Modeling and advanced control method of PVC polymerization

7/25/2019 Modeling and advanced control method of PVC polymerization

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Journal of Process Control 23 (2013) 664681

Contents lists available at SciVerse ScienceDirect

Journal ofProcess Control

journal homepage: www.elsevier .com/ locate / jprocont

Modeling and advanced control method ofPVC polymerizationprocess

Shu Zhi Gao a,Jie Sheng Wang b,, Xian Wen Gao c

a School of Informationand Engineering, Shenyang University of Chemical Technology, Liaoning, Shenyang 110142, Chinab School of Electronic and Information Engineering, University of Science & Technology Liaoning, Liaoning, Anshan114044, Chinac School of Information Science and Engineering,Northeastern University, Liaoning, Shenyang 110819, China

a r t i c l e i n f o

Article history:Received 27 July 2012

Received in revised form

21 December 2012

Accepted 23 February 2013

Available online 9 April 2013

Keywords:

PVC polymerization process

TS fuzzy neural network

Principal component analysis

Soft sensor

Harmony search

Segmental affine model

Generalized predictive control

a b s t r a c t

Based on data driven modeling theory, PVC polymerization process modeling and intelligent optimizationcontrol algorithm is studied. Firstly, a multi-TS fuzzy neural networks soft-sensing model combining

the principal component analysis (PCA) and fuzzy c-means (FCM) clustering algorithm is proposed to

predict the convention rate and velocity ofVinyle Chloride Monomer (VCM). The proposed hybrid learning

algorithm utilizing the harmony search (HS) andleast square method is used to adjust the model premise

parameters and consequent parameters. Secondly, the generalized predictive control (GPC) algorithm

of polymerizer temperature based on segmental affine is proposed. According to dynamic equation of

polymerizer temperature deduced by heat balance mechanism, the segmental affine model is built by

temperature and convention rate of the polymerizer. Then linear matrix inequality (LMI) method is

used to design the controller. Finally, simulation results and industrial application show the validity and

feasibility ofthe proposed control strategy.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

Polyvinylchloride (PVC) is one of the fivelargest thermoplasticsynthetic resins, andits production is second onlyto the polyethylene(PE)

and polypropylene (PP). PVC is a kind of general colophony, which is good in quality and is widely used. It has good mechanical properties,

anti-chemical properties and it is corrosion-resistant and difficult to burn. With vinyl chloride monomer (VCM) as a raw material, the

suspension method to produce polyvinyl chloride (PVC) resin is a kind of typical batch chemical production process. PVC polymerization

process is a complex control system with multi-variable, uncertain, nonlinear and strong coupling.

Domesticand foreign scholars havemade manyachievements on modeling,controlling and optimizationof PVC polymerization process

[18]. In 2001, Piao and Chen designed a smith-fuzzy controller to conquer the great inertia and time-delay of polymerization kettle [1].

In 2003, Yu and Dong added the double adjustment factors in the fuzzy controller of the polymerization kettle temperature, which can

on-line adjust the fuzzy rules dynamically [2]. Asua in Australia applied the fuzzy logic technique to the temperature control of polymer-

izing kettle and achieved good control performance [3]. In 2003, Huzmezan and Dumont proposed an indirect self-adaptive predictive

control strategy based on the conventional PID controller by using Laguerre function identification and predictive control, which can

shorten the production period of polymerizing kettle, improve the production ability and successfully applied in twenty-five polymerizingproduction process [4]. In 2005, Wu and Zhang proposed a multi-model predictive control strategy on the PVC polymerizing kettle tem-

perature control to achieve the satisfied application effect [5]. In 2006, Fu and Dai designed the traditional cascade structure controller by

utilizing the hybrid anti-windup PID control, forward feedback control and smith predictive control, which settled out the strong inertia

and big time-delay of the system [6]. In 2007, Yang and Zhang proposed the fuzzy controller connected with cascading PID algorithm

applied to the PVC production [7]. Marc-Andr Beyer and Wolfgang Grote proposed a self-adaptive controller composed of the nonlinear

differential geometry controller and the extended Kalman filter to effectively improve the controller performance in the case of model

mismatch [8].

Corresponding author. Tel.: +86 4125929699.

E-mail address:wang [email protected] (J.S. Wang).

0959-1524/$ seefrontmatter 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.jprocont.2013.02.008


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S.Z. Gao et al. / Journal of Process Control23 (2013) 664681 665

Fig. 1. Flowchart of PVC polymerizer process.

The PVC polymerization process is an industrial process with mass transfer, heat transfer and complex chemical reaction. From the

control point of view, it has characters of nonlinear, stronger coupling, slow time-varying and large time-delay, which is a typically

complex industrial controlled object. A great deal of uncertainty information and diverse datum make it difficult to control effectively

with traditional control methods, while the advanced control methods provide effective way for this kind of the complex control problem.

The paper proposed a data-driven integrated modeling and intelligent control of PVC polymerization process. Simulation results show the

effectiveness of the proposed control strategy.

Thepaper is organizedas follows. In Section 2, the PVC polymerizing process and the proposed advancedcontrolstrategyare introduced.

Thesoft-sensormodelbasedon multi TSFNN optimizedby HS algorithm is presentedin Section 3. In Section 4, theGPC of PVCpolymerizer

temperature based on piecewise affine is summarized. In Section 5, the application results of advancedcontrolstrategyin PVC polymerizing

process is introduced in details. Finally, the conclusion illustrates the last part.

2. Advanced control strategy of PVCpolymerization process

2.1. PVC polymerization process

A flowchart of the typical PVC polymerization kettle production process is shown in Fig. 1 [9].

In polyvinyl chloride (PVC) polymerizingprocess, allkinds of rawmaterials andauxiliary agents are placedinto thereactionkettle. They

are fully and evenly dispersed under the function of stirring. Then, we begin to ventilate the cooling water to the clipset of the reaction

kettle and baffle plate constantly in order to remove homopolymer. When the conversion rate of VCM reaches a certain value, there is a

proper pressure drop. Then, the reactions are terminated and the finished product is created.

The discussed polymerizing reaction selects SG-5 as the example. 26ton VCM is fed into the polymerization kettle. The conversion

rate is about 85%, the reaction temperature is 55.4C and the heat released from PVC polymerizing reaction is 1600kJ/kg. The important

parameters of polymerizing reaction process is shown in Table 1.


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666 S.Z.Gao et al. / Journal of Process Control23 (2013) 664681

Table 1

Polymerization parameters table.

