Reactor Polimeric

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ISA Transactions 51 (2012) 2229

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ISA Transactions

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

Design of a self-tuning regulator for temperature control of a polymerizationreactor

D. Vasanthi , B. Pranavamoorthy, N. PappaDepartment of Instrumentation Engineering, MIT campus, Anna University, Chrompet, Chennai-600 044, India

a r t i c l e i n f o

Article history:

Received 20 April 2011Received in revised form

14 July 2011

Accepted 29 July 2011

Available online 20 August 2011

Keywords:

Online estimation

Unscented Kalman filter

Self-tuning control

a b s t r a c t

Thetemperaturecontrol of a polymerization reactor describedby Chyllaand Haase, a controlengineering

benchmark problem, is used to illustrate the potential of adaptive control design by employing a self-tuning regulator concept. In the benchmark scenario, the operation of the reactor must be guaranteed

under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer.The conventional cascade control provides a robust operation, but often lacks in control performanceconcerning the required strict temperature tolerances. The self-tuning control concept presented in this

contribution solves the problem. This design calculates a trajectory for the cooling jacket temperature inorder to followa predefined trajectory of thereactor temperature. Thereactionheat andthe heat transfer

coefficient in the energy balance are estimated online by using an unscented Kalman filter (UKF). Twosimple physically motivated relations are employed, which allow the non-delayed estimation of both

quantities. Simulationresults under modeluncertainties show the effectiveness of the self-tuning controlconcept.

2011 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Polymerization is the process of reacting monomer molecules

together in chemical reactions to form three-dimensional net-

works of polymerchains. The widely used reactors in the chemical

industry for the production of fine pigments, chemicals, polymers

and pharmaceuticals are batch and semi-batch reactors. Measure-

ment and control of polymerization reactors is very challenging

due to the complexity of the polymerization kinetics. In the liter-

ature, hierarchical approaches to the control system design, and

reviews of traditional regulatory techniques and advance control

strategies for batch and semi-batch process are presented [1,2].

Often the reactions show exothermic behavior, and tight specifi-

cations have to be met. Therefore, an exact temperature control is

required. In many cases, conventionallinear control algorithmsarereported not to fulfil this requirement. Industrial polymerization

reactors are usually controlled by a cascade structure consisting of

a master controller for the reactor temperature and an underly-

ing slave controller for the cooling circuit. The cascade controller

gives a robust operation but fails to meet the strict temperature

tolerances[3]. Hence there is a need to employ advanced control

techniques such as the concepts of adaptive control [4]to satisfy

the control requirements.

Corresponding author.

E-mail address: [email protected](D. Vasanthi).

Therefore, various control concepts have been used in theliterature to deal with the benchmark problem. A model predictive

controller is used in [5] combined with an extended Kalman filter

for the estimation of the reaction heat and heat transfer coefficient.

A nonlinear adaptive controller is designed in [6] to adjust the

cooling jacket temperature, which serves as the set point for

an underlying proportionalintegral (PI) controller of the cooling

jacket. A further approach [7] illustrates the potential of feed-

forward control by extending the conventional cascade control

concept in the framework of a two degree of freedom control

concept.

This paper solves the problem by employing an unscented

Kalman filter (UKF) for the non-delayed online estimation of

the reaction heat and heat transfer coefficient which is used to

calculate the trajectory for the cooling jacket temperature, whichin turn enables the reactor temperature to follow the predefined

trajectory for the case of polymer A.

2. The ChyllaHaase bench mark reactor

2.1. Polymerization reactor

The industrial polymerization process described by Chylla and

Haase[7]consists of a stirred tank reactor with a cooling jacket

and a coolant recirculation; seeFig. 1.The reactor temperature is

controlled by manipulating the temperature of the coolant, which

is recirculated through the cooling jacket of the reactor. The slave

0019-0578/$ see front matter 2011 ISA. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.isatra.2011.07.009
http://dx.doi.org/10.1016/j.isatra.2011.07.009http://www.elsevier.com/locate/isatranshttp://www.elsevier.com/locate/isatransmailto:[email protected]://dx.doi.org/10.1016/j.isatra.2011.07.009http://dx.doi.org/10.1016/j.isatra.2011.07.009mailto:[email protected]://www.elsevier.com/locate/isatranshttp://www.elsevier.com/locate/isatranshttp://dx.doi.org/10.1016/j.isatra.2011.07.009


