polymerization reactor (Van Brempt et al., 2001). Thispopularity is due to their ability to capture the nonlineardynamics of the process (Zhang, 2008; Shafiee et al., 2008;Yüce et al., 1999). Various nonlinear model-based controltechniques such as MPC, NN-based controller and GMC haveappeared in the literature (Özkan et al., 2009; Alipoor et al.,2009; Ekpo and Mujtaba, 2008; Seki et al., 2001; Ali et al.,2010; Hur et al., 2003). Among all model-based nonlinearcontrollers, MPC is particularly popular for the dynamicoptimization and control of chemical reactors (Shafiee et al.,2008; Sui et al., 2008). A number of applications of MPC in the

gmail.com (M.A. Hosen). 30 July 2013

are listed in Table 1. Neural networks (NNs) offer the ability

neers. Published by Elsevier B.V. All rights reserved.

904 chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

Nomenclature

A [m2] heat transfer areaAd [s−1] frequency factor for initiator decompositionAp, At [1/mol s] frequency factor for propagation and ter-

minationCp [J/g K] specific heat of reactor mixtureEd, Ep, Et [J/mol] activation energy for decomposition,

propagation and terminationf [–] initiator efficiencyH [–] Hamiltonian�H [J/g K] heat of reactionI [mol/l] initiator concentrationI0 [mol/l] initial initiator concentrationkd [s−1] rate constant for decompositionkp, kt [l/mol s] rate constants for propagation and termi-

nation, respectivelyktc [l/mol s] termination by combination rate constantM [mol/l] monomer concentrationM0 [mol/l] initial monomer concentrationQ [W] heater powerR [J/mol K] gas constantRm [mol/s] rate of polymerizationTj [K] jacket temperatureT [K] reactor temperatureTsp [K] reactor temperature setpointt, tf [s] time and polymerization timeU [W/(m2 K)] average heat transfer coefficientV [l] reactor working volumeX [%] monomer conversionXn [–] number average chain length�0 [mol/l] zeroth moment of dead polymer� [g/l] density of reactor mixture

Q (k)

T (k), X (k)

Kineticparameters

Mechanistic Model- Based on Mass and Energy Balance

Experimental I/O data

Solver

Mechanistic Model- based on Mass and Energy Balance

Experimental I/O data

NN- Kinetics Models

T0 , I0 , Q 0

Fig. 1 – Hybrid model of polystyrene batch reactor (Hosenet al., 2011a). Based on initial conditions and operatingparameters, and heater duty, this hybrid model directlypredicts the reactor temperature as well as monomerconversion. The NN kinetics models are developed offlinewith experimental data and then the NN models areconnected with the mechanistic (mathematical) model in

to produce nonlinear models of industrial systems owing totheir ability to approximate nonlinear functions and learnthrough experimental data (Qin and Badgwell, 2003; Mujtabaet al., 2006; Günay and Yildirim, 2013; Grondin et al., 2013).Most of the nonlinear predictive control algorithms based onNNs imply the minimization of a cost function by using com-putational methods for obtaining the optimal command tobe applied to the process. In a recent study, Salau et al. (2009)used MPC and a conventional PID to control the temperatureof gas-phase polyethylene reactor.

Özkan et al. (2009) investigated the online temperaturecontrol of a cooling jacketed batch polystyrene (PS) polymer-ization reactor using GMC. They achieved the temperaturecontrol of the polymerization reactor experimentally and the-oretically, and the control results are compared with thepreviously published literature work. Shafiee et al. (2008)applied nonlinear model predictive control (NMPC) based ona piecewise linear Wiener model to a polymerization reactorto control the reactor temperature. In another study, Kareret al. (2008) studied a self-adaptive predictive functional con-trol algorithm as an approach to the control of the temperaturein an exothermic batch reactor. Nagy et al. (2007) and Khanikiet al. (2007) also used nonlinear model predictive control(NMPC) for the set point tracking control of an industrial batchpolymerization reactor.

Besides MPC, artificial intelligence (AI)-based modeling and

control techniques offer flexible and powerful solutions to thedynamic optimization and control of polymerization reactors

series to construct the detailed PS reactor model.

(Stephanopoulos and Han, 1996). A number of applicationsof AI in the control of batch polymerization reactor tem-perature are listed in Table 1. The literature is rich in theapplication of different AI-based techniques to control poly-merization reactors. It includes fuzzy logic controllers (Alipooret al., 2009; Fileti et al., 2007; C etinkaya et al., 2006; AltIntenet al., 2006; Ghasem, 2006), neural network-based controllers(Zhang, 2008; Ekpo and Mujtaba, 2007, 2008) and geneticalgorithm-based controllers (AltInten et al., 2006, 2008).

In this work, two artificial intelligence-based controllers(NN-MPC and FLC) and one nonlinear model-based controller(GMC) are developed and used to track the optimum set pointof batch polymerization reactors. PS polymerization in a batchreactor is adopted for this study to check the efficiency ofdifferent advanced controllers.

2. Modeling of batch polystyrene reactor

Polystyrene product is produced by following a complexreaction mechanism in a batch reactor. The free radical poly-merization process is commonly used to produce PS (Özkanet al., 2000). It is necessary to thoroughly understand the reac-tion mechanism and effective operating variables in order todevelop a detailed model for the PS polymerization reactor.Researchers are still facing challenges to develop an effectivemodel that leads to optimize the performance of a PS reactor(Herrera and Zhang, 2009).