Symbol Physical meaning Symbol Physical meaning

HR Reaction exothermic coefficient Qi Heat removed from injected water

m0 Initial quality of VCM Ti0 Inlet temperature of injected water

mv Residual mass of VCM ui Injected water flow

mp PVC quality after conversion Qs Heat removed from sealing water

Rc PVC conversion rate Ts0 Inlet temperature of sealing water

Cw Specific heat of water us Sealing water flow

Cp Specific heat of PVC Qf Heat-changing value of reactor materialCv Specific heat of VCM Tw0 Inlet temperature of cooling water

Qj Heat removed from jacket water V Volume difference

Tj0 Inlet temperature of jacket water w Density of water

Tj Outlet temperature of jacket water p Density of PVCuj Jacket water flow v Density of VCM

Qb Heat removed from baffle water Aj Jacket size

Tb0 Inlet temperature of baffle water Kj Heat-transferring coefficient of jacket

Tb Outlet temperature of baffle water Ab Baffle size

ub Baffle water flow Kb Heat-transferring coefficient of baffle

2.2. Relationship between polymerizing temperature and conversing rate

The factors influencing conversion velocity are initiator concentration, reaction temperature and polymerize degree. Polymerization

velocity is given by the following equation.

Rc= Kp[M] Ri2Kt

1/2(1)

where Ri is initiator velocity, Kp is a constant of chain increasing velocity, Rc is chain increasing ratio (polymerization velocity),Kt is the

termination velocity constant, and [M] is the monomer concentration. That is to say the polymerization reaction ratio is proportional to

the square of initiator velocity.

Kp = AeE/RT (2)

where Kpis the polymerization velocity constant, Eis the activation energy, R is the air constant, and Tis the absolute temperature.

Itcan beseen fromEq. (1) that the reaction velocity has relationship with initiator concentration and reaction temperature of constant

kind. From Eq. (2), when T increases, Kbecomes larger so that the polymerization velocity becomes larger too. Substitute (2) into (1) to

get:

Rc= AeE/RT[M] Ri

2Kt1/2 (3)

where Rcis chain growth rate (polymerizing rate).

It is known from Eq. (3) that the polymerizing rate of VCM (conversion rate) is the function of temperature. The polymerization

degree decreases with an increase in temperature. Therefore, polymerization degree only has a relationship with temperature for the VCM

polymerization reaction. Ultimately, the accuracy of the conversion velocity soft-sensor model has a direct influence on the product quality

and type of PVC.

2.3. Structure of advanced control strategy in PVC polymerizing process

The structure diagram of data-driven integrated modeling and advanced control strategy of the PVC polymerizing process is shown in

Fig. 2. Firstly, a multi TS fuzzy neural networks soft-sensing model is proposed to predict the conversion velocity and conversion rate

based on principal component analysis (PCA) method and fuzzy c-means (FCM) clustering algorithm. Then the generalized predictive

control algorithm based on the piecewise affine strategy is used to control the polymerization kettle temperature in order to reduce the

production costs and improve PVC product quality.

3. Soft-sensor modeling of polymerizing process based onmulti TS FNN optimized by HS algorithm

Thepolymerizationcycle and conversion ratio are importantquality indices in PVCproduction process. Thereforeit is critical to shorten

the production cycle of every polymerizer, increase the conversion ratio to a certain degree and ensure the control accuracy in order

to strengthen the ability of the instruments and improve product quality. The traditional polymerization monomer conversion ratio is

controlled to lower than 85%. However with the development of bigger polymerizer, the increase in conversion ratio of every polymerizer

has an important significance for enhancing the production capability of the polymerizer device and reducing the production costs.

Currently, the nonlinear soft-sensor modeling methods based on sample datum mostly adopt a single model structure. Based on the

guiding ideology of divide and conquer on the sum task decomposition, many manifold model structures have been put forward, such as

multiple neural networks (MNN), stacked NN (SNN) and distributed NN (DNN) [10,11]. So according to the principle that multiple models

can enhance the overall accuracy and robustness of a predicative model, a multi TS fuzzy neural network soft-sensing model combining

with fuzzy c-means (FCM) clustering algorithm is proposed to predict the conversion rate and velocity of VCM in the PVC polymerizing

production process.


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VCM PVC

Multi T-S fuzzy neural

networks

Harmony search Optimization

algorithm

Soft-sensor modelling

Principal component analysis

Segmental affine model of

temperature and convention

rate

Temperature advanced

control strategy

Generalized predictive control

Convention

rate model

Polymerizationkettle

temperature

Sealingwater

flow

Tempetureof

coolingwater

Temperature

mechanism

model

PVCpolymerizing process

Fig. 2. Advanced control structure of PVC polymerize process.

3.1. Multi TS fuzzy neural network soft-sensormodel

According to the characteristics of a polymerization process, 10 process variablesrelated withthe conventional rate and velocity of VCM

are identifiedas the secondaryvariables of the soft-sensor model, which respectively are kettle inside temperature (TIC-P101), kettle inside

pressure (PIC-P102) and baffle flow (FIC-P101), clip set of water flow (FIC-P102), infuse water flow (FIC-P104), seal water flow (FIC-P105),

cooling water inlet temperature, clip set of water outlet temperature (TI-P109), damper water outlet temperature (TI-P110) and injecting

water and seal water inlet temperature (cold cistern exit temperature, TIC-WA01).

3.1.1. Structure of multi TS fuzzy neural network soft-sensormodel

Considering a multiple-input multiple-output (MIMO) system, its training samples can be expressed as [12]:D = {Y,Xi|i = 1, 2, . . . , m},whereY= {yj|j = 1, 2, . . . , n} is the output matrix (n denotes the sample size of a training set and m shows the number of input variables)and Xi = [x1i, x2i, . . . , xni]

(i = 1,2, . . . , m) indicates the i-th input variable. The FCM algorithm partitions a collection ofn data points(X= {x1, x2, . . . , xn}) into cfuzzy clusters (2 c n). V= {v1, v2, . . . , vc} is a set of corresponding cluster centers in the data setX. uij(0 uij 1) is the membership degree of dataxjbelongingto the cluster center vi. Theobject function of theFCM algorithmis to findU= [uij]cnand V= (v1, v2, . . . , vc) to make the formula (4) smallest.

Jm(U,V) =

ci=1

nj=1

(uij)m||xj vi||

2 (4)

AssumeD is partitioned intoCclusters {D1,D2, . . . , Dc}by theFCM algorithm. Thecsub-models{M1,M2, . . . , M c} are established basedon the TS fuzzy neural network by adopting the subset {Di|i = 1,2, . . . , c }. Multi TS FNN configuration based on the FCM algorithm [13]is shown in Fig. 3.