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D. Vasanthi et al. / ISA Transactions 51 (2012) 2229 23

Fig. 1. Schematic diagram of a polymerization reactor.

controller can act in two modes: in cooling mode, cold water isinserted into the recirculation loop, whereas, in heating mode,

steam is injected into the recirculating water stream.The polymerization process is simulated for a product which

comprises a specific recipe [3]which is given below.The recipe for each batch of a specific polymer consists of a

heating phase from 0 to 1800 s, a feed phase from 1800 to 6000 s,and a holding phase from 6000 to 9600 s.

1. Initial charges of solids (prepolymer, monomer) and water areplaced into the reactor at ambient temperature, Tamb.

2. The temperature of the initial charge is raised to the reactiontemperature set pointTset at 1800 s.

3. After 1800 s, pure monomer is fed into the reactor at 7.560 103 kg/s until 6000 s.

4. After the feed addition has stopped, the temperature of thereaction is held at its set point value Tset until 9600 s.

The above recipe for a specific product comprises two consecutivecontrol tasks.

Heating up of the reactor to a constant set point before themonomer feed starts.

Keeping the reactor temperature T(t) within a toleranceinterval of 0.6 K during the monomer feed and after asubsequent specified holding period.

Thereby, the monomer feed starts and ends abruptly at specifiedtime points. The polymer is produced in five subsequent batches,and is removed between the batches. However, the reactor is onlycleaned after the fifth batch. The control tasks are complicated byseveral features of the polymerization process.

Changing ambient temperatures in winter and summer. The heat transfer coefficient decreases significantly during a

batch due to an increasing batch viscosity, and from batch tobatch due to surface fouling.

The reaction kinetics is nonlinear. Impurity of the monomer.

2.2. Polymerization reactor model

A dynamic model of a polymerization reactor has been derivedby Chylla and Haase based on simplified kinetic relations [7].The temperature dynamics are captured by considering energybalances for the reactor and the cooling jacket. The reactor modelcomprises the material balances (1) and (2) for the monomer mass

mM(t) and the polymer mass mP(t), the energy balance(3) withthe reactor temperatureT(t), and the energy balances(4)and(5)

Table 1

Variables and parameters of the reactor model.

Variable Variable name Unit

minM(t) Monomer feed rate kg/s

Qrea = H Rp Reaction heat kW

Rp Rate of polymerization kg/s

H Reaction enthalpy kJ kg1

U Overall heat transfer coefficient kWm2 K1

A Jacket heat transfer area m2

(UA)loss Heat loss coefficient kW/K

Cp,M, Cp,P,Cp,C Specific heat at constant press ure kJkg1 K1

1, 2 Transport delay in jacket and recirculation

loop

s

Tj =

(Tinj + Tout

j )/2

Average cooling jacket temperature K

Kp(c) Heating/cooling function K

p Heating/cooling time constant s

of the cooling jacket and the recirculation loop with the outlet

and inlet temperatures of the coolant C. Further variables and the

parameters of the reactor model are listed inTable 1.

dmM

dt= minM(t) +

Qrea

H(1)

dmP

dt=

Qrea

H(2)

dT

dt=

1

i miCp,i[minM(t) Cp,M(Tamb T) UA(T Tj)

(UA)loss(T Tamb) + Qrea] (i = M, P,W) (3)

dToutj

dt=

1

mcCp,C[mcCp,C(T

inj (t 1) T

outj ) + UA(T Tj)] (4)

dTinj

dt=

dToutj (t 2)

dt+

Toutj (t 2) Tin

j

p+

Kp(c)

p. (5)

The available measurements of the process are the temperatures

of the reactor and cooling circuitry. The heating/cooling function

Kp(c) is influenced by an equal-percentage valve with valve

positionc(t)and the following split-range valve characteristic:

Kp(c) =

0.8 30c/50 Tinlet Tin

j (t) , c50%.