Traditionally, polymerization reactors are modeled basedon the mass and energy balance equations (Kiparissides,1996). This conventional modeling technique usually suffersfrom high prediction errors (Konakom et al., 2008). A signif-icant percentage of prediction errors arise from the kineticmodel of polymerization reactor. This is due to the fact that thepolymerization reactions are complex and researchers makemany assumsptions or avoid some reactions in developing thekinetic model (Hosen et al., 2011a). In addition, the kineticparameters for FRP are either partially known or completelyunknown.

Considering the abovementioned issues, Hosen et al.(2011a) recently developed a hybrid model for PS batch reactor

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916 905

Table 1 – Recently applied control algorithms in batch polymerization systems to control the batch reactor temperature.

Researcher Type ofresearchpaper

System Manipulatedvariable

Controller Nature ofresearchwork

Özkan et al. (2009) Control FRP of styrene in BR Heater power Applied Generic model control(GMC)

Simulation andexperimental

Alipoor et al. (2009) Control FRP of styrene in BR Jacket H&C Applied rule-based Takagi–Sugenofuzzy controller with ANFISmethod

Simulation

Zhang (2008) Control FRP of MMA in BR Heater power Stacked neural network model SimulationSui et al. (2008) Control FRP of styrene in BR Jacket H&C Explicit moving horizon (model

predictive) controller and anexplicit moving horizon estimator

Simulation

Ekpo and Mujtaba (2008) Control FRP of MMA in BR Heater power GMC-NN and IMBC; the controlvector parameterization (CVP)technique is used to pose theoptimal control problem as an NLPproblem, which is solved usingSQP method within gPROMS

Simulation

Cho et al. (2008) Control General batch reactor Jacket H&C Iterative learning dual-modecontrol

Simulation

Beyer et al. (2008) Control FRP in BR-general Jacket H&C Adaptive exact linearizationcontrol (AELC) with Sigma-pointKalman filter

Simulation

AltInten et al. (2008) Control FRP of styrene in BR Heater power Self-tuning PID control with GA ExperimentalNagy et al. (2007) Control FRP of MMA in BR Heater power Feedback nonlinear model

predictive controlExperimental

Khaniki et al. (2007) Control FRP of MMA in BR Jacket H&C Applied globally linearizingControl (GLC) and MPC methods tocontrol the temperature

Simulation

Fileti et al. (2007) Control FRP of MMA in BR Coolant flowrate

PID-fuzzy logic controller Experimental

Ekpo and Mujtaba (2007) Control FRP of styrene in BR Heater power Dual mode control with PID,GMC-NN and DIC

Simulation

Zeybek et al. (2006) Control FRP of styrene in BR Heater power Generalized delta rule (GDR)algorithm with generalizedpredictive control (GPC)

Experimental

Özkan et al. (2006) Control FRP of styrene in BR Heater power Nonlinear generalized predictivecontrol; Levenberg–Marquardtalgorithm is applied in theestimation of process parameters

Experimental

C etinkaya et al. (2006) Control FRP of styrene in BR Heater power Fuzzy-relational models-dynamicsmatrix control (fuzzy-DMC) andcompared with NLGPC

Experimental

AltInten et al. (2006) Control FRP of styrene in BR Heater power Fuzzy control method with geneticalgorithm

Experimental

FRP = free radical polymerization; MMA = methyl methacrylate; BR = batch reactor; H&C = heating and cooling.

anTtdksmt

(

s represented schematically in Fig. 1. They developed offlineonlinear NN models to get kinetic parameters of this process.he kinetic parameters are the most effective state parame-

ers for this process as process temperature variation directlyepends on these parameters. Later, they combined these NNinetics models with the first principle mechanistic model ineries to get a detailed PS reactor model. They followed theethodology explained below to develop a hybrid model for

he PS reactor (Hosen et al., 2011a).

(i) Firstly, implement the available conventional model andcheck the model prediction error with experimental data.

(ii) Conduct sensitivity analysis for the reactor temperatureand kinetic parameters against reactor operating vari-ables, and determine the effective operating parametersagainst kinetic parameters.

iii) Conduct experiments to determine the reactor tem-

perature profiles by varying the effective operationparameters. These include initial reactor temperature

(T0), initial initiator concentration (I0) and initial heaterduty or heater power (Q0).

(iv) Parameter estimation analysis (using a nonlinear leastsquare algorithm) is performed to estimate the kineticparameters with the help of the conventional model(implemented in step i) and experimental data (collectedin step iii). The estimated kinetic parameters involvefrequency factors and activation energies for the decom-position, propagation and termination reaction steps (Ad,Ap, At, Ed, Ep and Et).

(v) Develop three artificial neural network models to predictthe kinetic parameters under the reactor operating con-ditions. Each NN model predicts the frequency factor (Ai)and activation energy (Ei) for the respective reaction stepswhere the initial reactor operating conditions (T0, I0 andQ0) are used as inputs for NN.

(vi) Finally, combine the trained NN-based kinetic model with

the mechanistic model and validate the hybrid modelwith experimental data.

906 chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

Hosen et al. (2011a) validated the developed hybrid modelwith experimental data and claimed that this hybrid modelprediction accuracy is superior to any other published PSreactor model. In the present work, this hybrid model is usedto design and simulate the proposed controllers. For thecontrol study purpose, the reactor temperature is chosen asa controlled variable while heater duty is employed as themanipulated variable. As can be seen in Fig. 1 that this hybridmodel can predict T(t) with time for any value of Q(t). Thus, itis assumed that this model can represent the actual plant inthe simulation study to check the controller’s performance.