3.1.2. Model dimensionality reduction based on principal component analysis

If the input vector dimension of the TS model is too long, the network topology will be complex and training will become very

complex. Therefore, the principal component analysis (PCA) method [10] is adopted to reduce the model dimension of the TS model. The

Fig. 3. Multi TS FNN configurationbased on FCM algorithm.


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Table 2

Accumulated contributed ratio of different principal.

PCs Eigenvalues Percentage of eigenvalues (%) Cumulated percentage (%)

1 1.1620 59.51 59.51

2 0.3278 16.79 76.30

3 0.1575 6.07 84.36

4 0.1185 7.34 90.43

5 0.0958 4.91 95.34

6 0.0366 1.87 97.21

7 0.0249 1.27 98.488 0.0185 0.95 99.43

9 0.0111 0.57 100.00

10 0 0 100.00

PCA approach uses all of the original variables to obtain a smaller set of new variables (principal components PCs) that can be used to

approximate the original variables. PCs are uncorrelated and are ordered so that the first few retain most of the variation present in the

original set.

The principal component analysis method is adopted to tackle the historical datum composed of the input variables of the soft-sensor

model. The analysis results are shown in Table 2. The variance contribution ratio of the former 4 principal components reaches 90.43%, so

the corresponding principal variables are selected as input variables of the soft-sensor model.

3.2. TS fuzzy neural networks based on harmony search algorithm

3.2.1. Structure of TS fuzzy neural networks soft-sensormodel

The TakagiSugeno (TS) fuzzy model has the ability to construct inputoutput mapping based on human knowledge (in the form of

fuzzy if-then rules) and stipulate inputoutput data pairs [12]. The architecture of the TS fuzzy model under study is shown in Fig. 4.

The model inputs areXr(r= 1, . . . , 4). The fuzzy linguistic variable of eachxiis represented as:

T(xi)= {A1i, A

2i, . .. , A

mii } (5)

whereAji(j = 1,2,3, . . . , mi)isthejth language variable value ofxi, a fuzzy set definedin the domainUx, whose correspondingmembership

functions is defined as follows.

Aji

(xi) (i = 1,2, . . . , r ; j = 1,2,3, . . . , mi) (6)

The VCM conversion and conversion velocity are model outputs (fh, h = 1,2). So the formof thejthfuzzy rule inthe TS model may berepresented as:

Ifx1

isAj

1, x

2isAj

2, . . . , x

risAj

r Thenyj = pj

0+ pj

1x

1+, . . . , pj

rxr

(j = 1,2, . . . ,m;m =

mi=1

mi) (7)

The TS model in Fig. 4 is consisted of the antecedent network and the consequent network. The antecedent network is used to match

the antecedent component of fuzzy rules and the consequent network is used to generate the consequent component of fuzzy rules.

3.2.1.1. Antecedent network. There are four layers in the antecedent network. The first layer is input layer to transfer input values to the

next layer, in whichthe number of nodesN1 = r. Each node in the second layer represents a language variable to compute the membershipfunctiongijof every input component. Each node of the third layer represents a fuzzy rule to matchthe antecedent component of the fuzzy

rules and then calculate the fitness of each rule. The number of the fourth layer is the same as the third layer, whose function is to realize

the normalization calculation represented as follows.

l =lmk=1

k=

exp[r

i=1(xi cij)

2/22ij

]

mk=1

exp[

ri=1

(xi cij)2/22

ij]

(8)

3.2.1.2. Consequentnetwork. Thefifthlayeris called fuzzydecisionlayerfl = Wl l, inwhichWl = wl0 + wl1x1 + wlrxr(l = 1,2, . . . , m).The sixth layer is called defuzziation layer, whose node number is in correspond with the number of output variables.

The Hybrid algorithm combining HS algorithm and minimum least square method is used to the fine tuning the consequent and

antecedent parameters for each TS sub-model in this paper.

3.2.2. Harmony search optimization algorithm

Harmony search (HS) proposed by Geem et al. [14] is a derivative-free and meta-heuristic algorithm (also known as soft computing

algorithm or evolutionary algorithm) mimicking the improvisation process of musicians. In the process, each musician plays a note for

finding the best harmony. Likewise, each decision variable in the optimization process has a value for finding a best vector all together.

Since its inception, HS has found several applications in a wide variety of practical optimization problems such as pipe-network design,

structural optimization, vehicle routing problem, combined heat and power economic dispatch problem, and Dam Scheduling [1520].

The instruments i(i = 1,2, . . . , pop) are analogized with the i-th design variable of optimization problems by the HS algorithm. TheharmonyHj(j = 1,2, . . . , HMS) of every instrument tone is equivalent to thej-th solution vector of optimization problems and its estimateis in analogy with objective function. First, the HS algorithmproduces HMSinitial solutions (harmony), which are put in harmony memory

storage HM. Then a new solution is searched in HM by probabilityphmcrand outside HM by probability 1phmcr with a possible variable


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Fig. 4. Structure diagram of TS fuzzy neural network.

range of HM. Local disturbance is produced in this algorithm for a new solution by probabilityppar. Then it is determined that the objective

function value of the new solution is any better than the worst solution. The worst solution will be replaced if a worse solution arises are

continuously produced until it reaches the predetermined iteration.

3.2.3. Algorithm procedure

The algorithm procedure of the proposed hybrid learning algorithm to adjust the parameters of TS fuzzy neural network is shown

below.

Step 1: Initialize the HS algorithm parameters. The parameters include the population sizepop, searching space dimensionD (the number

of premise parameters), harmonicmemory storage HMS, memory storage selectingprobabilityphmcr, tone adjustment probabilitypparand

iterative number n. Set the iterative number n= 1. In the searching space, randomly initialize population individuals. The i-th individual

vector is expressed asXnid

(1 i pop, 1 d D).Step 2: Each individual vector of the population is taken in turn as premise parameters TS fuzzy neural network. Then the excitation

intensity and normalized excitation intensity of all rules are calculated. Therefore, conclusion parameters are distinguished by using least

square method. Finally, according to the Eq. (35), therootmean squareerror(RMSE) produced by the individualsTS fuzzy neuralnetwork

is calculated, which is set as the fitness value RMSEni of the individual.

RMSE =

Nk=1

(yk y

k)

2

N (9)


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Fig. 5. Predictive output of convert ratio of VCM.

Step 3: Initialize the harmony memory. The HM matrix is filled with as many randomly generated solution vectors as the HMS as shown

by Eq. (36).

HM =

x11 x12

x1D1 x1D

x21 x22

x2D1 x2D

......

......