(6)


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24 D. Vasanthi et al. / ISA Transactions 51 (2012) 2229

Table 2

Empirical relations for the polymerization rateRp, the jacket heat transfer areaA, and the overall heat transfer coefficientU.

Variable Variable Variable name Unit

Rp = ikmM i Impurity factor

k = k0exp

ERT

(k1)

k2 First-order kinetic constant s1

= c0exp(c1f) 10c2(a0/Tc3) Batch viscosity kg m1 s1

f =mP/(mM+ mP+ mC) Auxiliary variable

k0, k1, E, R, a0, c0, c1, c2, c3 ConstantsR Natural gas constant kJ kmol1 K1

A=

mMM

+ mPP

+ mWW

PB1

+ B2 M, P, C Densities kg m3

B1 Reactor bottom area m

P Jacket perimeter m

B2 Jacket bottom area

U= 1h1 +h

1f

h = d0exp (d1wall) Film heat transfer coefficient kW m2 K1

wall = c0exp (c1f) 10c2(a0/Twall c3) Wall viscosity kg m1 s1

Twall =

T+ Tj/2 Wall temperature K

h1f Fouling factor depending on batc h no. m2 K/kW

d0, d1 Constants

Table 3Data for reactor parameters.

Symbol Unit Value

R kJ kmol1 K1 8.314

(UA)loss kW K1 0.00567567

p s 40.2

1 s 22.8

2 s 15.0

i [0.8, 1.2]

1/hf m2 K kW1 [0.000, 0.176, 0.352, 0.528,0.704]

Tamb K 280.382 (winter), 305.382 (summer)

Tinlet K 294.26

Tsteam K 449.82

Forc< 50%, ice water with inlet temperature Tinletis inserted inthe cooling jacket, whereas a valve position c > 50% leads to a

heating of the coolant by injecting steam with temperature Tsteaminto the recirculating water stream [7,5].

Various disturbances and uncertainties are specified in order

to model the following practical problems with the control ofpolymerization reactors.

The impurity factor i [0.8, 1.2] in the polymerization rateRPis random and constant during one batch; it tries to modelfluctuations in monomer kinetics caused by batch-to-batch

variations in reactive impurities. The fouling factor 1/hfin theoverall heat transfer coefficient Uincreases with each batch and

accounts for the fact that during successive batches a polymer

film builds up on the wall, resulting in a decrease ofU[7,6]. The delay times 1 and 2 of the cooling jacket and the

recirculation loop may vary by 25% compared to the nominal

values inTable 3.

The ambient temperatureTamb is different during summer and

winter. This affects the temperature of the monomer feedminM(t), as well as the initial conditions T(0), T

inj (0), T

outj (0)

given byTamb.

Measurement noise is added to the temperature measurements

with standard deviation (y) = 0.5.

Process noise is added with standard deviation =0.3162.

Table 2summarizes the empirical relations for Rp,A, andUtakenfrom [8,3,7]. A detailed description of these relations is given in [3].

The parameter values of the model and of polymer A are listed inTables 3and4.

Table 4Data for polymer A.

Symbol Unit Value for polymer

mM,0 kg 0.0

mP,0 kg 11.227

mW kg 42.75

M kg m3 900.0

P kg m3 1040.0

W kg m3 1000.0

Cp,M kJ kg1 K1 1.675

Cp,P kJ kg1 K1 3.140

Cp,W kJ kg1 K1 4.187

MWM kg kmol1 104.0

mc kg 42.750

mc kg/s 0.9412

Cp,C kJ kg1 K1 4.187

k0 s1 55

k1 m s kg1 1000

k2 0.4

E kJ kmol1 29,560.89

c0 kg m1 s1 5.2 105

c1 16.4

c2 2.3

c3 1.563

a0 K 555.556

Hp kJ kmol1 70,152.16

d0 kW m2 K1 0.814

d1

m s kg1 5.13

min,maxM kg/s 7.560 10

3tinM,0, t

inM,1

min [30, 100]

Tset K 355.382

In order to heat up the reactor to the specified set point Tset

before the monomer feed minM(t)starts, a trajectory is planned for

the desired reactor temperature T (t) by the polynomial set-up as

given by Eq.(7):

T (t)

=

Tamb + (Tset

Tamb)

5

i=3 ai t

theati

, if, t theat

Tset, ift> theat.