3. Minimum time optimal temperatureprofile

Recently, researchers have successfully developed and usedthe optimal temperature profile to control the polymeriza-tion reactor to get the desired polymer product quality andquantity (Zeybek et al., 2004, 2006; AltInten et al., 2008; Özkanet al., 2001). In this work, the optimization problem involvingminimum time optimal temperature policy has been formu-lated and solved for the PS batch reactor based on previouswork (Zeybek et al., 2006; Sata, 2007). This optimal temperatureprofile is then used in the control studies.

The objective of the optimization problem is to gener-ate an optimal temperature profile that leads to the desiredfinal polymer product quality and quantity with minimumtime (tf). Here, the number average molecular weight (Xn) andthe monomer conversion (X) indicate the polymer productquality and quantity, respectively. In order to minimize poly-merization end-time, polymerization reactor temperature isemployed as a control variable as the polymer product qual-ity and quantity directly depend on reactor temperature. Thetarget values for the optimization problem are chosen asX = 50% and Xn = 500 (Zeybek et al., 2006). The optimizationproblem is solved by using the Hamiltonian maximum princi-ple (Ponnuswamy et al., 1987). Both algebraic and differentialequations related to the PS reactor model are used in the opti-mization algorithm. The algebraic and differential equationsare as follows (Zeybek et al., 2006):

The rate of initiation

dI

dt= −kdI (1)

The rate of monomer decomposition

dM

dt= kp

(2fkdI

kt

)1/2

M = −k1I1/2M (2)

The rate of dead polymer disperses (zeroth moment)

d�0

dt= k4kdI (3)

where

kd = Ad exp(

− Ed

RT

)(4)

k1 = kp

(2fkd

kt

)1/2

= A1 exp(

− E1

RT

)(5)

A1 =(

2fAd

At

)1/2

Ap (6)

E1 = 2Ep + Ed − Et

2(7)

k4 = 2f

(1 − v

2

); v = ktc

kt(8)

X = M0 − M

M0(9)

Xn = M0 − M

�0(10)

The objective of the optimization problem is to calculatethe minimum time optimal temperature policy to achievea desired conversion, Xd, and the number average of chainlength, Xn, for a given initial condition. According to the Hamil-tonian principle, the following performance index needs tobe minimized to achieve this goal (Ponnuswamy et al., 1987;Hapoglu et al., 2000):

min tf = max

(−

∫ tf

0

dt

)(11)

In another form, the objective function can be expressedin terms of final time and weighted sum squares of differenceof monomer concentration (M) and zeroth moment (�0) fromtheir respective desired values (Ponnuswamy et al., 1987).

J =∫ tf

0

dt + w1[M(tf ) − Md

]2 + w2[�0(tf ) − �od

]2(12)

where w1 and w2 are the weighted function.By applying the Hamiltonian maximum principle,

Ponnuswamy et al. (1987) defined the relation of the objectivefunction for minimum time optimal temperature policy withthe Hamiltonian as follows

H = −1 + p1dI

dt+ p2

dM

dt+ p3

d�

dt(13)

or

H = −1 − p1kdI − p2k1MI1/2 + p3k4kdI (14)

where p1, p2 and p3 are costate variables that satisfy the fol-lowing equations.

dp1

dt= − ∂H

∂I= p1kd + 0.5p2k1MI−1/2 − p3k4kd (15)

dp2

dt= − ∂H

∂M= p2k1I1/2 (16)

dp3

dt= − ∂H

∂�0= 0 (17)

If T is unconstrained, the necessary conditions for optimal-ity are written as

H = 0;∂H

∂T= 0;

∂2H

dT2< 0 (18)

Hence, Eq. (14) can be written in the form of

(p3k4 − p1) kdI − p2k1MI1/2 − 1 = 0 (19)

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916 907

Table 2 – Reactor operating conditions and specifications.

Name of the parameters Value Units

Specific heat of reactor mixer (Cp) 1.96886 J/g KSpecific heat of jacketed water (Cc) 4.29 J/g KHeat of reaction, (�H) −57766.8 J/g KFlow rate of jacketed water (mc) 0.51 g/sGas constant (R) 8.314 J/mol KInlet temperature of jacketed water (Tji) 303.14 KAverage heat transfer coefficient (U) 55.1 W/(m2 K)Reactor working volume (V) 1.2 lReactor jacket volume (Vc) 1 lHeat transfer area of reactor (A) 0.0533 m2

Density of jacketed water (�c) 998.00 g/lDensity of reactor mixer (�) 983.73 g/l

eE

n

T

mpe

asfitmspc

4

Tseihto5taupNoresps

0 1400012000100008000600040002000

Tem

pera

ture

(K

)

360

365

370

375

380

385

0 12000100008000600040002000 14000

X (

%)

0

10

20

30

40

50

60

time (s)0 1400012000100008000600040002000

NA

CL

480500520540560580600620640

Fig. 2 – Optimum temperature profiles with differentinitiator concentrations [I0 = 0.013 mol/l (—), I0 = 0.016 mol/l(- - -), I0 = 0.019 mol/l (– –)].

Upon differentiation of H with respect to T, Eq. (14) can bexpressed in a new form with the optimality condition as inq. (18)

∂H

∂T= −

(p1EdKdI + p2E1k1MI1/2 − p3k4EdKdI

RT2

)(20)

Therefore, both Eqs. (19) and (20) can be solved simulta-eously to obtain the approximate optimal temperature

= −(E1/R)ln (Ed/A1p2MI1/2 (E1 − Ed))

(21)

Eq. (21) along with the model equations is used in the opti-ization process. The detailed procedure for the optimization

rocess can be found elsewhere (Hapoglu et al., 2000; Özkant al., 1998).