...

xHMS11 xHMS12

xHMS1D1 xHMS1D

xHMS1 xHMS2 x

HMSD1 x

HMSD

(10)

Step 4: Improvise a new harmony. Firstly, make a new vectorx. For each componentxiwith probabilityphmcr, pick the component from

memory,xi= xrand

()

i with probability 1 phmcr, pick a newrandom value in the allowed range.Then, forpitchadjustment, each component

xi: with probabilitypparchangexjby a small amount,x

i= x

i bw rand() with probability 1ppar, do nothing.

Step 5: Update the harmony memory. Ifxm is better than the worstxi in the memory, then replacexi byxm.Step 6: Check the stopping criterion. The HSA is terminated when the stopping criterion (e.g. maximum number of improvisations) has

been met. Otherwise, repeat from step 3.

Theparameters in theproposed hybrid learning algorithm are set as follows: population numberpop= 30,the iterationnumbern is 100,

harmonic memory storage (HMS) of HS algorithms is 10, the searching probabilityphmcrof HMS is 0.95, and tone adjustment probabilitypparchanges from 0.3 linearly increasing to 0.99 with evolution iteration.

3.3. Simulation results

PVCgenerally haseight product grades: SG-1, SG-2,SG-3,SG-4, SG-5, SG-6, SG-7,and SG-8.The proposed soft-sensor model is established

based on thedatum of the SG-5 production process. However, the proposed methodcan be used forthe other grade productions by utilizing

new process datum. Aiming at the polymerization process in a 40,000 tons/year polyvinyl chloride (PVC) production line, 1500 uniform

and representative historical datum of five kettles are chosen as the experiment data. After the data pretreatment, the former 4 kettles

are selected as the training data to be used to train the Multi TS FNN and single TS FNN. The last kettle datum is used to verify the

performance of the soft sensor model. The results of adopting the two methods for validating the data prediction output and predictive

error are shown in Figs. 58.

Usually average relative variance (ARV) is calculated to measure the error between the predicted value and real-time measured value,

which is defined as the following equation.

ARV =

Ni=1

[x(i) x(i)]2N

i=1[x(i) x(i)]2

(11)

where Nis the numbers of comparative data, x(i) is the i-th real-time data,xis the average of measured datum, andx(i) is the predictivevalue. Obviously, the fact that the value of AVR is smaller shows that the prediction effect is better. ARV= 0 shows that the predictive effect

is ideal. ARV = 1 shows that the predictive effect is equal to the mean. Table 3 shows the compared results of AVR under the two methods.

Table 3

Predictive AVR.

M TS FNN TS FNN

AVR (conversion ratio) 0.104 0.139

AVR (conversion velocity) 0.132 0.214


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Fig. 6. Predictive output of rate of VCM conversion.

Fig. 7. Predictive error of convert ratio of VCM.

From Figs. 58 and Table 3, the multi TS FNN soft-sensor model based on the PCA method and FCM algorithm has higher precision of

prediction and generalization ability for the conversion and conversion rate of VCM proposed in the paper. The hybrid learning algorithm

combining the harmony search optimization algorithm and the least square method proposed in the paper can effectively adjust the

premise parameters and conclusion parameters of the TS model. Simulation results show that the prediction accuracy of the soft sensor

model proposed in this paper is higher. Optimization control of a PVC polymerization process based on the prediction model will surely

have a great significance on increasing the conversion rate of polymerization kettles and reducing the production costs.

Fig. 8. Predictive error of rate of VCM conversion.


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4. GPC of PVC polymerizer temperature based onpiecewise affine

Thediscussed polyethylene polymerization process is an intense exothermic reaction (1600kJ/kg) process. Heat of reactionis needed to

be removed intime to keep the reactionin constant temperature,so the transformationwill nothappen.Therefore,in order to guarantee the

quality of PVCproduction, Polymerizer temperature hasto be controlled in constant value required by the PVCpolymerizationtechnique.A

70 m3 polymerizer temperature of PVC production process is used as the controlled object. The GPC method of the polymerizer temperature

based on the piecewise affine is proposed in this paper and the stability of the controller is analyzed. In the end, simulation results show

the algorithm can better satisfy the control accuracy of polymerizer temperature.

4.1. Mechanismmodeling of polymerizer temperature

PVC polymerizing process is a typically batch exothermic reaction process. According to the heat balance principle, the total calories

instantaneouslyreleasedin polymerizingreaction is equal to the heat amountremovedby jacketwaterand baffle plate water,the absorbed

heat by injection water and sealing water, and the heat making the polymerizer temperature change. Thus the following equations are

obtained.

HRm0Rc= Qj + Qb+ Qi + Qs+ Qf (12)

where

Qj = Cwuj(Tj Tj0) (13)

Qb = Cwub(Tb Tb0) (14)

Qi = Cwui(T Ti0) (15)

Qs = Cwus(T Ts0) (16)

Qf = CvmvT+ CpmpT+ CwwVT (17)

The outlet temperature of the baffle plate water and jacket water is defined as follows [21].

Tj =T+ jTj0

1 + j, j =

CwujKjAj

(18)

Tb =T+ bTb0

1 + b, j =

CwubKbAb

(19)

Based on the Eqs. (12)(19), the differential equation of the polymerizer temperature is deduced as follows.

T=HRm0Rc Cwuj(T Tj0/1+ j) Cwub(T Tb0/1 + b) Cw(m0w(p v)/pv)Rc(T Ti0)

m0(Cv(1 Rc) + CpRc+ Cww(Rc(p v)/pv)) (20)

Onthe other hand, itis known fromEq. (3) that the polymerizing rate of VCM(conversion rate) is thenonlinear functionof temperature,

while the temperature is an important factoraffecting PVCproductionquality.To make sure the quality of PVCproduction, the polymerizer

temperature has to be controlled to a certain constant value. So the piecewise affine model is set up based on the conversion rate of VCM.

4.2. Piecewise affine system

4.2.1. Polyhedral elliptical set regional division

Consider the following piecewise affine system:

x(k+ 1) = Aix(k) + Biu(k) + bi

y(k) = Cix(k)

x(k)Xi, i I

(21)

wherex(k)Rn is thesystem state vector, u(k)Rm is thecontrolinput,y(k)Rp is the output variable,Ai, Bi, Ci(i = 1,2,...N) is respectivelythe state matrix and input matrix of the ith subsystem, bi is the constant affine vector, and N> 1 is the number of subsystems. Assuming

the state feedback controller of system (21) is:

u(k) = Kix(k) (22)

Substituting system (22) into system (21) to get:

x(k+ 1) = Aix(k) + bi (23)

where

Ai = Ai + BiKi (24)


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Based on the regional division of piecewise affine system, the regional division of subsystem can be represented in the form of elliptical

set, whose dimension is not more than the state space dimension. SoXi i, where iis ellipse, namely i = {x|||Eix+ ei|| 1}. Rewrite itinto the quadratic inequality LIM:

x(k)

1

T ETiEi

eTiEi 1 + e

Tiei

x(k)

1

0 (25)

Especially, whenXi = {x|d1< cTix < d2} (d1 and d2 are constants representing the state boundary of subsystem working region), the

coefficients of the corresponding elliptical set i= {x||E

ix+ e

i|| 1} can be represented as follows.