(7)


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Fig. 2. Conventional cascade control scheme.

Fig. 3. Self-tuning control scheme.

Fig. 4. Response with conventional cascade controller for nominal parameters and summer season: (i) results for first batch, (ii) results for fifth batch.

Here, a3 =10, a4 = 15, and a5 = 6. In this first interval t theat,the reactor is heated up to the set point Tset. For t > theat, the

temperature T (t) is kept constant at Tset. In the following, the

heat-up time is set to theat = 30 min, corresponding to the time

instant when the monomer feed minM(t)starts.

3. Self-tuning cascade control design

A very tight temperature control is necessary in order to

produce polymer of a desired quality. The controller should be

able to maintain the reactor temperature Twithin an interval of

0.6 K around the desired set point under all operation conditions

and disturbances. Commonly used for chemical reactors is a PI

cascade control structure, which provides a robust operation butoften lacks in control performance. The cascade control structure

is shown in Fig. 2. The master controller regulates the reactortemperature T by manipulating the set point Tsetj of the meancooling jackettemperature Tj. Theslavecontroller adjuststhe valveposition cin order to control the mean jacket temperature Tjset bythe master controller.

Since the nonlinear function is not approximated and theJacobean is not required, an unscented Kalman filter (UKF) is usedin preference to other algorithms.

In order to get an accurate response, it is desirable to calculatethe self-tuning parameters online. However, this requires theestimation of the time-dependent quantities, the reaction heat(Qrea) and the heat transfer coefficient (U), in successive batches.Fig. 3shows the block diagram of the considered adaptive controlscheme with a UKF [9,10], which uses the available temperature

measurements to estimateQreaandU. These estimates are used inthe online design of the self-tuning cascade control.


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Fig. 5. Response with self-tuning controller for nominal parameters and summer season: (i) results for first batch, (ii) results for fifth batch.

When compared with other forms of Kalman filter algorithms,a UKF has the following advantages.

It is a deterministic sampling approach. There is no approximation of the nonlinear function.

It captures the true mean and covariance more accurately. Calculation of the Jacobean is not required.

In a UKF the nonlinear function is not approximated and the

reactor model is used as given by Eqs. (1)(5); hence the estimates

obtained are accurate.

The uncertainties of the system are modeled as the system

noise in the state error covariance matrix, and the uncertaintiesin the measurement are modeled as the measurement noise in the


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Fig. 6. Response with conventional cascade controller for nominal parameters and winter season: (i) results for first batch, (ii) results for fifth batch.

measurement error covariance matrix. The estimated output not

only estimates the Qrea andUwhich cannot be measured online,but also gives a filtered output of the various parameters required

for taking the control action.

Tj = T +

1

U.A

i miCp,iT

minM(t)Cp,M(Tamb T)

Qrea + (UA)loss(T(t) Tamb)

. (8)ThusTj is found with the help of Eq.(8),and thisT

j is compared

with the current jacket temperature, Tj, and control action is taken

by manipulating the control valve, which in turn maintains thereactor temperature at its set point, and the error is kept within

the tolerance limit.

4. Simulation results and discussion

The process is simulated with the conventional PI cascadecontrol structure as well as the self-tuning control structure and

the performance of both the control schemes are compared.Fig. 4(i)(a)(c) and (ii)(a)(c) show the simulation results for the

process with conventional cascade control for batches 1 and 5 forthe summer season, respectively. The sampling time for the self-

tuning control is set to 1 s, which is the same as the sampling timeof the cascade controller. Fig. 5(i)(a)(h) and (ii)(a)(e) give the

simulation results for the process with self-tuning control for thesummer season for batches 1 and 5, respectively.

As per the recipe given in Section2.1,at 1800 s the monomer,

which is at ambient temperature, is added in the reactor, but thereactor is at an operating temperature ofTset = 355.382 K at that

instant. Therefore the reactor is initially cooled by the monomerfeed before the reaction, and hence there is a need to increase

temperature by means of increasing the jacket temperature. Theprocess exhibits an exothermic reaction; thus the heat inside the

reactor will be high, and so to compensate this there has to be

reduction in the jacket temperature. At the end of 6000 s, themonomer feed is stopped and the reaction will come to an end,

Table 5

Comparison of ISE and IAE values of both control schemes during summer.