In this study, the target values for the optimization problemre chosen as X = 50% and Xn = 500 (Zeybek et al., 2006). Table 2hows the reactor operating condition as well as reactor speci-cation that are used in simulation studies to develop optimalemperature profiles. The optimum temperature profiles with

inimum time for three different initiator concentrations arehown in Fig. 2. In the present work, the optimal temperaturerofile for I0 = 0.016 is used for tracking the set point in theontrol study.

. Batch polystyrene reactor system

he experimental system of the batch PS reactor used in thistudy is shown in Fig. 3. The apparatus consists of a 2.0 l jack-ted glass reactor with a mechanical agitator and other utilitytems. The top of the reactor has four inlets for the agitator,eater, thermocouple and reflux condenser. The turbine agi-

ator is used to stir the reactor mixture. The operating rangef the agitator motor is 50 to 2000 rpm. An electric heater of00 W is used to heat up the reactor mixture. A device calledhe triac module is used to control the heater power between 0nd 500 W as a system requirement. The heater is the manip-lated variable for this system and the amount of heatingower is determined by the controller used in this system.itrogen purges through the reactor mixture from the bottomf the reactor to provide an inert system for the reactions. Aeflux condenser is used to collect the vaporized solvent thatscapes with the nitrogen. One thermocouple is used to mea-ure the reactor temperature. Another two thermocouples are

ositioned at the inlet and outlet of the cooling jacket to mea-ure the coolant water temperature. The three thermocouples

are connected to the computer via an analogue to digital (A/D)converter. Water as a coolant flows at a fixed rate through thejacket with an operated pump. The pump can be controlled byboth manually and numerically.

In this study, the three main chemical components, styrene(99.9 mol%), toluene (99.9 mol%) and benzoyl peroxide (BPO)from Sigma-Aldrich, are used as monomer, solvent and ini-tiator, respectively. The details of the experimental procedurecan be found in elsewhere (Hosen et al., 2011a)

5. Design of proposed controllers

In this work, two artificial intelligence-based controllers (NN-MPC and FLC) and one nonlinear model-based controller(GMC) are used to control the PS polymerization reactor. Thepreviously developed hybrid model is used to determine thecontrol parameters in a simulation study. Minimal time opti-mal temperature profiles are used as the setpoint referencetrajectory. The controller’s performance criterion, integralabsolute error (IAE) along with other performance metrics areused to check the efficiency of the controllers in simulationand experimental studies.

5.1. Artificial intelligence-based controllers

In recent year, neural networks are widely used to capture thenonlinear dynamic processes as the neural network directly

908 chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

Fig. 3 – Experimental setup for the polystyrene batch reactor.

predicts the process output with high speed based on inputwithout detailed process knowledge (Khosravi et al., 2010).This data-based modeling technique offers a great advantagefor the model-based control algorithms. Computational loadsas well as programming complexity for NNs are much eas-ier than mathematical models (i.e. mathematical modelinginvolves a lot of differential and integral equations that leadto computational complexity and errors).

5.1.1. Neural network-based model predictive controlTime optimal control of the PS reactor provides temperaturetrajectories that can result in the production of polymers withdesired properties. Model predictive control (MPC) is widelyused to control the temperature of batch reactors (da Silvaet al., 2012). Eaton and Rawlings (1992) defined MPC as a controlscheme in which the control algorithm computes a manip-ulated variable profile that is optimized over a finite futuretime horizon, with an objective function subject to a numberof plant model and constraint functions. The first move of thisopen-loop optimal manipulated variable profile is then imple-mented until a new plant measurement becomes available.Feedback is incorporated by using the new measurements toupdate the optimization problem.

The cost function for MPC to optimize the control signal forthe PS reactor is defined as (Hosen et al., 2011b)

minu(k)

{J(k) =

N∑p=1

∥∥Tref (k + p∣∣ k) − T(k + p

∣∣k)∥∥2

Mp

+Nu−1∑q=0

∥∥�Q(k + q∣∣k)

∥∥2

�q

}, (22)

subject to

Qmin ≤ Q(k + p∣∣k ) ≤ Qmax, p = 0, . . ., Nu − 1,

�Qmin ≤ �Q(k + p∣∣k ) ≤ �Qmax, p = 0, . . ., Nu − 1,

Tmin ≤ T(k + q∣∣k ) ≤ Tmax, q = 0, . . ., N

where N and Nu denote as prediction horizon and con-trol horizon, respectively. Mp ≥ 0 and �q > 0 are diagonalweighting matrices with dimensions ny × ny and nu × nu,respectively, T(k + p

∣∣k) denotes the model predicted outputsfor the future sampling instant k + p. The reference trajec-tory, Tref (k + p

∣∣k) , is typically assumed to be constant overthe prediction horizon and equal to the desired set-point,i.e.

Tref (k + p∣∣k) = Tsp(k). (23)

MPC greatly improves the system control accuracy androbustness. However, MPC based on linear process modelsmay result in poor controller performance as most of theindustrial chemical processes are nonlinear. Therefore, MPCbased on nonlinear models is more desirable. NNs offer analternative nonlinear model for MPC in industrial systems,owing to their particular abilities of approximating nonlinearfunctions and learning through example.

In this work, the NN is trained to capture the forwarddynamics of the process. The NN model predicts the futureplant output based on the previous plant inputs and outputswith some delay. The structure of NN plant model for MPC isrepresented by Fig. 4.

Experimental data of reactor temperature (plant output)

for training the NN model are collected by varying the reac-tor heater power (manipulated variable). A total of 10,000 data

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916 909

T(t+1)

bi

bj

Input layer Hidden layer Output layer

TDL TDL

Q(t+1)

T(t-1)

T(t-2)

T(t)

Fig. 4 – NN structure with a total of 4 inputs [Q(t + 1), T(t),T(t − 1), T(t − 2)] and one output [T(t + 1)] for PS reactor. ThisNN model is used in MPC to optimize control signal, heaterduty (Q).