Ei = 2CTi/(d2 d1)

ei = (d2 + d1)/(d2 d1)(26)

4.2.2. Piecewise linearization

Linearizing system (20) at any point to obtain:

T=f

x

Rc

Rc+f

RcRc+

f

ujuj +

f

TT (27)

where

f

Rc=

HRm0 Cw(m0w(p v)/pv)(T Ti0)


fRc

= HRm0 Cw(m0w(p v)/pv)(T Ti0)m0(Cv(1 Rc) + CpRc+ Cww(Rc(p v)/pv))

2Cv+ Cp+ Cww (p

v)pv

(29)

f

uj=

Cw(T Tj0)

m0(Cv(1 Rc) + CpRc+ Cww(Rc(p v)/pv))

1

(1+ 0.0232uj)2

(30)

f

T =

(Cwuj/1 + j) (Cwub/1 + b) Cw(m0w(p v)/pv)Rc


Define state variables:

x =

T

Rc

x=

T

Rc

=

f/T f/Rc

M(E/RT2) 0

T

Rc

+

f/uj

0

uj +

M +1

M +2

y = [ 1 0 ] TRc

(32)

whereM = A[M](Rt/2Kt)1/2, iare the higher order components andbi = M +i.

4.3. Design of generalized predictive controller

Considering the piecewise affine system (21), the performance index of GPC in infinite time domain is defined as follows.

minu(k+m|k),m=0,1,...

J(k)

J(k) =

m=0

x(k+m|k)TQIx(k+m|k) +

m=0

u(k+m|k)TRu(k+m|k)(33)

where QI> 0 and R > 0 are the symmetric positive definite matrix,x(k+m|k) represents the state predictive value of model (23) at timek+m, u(k+m|k) is the value of the controlled input sequence {u(k|k), u(k+ 1|k), . . . , u(k+m|k)} at time k+m optimizing the rolling

indicator at time k.According to the characteristic of GPC,the controlled inputu(k+m|k) is fedintothe controlsystem, then atthe next moment; recalculatetheoptimization problem to receive differentcontrolled input sequences. Then feed the first term on thesystem, andso forth. That is to say

the rolling optimizationis realized. The quadratic Lyapunovfunction of system (21) at the momentk is defind asV(x(k|k)) = xT(k|k)Px(k|k).Let:

V(x(k+m+ 1|k)) V(x(k+m|k)) xT(k+m|k)QIx(k+m|k) uT(k+m|k)Ru(k+m|k) (34)

whenx(|k) = 0, V(x(|k)) = 0.

Jn+1(k) =

m=n+1

[xT(k+m|k)QIx(k+m|k) + uT(k+m|k)Ru(k+m|k)] (35)

Accumulate Eq. (35) from m= 0 t o m= to get:

V(x(k|k)) J(k) (36)


11/18


Then the upper determinate bound of the performance index functionJ(k) is defined as follows.

J(k) V(x(k|k)) (37)

Thus, the minimum performance index is equal to minimizeV(x(k|k)), that is to say:

minu(k+m|k),m=0,1,...

V(x(k|k)) (38)

In GPCalgorithm, a group of the state feedback control inputsare obtained by minimizingV(x(k|k)).Then merelythe first term of controlsequences is fed into the controlled system. At the next sampling moment, the statex(k+ 1|k) is measured again, and the correspondingsubsystem models as well as the corresponding state division are selected to calculate the feedback gain matrixKiagain.

4.4. Predictive control algorithm based on piecewise affine system

Theorem 1. Considering system (21),x(k|k) is the measured state value of the ith subsystem at time k, {Ai, Bi, bi} and {Ai+1, Bi+1, bi+1} arerespectively parameter matrixes of the ith and the i+ 1 th subsystems, where i I= {1,2, . . . , N }. ||Ei+1x+ ei+1|| 1 is the description ofxXi+1 in elliptical set. Control inputs u(k|k) u(k+ n|k) are free variables. The system switches fromXi to Xi+1 after n steps, where n isa known constant. If there exists Yi+1 = Ki+1Q, Q 0, > 0, > 0 and a group of control variables which meets the following LMI opti-mization problem. Then system (21) can switch to the equilibrium points in accordance with the desired order, and realize the asymptotic

stability. Scalar is the optimization performance index under arbitrary switching sequence.

min,u,Q,Yi

(39)

s.t.:

1

QI0.5x(k|k) I 0 0 0 0 0 0

......

. . ....

......

......

QI0.5x(k+ n|k) 0 0 I 0 0 0 0

R0.5u(k|k) 0 0 0 I 0 0 0

......

......

.... . .

......

R0.5u(k+ n|k) 0 0 0 0 0 I 0

x(k+ n+ 1|k) 0 0 0 0 0 0 Q

0 (40)

Q

Ai+1Q+ Bi+1Yi+1 Q+ bi+1bi+1T bi+1ei+1

T 0 0

Ei+1Q ei+1bi+1T

(I ei+1ei+1T) 0 0

QI0.5Q 0 0 I 0

R0.5Yi+1 0 0 0 I

0 (41)

wherex(k+ 1|k) x(k+ n+ 1|k) is got by recursive. Its specific form is described as follows.

x(k+ n+ 1|k) = An+1i x(k|k) +

nj=0

Anji Biu(k+j|k) +

nj=1

Anji bi (42)

The control strategy of Theorem 1 contains twosteps broadly, namely the control inputs divided into the free component input and the

feedback input constrained by terminal ellipsoid set.

(1) When the system does not switch to the terminally regional division, u(k+m|k),m = 0, . . . , n is free variable satisfying Theorem 1.Control sequence u(k+m|k),m = 0,1, . . . , n in limited time domain will compulse the system statex(k+m|k) fromXiintoXi+1aftern steps to enter the terminal ellipsoid set in the end.

(2) When the system switches to the terminal ellipsoid set, Ut: u(k+m|k) = Ki+1x(k+m|k), m n+ 1, Ki+1 = Yi+1Q1, where Ki+1is the

state feedback matrix. State feedbackcontroller makesthe system statestable to theorigin point.Jn+1(k) xT(k+ n+ 1|k)Px(k+ n+ 1|k)

is the upper determine bound of cost function in the infinite time domain, where the free componentu(k+m|k),m = 0, . . . , n and thestate feedback matrix K

i+1are all convex optimal solution of LMIs.