Control scheme ISE IAE

First batch Fifth batch First batch Fifth batch

Cascade control 764.5785 994.4308 1455.5 1719.6

Self-tuning control 54.960 8 85.6100 449.018 2 579.0522

but the polymerproduced in the reactor needs to be maintained atTset = 355.382 K. To maintain this Tset, again, there is an increasein the jacket temperature by means of steam inflow. Due to thisabrupt change in monomer feed there are major changes in thetemperature error and control valve stem position at 1800 and6000 s.

The deviation of the reactor temperature Tand desired reactortemperature T is due to the time delay in the control systemstructure chosen for the slave controller. The respective set pointfor the slave controller is adjusted by the master controller inthe case of conventional cascade control, whereas the respectiveset point is generated by a parameter adjustment mechanismin the case of this proposed self-tuning control scheme. Thesimulations with the cascade controlled reactor together with theself-tuning control illustrate that the temperature error can bereduced significantly compared to that of a conventional cascade

control scheme. The temperature error stays within the toleranceinterval of0.6 K during the heating stage as well as at the criticaltime points when the monomer feed starts and stops. There isalso significant improvement in the performance of the controlvalve.

As a measure of assessing control system performance, for boththe control schemes integral squared error and integral absoluteerror values are calculated for batches 1 and 5 respectively for thesummer season and are shown inTable 5.It is observed that bothISE and IAE are much lower for the self-tuning control schemecompared to the cascade control structure.

Furthermore, a robustness analysis is carried out in order tocompare the performance of the self-tuning control structure withrespect to the conventional PI cascade control structure. It is

assumed that the reactor is operated in the winter season wherethe low ambient temperature (Table 3) poses high demand on


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Fig. 7. Response with self-tuning controller for nominal parameters and winter season: (i) results for first batch, (ii) results for fifth batch.

the cascade control during the heating up of the reactor. The UKF

provides robust estimates of the reaction heat and heat transfer

coefficient, and the reactor temperature stays within the specified

tolerance interval of0.6 K with the self-tuning control scheme,

as shown inFig. 6(i)(a)(c) and (ii)(a)(c) andFig. 7(i)(a)(h) and(ii)(a)(f).

As a measure of assessing control system performance, for both

control schemes ISE and IAE values are calculated for batches 1

and 5, respectively, for the winter season and are shown in the

Table 6. It is observed that both ISE and IAE are much lower for

the self-tuning control scheme compared to the cascade controlstructure.


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Table 6

Comparison of ISE and IAE values of both control schemes during winter.

Control scheme ISE IAE

First batch Fifth batch First batch Fifth batch

Cascade control 848.0387 1175.6 1413.8 1717.3

Self-tuning control 58 .93 57 75.565 1 458 .649 6 556.1799

5. Conclusion

The Chylla and Haase polymerization process is a nonlinearand multi-batch process, for which temperature control is very

difficult. A self-tuning controller has been designed to obtain thedesired control performance. The performance of the self-tuningcascade control has been studied for batches 1 and 5 for the givenpolymer. Also estimates for the heat transfer coefficient U and

reaction heat Qreaare obtained using an unscented Kalmanfilterforthese batches. On comparison with a conventional cascade control,the performance of the self-tuning cascade control is found to besuperior, and it meets the control objective of maintaining the

reactor temperature within the tolerance interval of0.6 K fromthe set point.

References

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[3] Chylla RW, Randall Haase D. Temperature control of semi batch polymeriza-tion reactors. Computers Chemical Engineering 1993;17:25763.

[4] Astrom Karl J, Wittermark Bjorn. Adaptive control. second ed. Pearson

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[6] Clarke-Pringle Tracy, MacGregor John F. Non linear adaptive temperaturecontrol of multi product semibatch polymerization reactors. ComputersChemical Engineering 1997;21:1395409.

[7] Graichen Knut, Hagenmeyer Veit, Zeitz Michael. Feed forward control withonline parameter estimation applied to the ChyllaHaase reactor benchmark.Journal of Process Control 2006;16:73345.

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