Table 3 – MSE values for training, testing and validation.

Data size MSE

Training data 5000 5.36 × 10−6

Testing data 2500 4.13 × 10−6

Validation data 2500 4.69 × 10−6

pofT(

•

•

•

fi

i

M

wt

Maie5a

f

Table 4 – NN-MPC parameters.

Cost/prediction horizon (N2) 24Control horizon (Nu) 4Control weight factor (M) 0.09Move suppression factor (�) 0.003Optimization method Backtracking optimization

oint for each variable are recorded covering the range of batchperations. Finally, the collected data are split as follows: 50%or training, 25% for validation and 25% for testing the NN.he purpose of using the different data sets are as follows

Matignon, 2005):

Training dataset is used for model fitting to adjust or estimatethe weights of the neural network;

Validation dataset is used to minimize over fitting by monitor-ing and fine-tuning the NN model based on the cost functionand improve generalization; and

Testing dataset is used for testing and evaluating the NN pre-diction performance that cannot be used during networktraining.

The mean square error (MSE) is used as the cost functionor NN training to determine the optimum number of nodesn the hidden layer.

The mean square error (MSE) can be expressed mathemat-cally as follows:

SE = 1n

n∑k=1

(T(k) − T(k)

)2(24)

here n is the number of training data, T is the actual reactoremperature and T is the NN predicted reactor temperature.

The Levenberg–Marquardt method is used to minimize theSE. For the hidden layer, the sigmoidal function is selected

s the activation function in the nodes and a linear functions used for the output layer. Based on the minimizing of MSError values, 10 hidden nodes give the minimum MSE value of.36 × 10−6 for this system. The MSE values for training, testingnd validation are given in Table 3.

For MPC, it is necessary to optimize the tuning parametersor better performance before the online implementation. For

designing a good MPC controller it is important to specify thefollowing controller parameters (Hosen et al., 2011b):

• Sampling interval• Prediction and control horizons• Constraints on the manipulated and output variables• Weighting factors on input and output variables

In this work, a recently developed hybrid model (Hosenet al., 2011a) (as described in Section 2) is utilized to determinethe sampling interval, prediction, and control horizon. TheMarlin (1995) general tuning rule is use to determine the MPCsampling interval. As suggested by Sata (2007), a 3-s samplinginterval is selected to satisfy Marlin’s general rule. The pre-diction and control horizon are determined by trial and errormethod. Closed loop simulations are carried out with opti-mum setpoint tracking using the hybrid model to optimize theprediction and control horizon. Different values of predictionand control horizon are employed in simulation and the NN-MPC performance is checked based on controller performancecriterion, IAE. The simulation study shows that the predictionhorizon of 24 sample intervals and the control horizon valueof 4 sample intervals provide satisfactory control performance(see Hosen et al. (2011b) for more details). Design specificationsof the NN-MPC controller are given in Table 4.

5.1.2. Fuzzy logic controllerThe fuzzy logic controller (FLC) is one of the popular artificialintelligent-based controllers used in chemical plants (AltIntenet al., 2003). It has the ability to handle multi-valued logic thatallows intermediate values between conventional evaluationssuch as yes/no, positive/negative, true/false, and large/small.FLC can formulate mathematically the notation like positiveor negative and quickly predicts the possible desired output.

There are three main parts to fuzzy logic operations,namely fuzzification, fuzzy processing and defuzzification asseen in Fig. 5. Fuzzification processes the input data to obtainthe fuzzy input by the fuzzified the actual inputs. In fuzzyprocessing, predefined fuzzy rules produce the fuzzy outputsand defuzzification produces the actual controller output fora fuzzy output value. More details on fuzzy control and prac-tical applications of this controller can be found elsewhere(Abdullah et al., 2011; Rahnamoun and Armaou, 2011).

In this work, the Mamdani-type inference is used to deter-mine the fuzzy output (Cordón, 2011). The parameter values ofthe membership function in the FLC are listed in Table 5. Theparameters e and ce denote the input parameters for FLC interms of error (T – Tsp) and rate of error [e(t) – e(t − 1)], respec-tively. The parameter ‘Q’ is the output. The fuzzy inferenceused in this work can be illustrated in Table 5.

5.2. Generic model controller

Generic model control (GMC) is an advanced model-based con-

trol strategy, which embeds a linear or nonlinear model of asystem to compute an action in control (Samad et al., 2010).

910 chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

Actual

outputs Fuzzy

inputs

Control

inputs

Actual

inputs

FUZZY PROCESSING

Fuzzy rules: If temperature is

Negati vely Small, then heat is

Positively Smal l

If temperature is Positively Small

then hea t is Negative

Small.. etc.

FUZZIFICATION

Membership functio n of

inputs

DEFUZZIFICATION

Membership functions of

output

Fig. 5 – Operation of a fuzzy controller.

Table 5 – Membership function for FLC.

Membershipfunction for e

Left edge Center Right edge

NS Infinity −2 1ZR −0.5 0 0.5PS 0 1 2PM 0.5 2 3.5PL 2 4 Infinity

Membership function for ceN Infinity −0.1 0ZR −0.05 0 0.05P 0 0.1 Infinity

Membership function for TZ Infinity 20 40H1 20 40 60H2 40 60 80H3 60 80 100H4 80 200 320H5 200 300 400H6 280 380 Infinity

N = negative; NS = negatively small; ZR/Z = zero; P = positive;PS = positively small; PM = positively medium; PL = positively large;H(i) = intensity of heat, where i = 1, 2, . . ., 6.