12/18


0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

t(min)

Rc

*

*

*

)15.0,82(

)45.0,8.151(

)82.0,9.243(

Fig. 9. Oval plot ofPWA system.

4.5. System simulation

4.5.1. Piecewise affinemodeling

Basedon the dynamic equation of the polymerizer temperature by theheat balance mechanism of polymerizationprocess, the piecewise

affine model of the polymerizer temperature and conversion rate is set up. On the other hand, every state space subsystem is described by

ellipsoid set. Mechanism model is built as:

T=41600000 x ((4.167/1 + 0.0232uj)uj + 61549 + 51853 x)(T 18)

(41366 + 39000x) (43)

When control input is equal to zero, three equilibrium points are resolved, that is (Rc1, u)= ([82, 0.15], 0), (Rc2, u)= ([151.8, 0.45], 0)

and (Rc3, u)= ([243.9, 0.82], 0). In accordance with the three equilibrium points, the state space is divided into three ellipsoid sets, which

is shown in Fig. 9. They are respectivelyE1 =6.7, e1 =1; E2 =5.71, e2 =2.7, E3 =10 and e3 =7.5.

x=

0.0093 7.06 102

0.01 0

T

Rc

+

2.802 105

0

u+

61.54

0.069

x=0.01245 4.77 103

0.056 0

TRc+ 2.143 105

0

u+ 174.2230.0636

x =

0.005681 2.957 102

0.036 0

T

Rc

+

1.712 105

0

u+

200.86

0.0844

where x (x1, x2, x3), x1 (0,0.3), x2 (0.3,0.65), x3 (0.65,0.85). Within every ellipsoid set, the linearization is carried out near theequilibrium point to obtain the piecewise affine model of polymerizer system (temperature Tand conversion rate Rc).

4.5.2. GPC control based on piecewise affine model

According to the practical situation possibly occurred in polymerizering process, three main situations are studied in this section.

(1) While operation process is in good condition, the control effect curves are shown in Fig. 10. Sampling time is 6 s, predictive step is 40,

and control step is 10, as well asQ1 = 1, R1 = 81011, Q2 = 1, R2 = 610

12, Q3 = 1, R3 = 6101. Itcanbe seen from Fig. 10, the system

is able to trace the given output stably with good control effect.(2) While operation process is affected by the step interference of uncertain factors, in which the interference amplitude is 3 C and the

amplitude width is 15min, the control effect curves are shown in Fig. 11. It can be seen that the system may quickly overcome the

disturbance effect under the sudden step interference.

(3) While the controlled object is affected by the white noise disturbance with range (0.003, 0.003), the control effect curves are shown

in Fig. 12. It can be seen that the system has better robust performance and the temperature is controlled near the set-point value

under the white noise interference.

5. Application of advanced control strategy in PVCpolymerizing process

5.1. Application results of advanced control strategy

The industrial application results of the proposed advance control strategy in PVC polymerizing process is shown in Fig. 13(a)(c). Due

to the application of the advanced control technology of PVC polymerizing temperature based on piecewise affine, the control accuracy

of polymerizing temperature has been effectively improved. It can be seen from Fig. 13 that the system has good tracking performance,


13/18


Fig. 10. Control results of PVC process in normal working conditions.

Fig. 11. Control results of PVC process under step noise.

Fig. 12. Control results of PVCprocess under white noise.


14/18

S.Z.Gao et al. / Journal of Process Control23 (2013) 664681 677

Fig. 13. Real-time temperature curves of polymerize process.

makes the polymerizing temperature throughout controlled in a constant value of 55.4 in the reaction process, and has strong robustness

to the outside disturbance, which improves the PVC product quality.

5.2. Industrial application effect

Combined with the technical characteristics and requirements of 40 thousand tons/year PVC polymerizing process, the industrial appli-

cation of the advanced control strategy of PVC polymerizing process is carried out. Its application value is mainly reflected in two aspects:

increasing PVC product quality and reducing production cost of VCM.


15/18


Table 4

VCM production costs before and after optimized control (RMB/ton).

Item Unit Number Unit Price Sum of money Total cost ratio (%)

Material costs Carbide ton 1.5 2250 3375 62.41 (62.92)

Chlorine ton 0.65 1500 975 18.03 (18.18)

Hydrogen ton 0.02 10,000 200 3.70 (3.73)

Liquid alkali ton 0.015 500 7.5 0.14 (0.14)

Catalyst kg 1.1 20.5 22.55 0.42 (0.42)

Water Ton 30 2 60 1.11 (1.11)

Electric KW h 265 0.35 92.75 1.72 (1.73)Nitrogen nm3 100 0.3 30 0.55 (0.56)

Labor costs Single 1 45 (41) 45 (41) 0.83 (0.76)

Manufacturing costs 600 (560) 600 (560) 11.09 (10.44)

Sum 5407.8 (5363.8) 100

Table 5

PVC product performance index (GB/T5761-2006, FDJH/JS01-0200.13).

Inspection

item

Viscosity

(ml/g)

Apparent

density

(g/ml)

100g

plasticizer

absorption

capacity (g)

Volatile

matter (%)

Sieve residue % Number of

impurity

particle

Whiteness

(%)

Numberof

fisheyes/

400cm2

Residual

vinyl

chloride

(g/g)

250m

sieve mesh

63m

sieve mesh

SG5 index

Superior 118107 0.48 19 0.40 2.0 95 16 78 20 5

First 118107 0.45 17 0.40 2.0 90 30 75 40 10

Eligible 118107 0.42 0.50 8.0 85 80 70 90 30

5.2.1. Reducing production costs

VCM producingcosts are composedof three parts: raw materialcosts, labor costs andthe manufacturing costs. The raw materialcosts are

constantfor the given production yield. Whenthe proposed advancedcontrol strategy is applied in the PVC production process, the artificial

cost and the manufacturing cost are relatively reduced, so the total production costs declines. The VCM productions costs before and after

utilizing the optimized control method are listed in Table 4. The data in the brackets with bold fonts are the costs when the optimized

control methodis used. The decliningvalue of costs is 5407.85363.8= 44RMB/ton. For a 40thousand tons/year PVC polymerizingprocess,

the economic benefits obtained by reducing the cost is 44RMB/ton40,000 ton/year= 1760thousand RMB/year.

5.2.2. Improve product qualityProduction capacity of PVC device is 40,000 tons/year, the PVC production type is SG-5, and its performance index standard of product

quality is in accordance with GB standard described in Table 5.