The method uses only two tuning parameters. Furthermore,the nonlinear model does not need to be linearized as it util-izes the nonlinear model itself.

The GMC algorithm has been implemented recently asone of several advanced process control schemes in chemi-cal engineering (Ekpo and Mujtaba, 2008). With the inclusionof nonlinear process models into the controller algorithm,GMC proves to be of an advantage as the process mod-els can be used as they are without any linearization. It isrelatively easy to employ the GMC algorithm in computerprogramming and a very effective response can be achievedby tuning only two GMC parameters, K1 and K2.

The GMC algorithm can be written in general form as fol-lows (Ghasem et al., 2007):

dy/dt = K1(ysp − y) + K2

∫(ysp − y)dt (25)

where y and ysp denote the current and setpoint value of con-

trol variables, respectively. The GMC parameters (K1 and K2)are tuned based on the tuning curve given by Lee and Sullivan

(1988). The first expression in Eq. (25) drives the process backto steady state due to change in dy/dt. K2 is tuned to make theprocess have a zero offset.

For the PS polymerization reactor system, Eq. (25) can bewritten as

dT/dt = K1(Tsp − T) + K2

∫(Tsp − T)dt (26)

An energy balance model of the reactor that reveals therelation between the controlled variable and the manipulatedvariable is important. Eq. (4) from the literature work of Hosenet al. (2011a) represents the energy balance equation for PSbatch reactor.

dT

dt= Q + (−�H) Rm V − UA (T − Tj)

V� Cp(27)

Combining Eqs. (26) and (27) gives Q yields

Q ={

K1 (Tsp − T) + K2

∫ t

0

(Tsp − T) dt

}V�Cp +

UA(

T − Tj

)− (−�H)RmV (28)

The integral part of Eq. (28) has to be approximated bynumerical integration (5th order Runge–Kutta integration).The kinetic model equations from Hosen et al. (2011a) are usedto get the estimated value of heat released (− �HRm) from thereactions. Table 6 shows the parameters in GMC algorithm.

6. Results and discussion

In this study, three controllers are applied to investigate theaccuracy and performance in controlling the batch reactor forPS production. The aim of the study is to implement these con-trollers in the regulation of the optimal temperature profile toproduce the desirable (predetermined) polymer target, namelyXn, and end-of-reaction monomer conversion (X). Before theinitiator is introduced into the reactor to initiate the polymer-ization, the reaction mixture consisting of monomer (styrene)and solvent (toluene) is maintained at a constant starting tem-perature of 364.4 K. This is the predetermined starting temper-ature of the optimal temperature profile at I0 = 0.016 mol/l. The

generation of the optimal temperature trajectory is explainedpreviously in Section 3. The three controllers are employed

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916 911

Table 6 – Important parameters and control variables of GMC controller.−�H(J/mol) V (l) U (W/m2 s) A (m2) � (g/l) Cp (J/g K) K1 K2

57766.8 1.2 55.1 0.053 983.73 1.96886 0.01 0.000012

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Te

mp

era

ture

(K

)

362

364

366

368

370

372

374TspTr , NN-MPC

time (s)

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

He

ate

r p

ow

er

(wa

tt)

100

120

140

160

180

200

220

240

nt tra

bpct

6

IftXiemidTtmbt0lNatsrra

erp

Fig. 6 – Optimal setpoi

y manipulating the heater power to control the reactor tem-erature. The proposed controllers are tested with two studyases: the optimal tracking of setpoint and disturbance rejec-ion study with the optimal tracking of setpoint.

.1. Online optimal control of polystyrene reactor

n the present work, concentrations of 0.016 and 6.089 mol/lor initiator and monomer loading are chosen to producehe desired target as described in Section 3 (X = 50% and

n = 500). Firstly, the NN-based MPC controller is investigatedn real-time to track the optimal setpoint trajectory. Thexperimental results of optimal setpoint tracking for PS poly-erization using NN-MPC are shown in Fig. 6. When the

nitiator is introduced to the reactor, the reactor temperatureecreased suddenly and fell below the setpoint at nearly 1 K.his is because the initiator (at room temperature) is added

o the reactor while the reactor temperature is at approxi-ately 364.4 K. The MPC controller immediately takes action

y increasing the heater power (Q) to level up the reactoremperature as setpoint, resulting in maximum overshoot of.5 K. Later, the temperature decays, decreasing in an oscil-atory manner within 730 s. From this point onwards, theN-MPC performance is good in terms of offset, overshootnd undershoot. However, a small oscillation can be observedhroughout the batch operation. Fig. 6 also shows the tran-ient response of the manipulating variable, heater power. Theegulation is smooth. It is worth mentioning that the heateregulation is initially at Q = 150 W and it increases gradually atpproximately 200 W at the end of the batch run.

The same initial operating condition is applied for thexperimental study of FLC to control the PS polymerization

eactor. Fig. 7 shows the experimental results of optimal set-oint tracking for FLC. The overall performance of the FLC is

cking using NN-MPC.

good to track the optimal setpoint. However, FLC took moretime to come back to the setpoint after the initiator load-ing disturbance occurred. The manipulated variable (Q) alsooscillates significantly.

Fig. 8 depicts the setpoint tracking performance of GMCcontroller. As can be seen in Fig. 8, the reactor tempera-ture immediately dropped by 2 K when the initiator addedinto the reactor to initiate the reactions. This is because theinitiator temperature is lower than the reactor steady statetemperature. The GMC controller takes it as a disturbanceand increases the value of manipulated variable (Q), whichreaches a peak value at approximately 220 W. This extra effortof the controller increases the control variable, exceeding thesetpoint value, and a maximum overshoot (by 2 ◦K) can beobserved in the GMC tracking. However, the controller is ableto achieve stable setpoint tracking at the time instance of1900 s. After this time, the controller closely tracks the set-point profile without any offset. As seen in Fig. 8, the controllerproduces a smooth manipulation with minimum oscillation.

6.2. Optimal tracking with disturbance

Normal real operation of any chemical process always encoun-ters disturbances due to existence of impurities, externalconditions variation and changes of internal condition. In thisinvestigation, two step disturbances are made in the processoperation. Disturbances are made by increasing the valuesof the coolant flow rate and the inlet jacket temperature ata certain time from their normal operating values. The firstand second step disturbances are introduced at time 2500and 4500 s, respectively in the same experimental run. In thefirst disturbance, the coolant flow rate is increased from 60

to 100 ml/s at time 2500 s. Fig. 9 shows that the NN-MPC con-troller tracks the trajectory without significant overshoot or

912 chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Tem

pera

ture

(K

)

362

364

366

368

370

372

374TspTr , FLC

time (s)

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

He

ate

r pow

er

(watt

)

100

120

140

160

180

200

220

240

Fig. 7 – Optimal setpoint tracking using FLC.

offset when the change of flow rate is made. There is a lit-tle oscillation of temperature in tracking the profile. Due tothe increase of cooling water flow rate, the controller actsin such a way to remove the disturbance by increasing theheater output. This is due to the fact that increasing the flowrate enhances the heat transfer from the reactor mixture tothe water jacket. This will reduce the temperature inside thereactor. These are also observed in Figs. 10 and 11 for setpointtracking with disturbance using FLC and GMC, respectively.Another disturbance is introduced at the time of 4500 s where

the inlet jacket temperature is increased from 303 to 323 K. InFigs. 9–11, it can be seen that the controllers act in such a way

100 0 200 0 300 0 400 0 500 0 60

Te

mp

era

ture

(K

)

362

364

366

368

370

372

374

tim

1000 2000 300 0 400 0 500 0 60

He

ate

r p

ow

er

(watt

)

100

120

140

160

180

200

220

240

Fig. 8 – Optimal setpoint

to eliminate the disturbance by reducing the amount of heatinput to the reactor mixture and overshoot occurred when thedisturbance is introduced. In comparison to the previous dis-turbance, the action of manipulated heater is more drastic.As can be seen from the figures, there is a sharp drop in themanipulated values.

6.3. Performance evaluation of NN-MPC with FLC &GMC

The polymerization reaction involves a complex reactionmechanism making the system nonlinear in nature. The aim

00 700 0 800 0 900 0 1000 0 1100 0

TspTr , GMC

e (s)

00 700 0 800 0 900 0 10 000 11 000

tracking using GMC.

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916 913

100 0 2000 3000 4000 5000 6000 70 00 80 00 90 00 10000 110 00

Te

mp

era

ture

(K

)362

364

366

368

370

372

374TspTr , NN -MP C

time (s )

1000 200 0 300 0 400 0 5000 6000 7000 8000 9000 10 000 11000

He

ate

r po

wer

(wa

tt)

100

120

140

160

180

200

220

240

istur

ouiG

sIitcChH

Fig. 9 – Optimal tracking with d

f this study is to achieve a better, smooth performance bysing different advanced controllers. In this section, the exper-

mental results of NN-MPC are compared with that of FLC andMC.

As discussed in Section 6.1, Figs. 6–8 show the optimaletpoint tracking using NN-MPC, FLC and GMC, respectively.t can be seen in all of these figures, the reactor temperaturemmediately drops to 2–3 K from the setpoint when the initia-or is added to initiate the polymerization. This is because theharging initiator is stored at a room temperature of 303 K.onsequently, the controllers act through manipulating theeater power to bring the temperature closer to the setpoint.

owever, it is observed that the controllers overreact causing

1000 20 00 30 00 40 00 50 00 60

Tem

pera

ture

(K

)

362

364

366

368

370

372

374

tim

1000 20 00 30 00 40 00 50 00 60

He

ate

r p

ow

er

(wa

tt)

100

120

140

160

180

200

220

240

Fig. 10 – Optimal tracking with dis

bance rejection using NN-MPC.

a significant overshoot over the setpoint. The maximumovershoots are 0.5, 1 and 2 K for NN-MPC, FLC and GMC,respectively. The NN-MPC takes only 730 s to return back tosetpoint from overshoot while FLC and GMC took about 1000and 1900 s, respectively. More oscillations are observed forFLC while NN-MPC and GMC tracking the setpoint with littleor without oscillation. Figs. 6–8 also depict the time evolutionof heat input into the reactor mixture. Due to the largetemperature difference in the initial stage, the manipulationof heater power increases tremendously until it reaches themaximum value at approximate 250 W. More oscillations arealso observed in the action of the manipulated variable for

FLC than the NN-MPC and the GMC.

00 7000 8000 9000 10 000 11 000

TspTr , FLC

e (s)

00 70 00 80 00 90 00 10 000 11 000

turbance rejection using FLC.