Nowcollectten batches of PVC product quality for comparison. The PVC productsgrades before andafter utilizing the proposed advanced

optimization control strategy are shown in Tables 6 and 7. It can be seen from that the superior grade of PVC products is 40% and the first

grade of PVC products is 60% before implementing the advanced control strategy. After implementing the advanced control methods, the

superior grade of PVC products is 60% and the first grade of PVC products is 40%. In sum the product excellence rate of PVC product quality

improved 20%.

Table 6

PVC product inspection report (before optimization).

Inspection

item

Viscosity

(ml/g)

Apparent

density

(g/ml)

100g

plasticizer

absorption

capacity (g)

Volatile

matter (%)

Sieve residue (%) Number of

impurity

particle

Whiteness

(%)

Number of

Fisheyes/

400cm2

Residual

vinyl

chloride

(g/g)

Grade

250m

sieve mesh

63m

sieve mesh

Batchnumber

5-11001 112 0.54 23 0.12 2.0 98 29 86 40 10 First

5-11002 114 0.54 23 0.18 1.2 98 20 83 38 10 First

5-11003 114 0.55 22 0.14 1.2 98 16 82 18 5 Superior

5-11004 114 0.54 22 0.16 1.2 98 15 83 18 4 Superior

5-11005 113 0.54 23 0.16 1.2 98 16 82 17 5 Superior

5-11006 113 0.55 23 0.12 1.2 97 16 83 18 5 Superior

5-11007 114 0.54 22 0.12 1.2 98 24 82 32 8 First

5-11008 114 0.54 22 0.30 1.2 98 26 82 34 8 First

5-11009 113 0.54 21 0.20 1.2 98 26 80 30 10 First

5-11010 112 0.54 22 0.18 1.2 98 24 80 30 10 First


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Table 7

PVC product inspection report (after optimization).

Inspection

item

Viscosity

(ml/g)

Apparent

density

(g/ml)

100g

plasticizer

absorption

capacity (g)

Volatile

matter (%)

Sieve residue (%) Number of

Impurity

particle

Whiteness

(%)

Number of

fisheyes/

400cm2

Residual

vinyl

chloride

(g/g)

Grade

250m

Sieve mesh

63m

Sieve mesh

Batchnumber

5-11106 113 0.55 23 0.16 1.2 98 29 86 20 5 Superior

5-11107 114 0.54 22 0.14 1.2 98 14 85 18 5 Superior

5-11108 114 0.55 23 0.12 1.2 98 10 86 18 5 Superior

5-11109 113 0.54 23 0.18 2.0 98 10 85 26 5 First

5-11110 114 0.54 22 0.14 1.2 98 16 84 25 5 First

5-11114 113 0.54 23 0.16 1.2 98 14 82 13 5 Superior

5-11115 112 0.53 23 0.14 1.2 98 16 83 20 5 Superior

5-11116 114 0.54 23 0.10 1.2 98 17 83 34 5 First

5-11117 114 0.55 22 0.16 1.2 98 10 82 10 5 Superior

5-11118 114 0.54 22 0.16 1.2 98 9 82 24 5 First

6. Conclusions

PVC polymerizing process is a complex industrial process object and its temperature is nonlinear and difficult to control. This paperapplies soft-sensor method, piecewise affine technology and advanced control algorithm to control the temperature of polymerizing pro-

cess and designs advanced control strategies consisted of multiple model soft-sensor measurement strategy based on harmony search

optimization and the piecewise affine based GPC strategy for polymerization kettle temperature. Simulation results and industrial appli-

cation indicate the feasibility and validity of the proposed advanced control method. It can meet the requirements of real-time control for

PVC polymerizing process and further improve the PVC product quality and reduce the production costs.

Acknowledgments

This work was supported by the Key Program of National Natural Science Foundation of China (61034005), the Postgraduate Scientific

Research and Innovation Projects of Basic Scientific Research Operating Expenses of Ministry of Education (N100604001), the Program

for Liaoning Excellent Talents in University of China (LJQ2011027) and the Program for China Postdoctoral Science Foundation of China

(20110491510).

Appendix A. Stability analysis

The piecewise quadratic Lyapunov stability method based on elliptical set is used in this paper, in which the continuous state sets are

substituted with a group of elliptical sets. That is to say, in every state partition, a quadratic Lyapunov function is found to be positive in

the state partition. Consider the following discrete piecewise affine system:

x(k+ 1) =

Ni=1

i(k)Aix(k) +

Ni=1

i(k)Biu(k) +

Ni=1

i(k)bi x(k)Xi, i I (44)

where i(k) is the switch symbol vector, satisfying i: Z+ = {0,1,2, . . .} {0,1},

Ni=1i(k) = 1. i(k0) = 1(i = {1,2, . . . N }) represents

that the i subsystem works at the sampling time k0, in which N > 1 is the number of the subsystems.

Theorem 2. For system (44), if the following LMI has a solution, the controller u(k) = YiQi1x(k) can make the system asymptotically

stable.

Qi = QT

i > 0,Qj = QT

j > 0, i> 0Qi (AiQi + BiYi)

T (EiQi)T

AiQi + BiYi Qj ibieTi

EiQi ieibTi

i(I eieTi)

> 0

x(k)Xi, i , j I

(45)

The prove process ofTheorem 1 is descried as follows.

Assume u(k) = Kix(k) and substitute it into the discrete-time piecewise affine system (46), then get:

x(k+ 1) =

Ni=1

i(k) Aix(k) +

Ni=1

i(k)bi, x(k)Xi, i I

whereAi = Ai + BiKi.


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Structure the quadratic piecewise Lyapunov function:

V(k) =xT(k)(

Ni=1

i(k)Pi)x(k)

where Pi> 0. Ifand only ifx(k) = 0, V(k) = 0. Because

V(k+ 1) V(k) =xT(k+ 1)(

Ni=1

i(k+ 1)P

i)x(k+ 1) xT(k)(

Ni=1

i(k)P

i)x(k) 0

It is suitable for all i I. Wheni(k) = 1,l /=i(k) = 0, j(k+ 1) = 1, l /=j(k+ 1) = 0, the same formula was established. Thus,V(k+ 1) V(k) < 0 (x(k) /= 0) is equal to the following formula:

V(k+ 1) V(k) = xT(k)( ATiPj Ai Pi)x(k) +x

T(k) ATiPjbi + b

TiPj Aix(k) + b

TiPjbi< 0,where i, j I.