914 chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916

1000 20 00 30 00 40 00 50 00 6000 7000 8000 9000 10 000 11 000

Tem

pera

ture

(K

)

362

364

366

368

370

372

374TspTr , GMC

time (s)

1000 20 00 30 00 40 00 50 00 60 00 70 00 80 00 90 00 10 000 11 000

He

ate

r p

ow

er

(wa

tt)

100

120

140

160

180

200

220

240

dist

Fig. 11 – Optimal tracking with

Figs. 9–11 depict the experimental results of NN-MPC, FLCand GMC control for disturbance rejection along the optimaltrajectory. The same experimental procedure is followed toexamine the controller’s stability with disturbance. The dis-turbances are introduced as discussed in the previous section.The polymerization begins when the reactor experiences adrop of temperature to 2 K. The three controllers adjusted themanipulated variable (by increasing the heater power) to reachthe optimal setpoint. The first stable tracking is found at time750 s for the NN-MPC while the FLC and the GMC took moretime (1400 and 2000 s, respectively). The first disturbance isintroduced at time 2500 s. Due to the impact of changing thecooling water flowrate, the temperature drops from the set-point profile. In order to reject the disturbance, the controllertries to work up to the setpoint. After 400 s of the disturbanceintroduction, the NN-MPC controller is able to bring the tem-perature closer along the setpoint profile with little oscillation.The oscillation with offset (around 2 K) can be found for theFLC and the GMC and they have taken more time to comeback the setpoint (approximately 1000 s).

At a time of 4500 s, the inlet jacket temperature is increasedfrom its nominal temperature to introduce the second dis-turbance, and again the controllers acted to the response bydecreasing the manipulated variable instantaneously as thereactor temperature increases with the increase of coolant

temperature. The performance of the NN-MPC is better than

Table 7 – Control performance criteria in terms of maximum ov

Controller Maximum overshoot (K) Average offset (K)

NN-MPC 0.5 0.1

FLC 1.5 0.6

GMC 2.5 0.2

Settling time 1: Stable setpoint tracking just after reaction start-up.Settling time 2: Stable setpoint tracking after 1st disturbance.Settling time 3: Stable setpoint tracking after 2nd disturbance.

urbance rejection using GMC.

the corresponding FLC and GMC in terms of oscillatory behav-ior, offset and stable setpoint tracking in this case as well.The significant oscillation is observed throughout the setpointtracking with and without disturbance for the FLC. Table 7shows the calculated control performance criteria in termsof maximum overshoot, average offset and settling time forsetpoint tracking with disturbances. As can be seen in Table 7,the NN-MPC is able to reject the disturbance better than othercontrollers.

Besides the time-profile response analysis, comparison canalso be made using quantitative and qualitative performancecriteria. The results of the IAE and the integral square error(ISE) are taken as quantitative performance criteria and thetarget conversion and the number of average chain length areused as qualitative performance criteria for all controllers. Theresults are presented in Table 8. All the criteria investigatedclearly show that the NN-MPC controller is superior to the FLCand GMC. Furthermore, NN-MPC controller is able to reject thedisturbance better than the other two controllers in term ofresponse after the disturbance introduction. It is noticed thatthe NN-MPC also demonstrates minor oscillations, especiallyat the time of startup and with smaller magnitude than inthe FLC and GMC. Overall, the NN-MPC strategy secures supe-riority in term of the qualitative and quantitative criteria. Inaddition, the controller performance can be evaluated analyt-

ically. The Xn value and polymer conversion are determined

ershoot, average offset and settling time.

Settling time 1 (s) Settling time 2 (s) Settling time 3 (s)

750 400 5001400 1000 9002000 1000 1400

chemical engineering research and design 9 2 ( 2 0 1 4 ) 903–916 915

Table 8 – Quantitative and qualitative comparison of controller’s performance with disturbances.

Performance

Case Controller Xn X (%) IAE ISE

Desired 500 50Optimum tracking withoutdisturbance

NN-MPC 496 52.8 2513 2036FLC 481 53.7 2954 2085GMC 473 54.2 3252 3552

Optimal tracking withdisturbances (coolant flowrate and coolant tempt)

NN-MPC 482 53.2 3369 2647FLC 402 57 4634 4028GMC 430 58 3846 3232

arteNihHiiss

7

IatcilPDptcvbbtoaNpoift

R

A

A

A

t the end of polymerization. The quantitative and qualitativeesults for different controllers are presented in Table 8. As perhese results, the NN-MPC control strategy also gives the near-st value of Xn and conversion (X) target. In conclusion, theN-MPC gives the best numerical results for setpoint track-

ng and the end use polymer quality. According to Table 8, aigher conversion (more than 50%) is achieved using the GMC.owever, polymer quality (molecular weight) is much more

mportant than conversion in this system. A higher conversions not acceptable with poor polymer quality, because conver-ion can only be reached with the deviation of the optimumetpoint by the controller.

. Conclusion

n this work, a simulation and an experimental investigationre performed for the temperature control in the batch solu-ion polymerization of styrene. The polymerization reactorontrol is a challenging task as the polymerization reactions complex and nonlinear in nature. Three advanced non-inear controllers are designed and implemented in a realS plant. The controllers used are NN-MPC, FLC and GMC.ue to the lack of available online sensors to measure theolymer properties, temperature is used to infer an objec-ive of having the desired conversion and number averagehain length (Xn). The proposed controllers are tested witharious implementations including the optimal temperatureatch recipe and process disturbance rejection. Two distur-ances are introduced (changed operating parameters) in realime to check the stability of these controllers. The resultsf the NN-MPC are highlighted and compared to the otherdvanced controllers. The experimental results reveal that theN-MPC is superior to track the optimal reactor temperaturerofile without noticeable overshoot as observed in the casef a FLC or GMC with and without disturbances. In conclusion,

t is clear that the NN-MPC implemented in this work outper-orms than other advanced controllers in terms of setpointracking and load rejection capabilities.

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