Transform it to the matrix style:x(k)1

TATiPj Ai Pi A

TiPjbi

bTiPj Ai b

TiPjbi

x(k)1

< 0

wherex(k)Xi. It can be expressed as the elliptical set Ei+1x(k) + ei 1. Therefore:

x(k)1

T

ETiEi E

Tie i

eTiEi 1+ e

Tiei

x(k)1 0

According to Sprocedure, there exists to make the following formula established.ATiPj Ai Pi E

TiEi A

TiPjbi E

Tiei

bTiPj Ai e

TiEi b

TiPjbi (1+ e

Tiei)

< 0

Transform it into the following equation:Pi + E

TiEi E

Tiei

eTiEi (1 + e

Tiei)

ATibTi

Pj

Ai bi> 0

Based on the shur-supply theorem, the above formula is equal to:Pi + E

TiEi E

Tiei A

Ti

eTiEi (1 + e

Tiei) b

Ti

Ai bi P1j

> 0

Multiply diag

I,

0 II 0

on the both sides of the above equation and let Pi = Q

1i , Pj = Q

1j

, then obtain:

Q1i + ETiEi ATi ETi e iAi Qj bieT

iEi b

Ti (1 eT

iei)

> 0

Multiply diag[Q,I,I] on the both sides of the above equation, then obtain:

Qi + QiE

TiEiQi Qi A

Ti QiE

Tie i

AiQi Qj bieT

iEiQi b

Ti

(1 eTiei)

> 0

Based on the shur-supply theorem, the above formula is equal to:Qi + QiE

TiEiQi ( AiQi)

T

AiQi Qj

+

QiE

Tiei

bi

1(1 eTiei)

1 eT

iEiQi b

Ti

> 0

Due to (I eTe)1

= I+ eT(I eeT)1e, obtain:

Qi ( AiQi)T

AiQi Qj

+

QiE

Ti(I eie

Ti)1EiQi QiE

Ti(I eie

Ti)1eib

Ti

bieTi(I eie

Ti)1EiQi

1bieTi(I eie

Ti)1eib

Ti

> 0

It is equal to the following equation.

Qi ( AiQi)

T

AiQi Qj + QiE

Ti

1bieTi (I eieTi)

1

EiQi 1eibTi > 0


18/18


Apply the shur-supply theorem, the above formula is equal to:Qi ( AiQi)

TQj

AiQi Qj 1bie

Ti

EiQi 1eib

Ti (I eie

Ti)1

> 0

Let Yi = KiQi, that is to say Ki = YiQ1i

. So the theorem is proved.

References

[1] C.J. Piao, C.L. Chen, Application of fuzzy control in polymerizing-kettle system and simulation research,Journal of SystemSimulation 5 (13) (2001) 558566.[2] H.Y. Yu, C.Y. Dong, Fuzzy control of temperature of polymerizing-kettle and simulation research, Journal of Liaoning Technical University 1 (22) (2003) 8083.[3] J.M. Asua, Polymer Reaction Engineering, Blackwell Publishing Ltd., Australia, 2007.[4] H. Mihai,G.A.Dumont,WilliamA. Gough, S.Kovac, Adaptive control ofdelayedintegrating systems:a PVCbatch reactor,IEEE Transactions onControlSystemsTechnology

11 (3) (2003) 390398.[5] J.G. Wu, P.J. Zhang, PVC polymerization kettle temperature system based on double model predictive functional control, Journal of Nanjing University of Science and

Technology 29 (4) (2005) 441445.[6] L. Fu, G.Z. Dai, Research on control problem with long time delay in polymerizing process of PVC, in: Proceedings of the6th World Congress on Intelligent Control and

Automation, 2006, pp. 77167719.[7] Q.L. Yang, H.P. Zhang, Intelligent optimizationcontrol of VCMpolymerizationreactionprocess,Automation andInstrumentsin Chemical Industry 34 (2) (2007)6668.[8] B. Marc-Andr, G. Wolfgang, R. Gunter, Adaptive exact linearization control of batch polymerization reactors using a Sigma-Point Kalman Filter, Journal of Process

Control 18 (78) (2008) 663675.[9] X.W. Gao, S.Z. Gao, J.S. Wang, Soft-sensor modeling of PVC polymerizing process, Journal of Chemical Engineering of Japan 45 (3) (2012) 210218.

[10] J. Wu, Y. Xu, H.Y. Ou, Modular fuzzy logic systembased on principal componentregression analysis, Journal of Xian Jiaotong University 36 (12) (2002) 13111314.[11] W. Zhong, J.S. Yu, Study on soft sensing modeling via FCM-basedmultiple models, Journal of East China University 26 (1) (2002) 8387.[12] M.-Y. Chen, D.A. Linkens, Rule-base self-generation and simplification fordata-driven fuzzy models, Fuzzy Sets and Systems 142 (2) (2004) 243265.[13] J.S. Wang, Y. Zhang, S.F. Sun, Multiple TS fuzzy neural networks soft sensing modeling of flotation process based on fuzzy c-means clustering algorithm, Advances in

Neural Network Research and Applications, LNEE 67 (2010) 137144.[14] Z.W. Geem, J.H. Kim, G.V. Loganathan, A new heuristic optimizationalgorithm: harmony search, Simulation 76 (2) (2001) 6068.[15] Z.W.Geem, J.H.Kim, G.V.Loganathan, Harmony search optimization: applicationto pipe network design, InternationalJournal of Modellingand Simulation22 (2) (2002)

125133.[16] S.L. Kang, Z.W. Geem, A new structural optimizationmethod based on theharmony search algorithm, Computersand Structures 82 (910) (2004) 781798.[17] Z.W. Geem, K.S. Lee, Y. Park, Application of harmony search to vehicle routing, American Journal of Applied Sciences 2 (12) (2005) 15521557.[18] A. Vasebi, M. Fesanghary, S.M.T. Bathaeea, Combined heat and power economic dispatch by harmony search algorithm, International Journal of Electrical Power and

Energy Systems 29 (10) (2007) 713719.[19] Z.W. Geem, Optimal scheduling of multiple dam systemusing harmony searchalgorithm, Lecture Notes in Computer Science 4507 (2007) 316323.[20] Z.W. Geem, J.C. Williams,Harmony searchand ecological optimization, International Journal of Energy and Environment 2 (1) (2007) 150154.[21] S.A. Zulkeflee, N. Aziz, C.K. Chan, Temperature control in polyvinyl chloride production: internal model control (IMC) and proportional, integral and derivative (PID)

controller implementation, in: International Conference on Control, Instrumentation and Mechatronics Engineering, vol. 5, Johor Bahru, Johor, Malaysia, 2007, pp.805811.

Modeling and advanced control method of PVC polymerization

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