simulation and control of distillation process

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Simulation and Control of Distillation ProcessAsha Rani, Vijander Singh, and J.R.P Gupta

Instrumentation and Control Engineering Division, Netaji Subhas Institute of Technology,

University of Delhi, Delhi

Abstract—The precise control of distillate quality is the objective of the present work and is achieved by controlling thetemperature profile of the distillation process. The generic mathematical models of multicomponent distillation and reactivedistillation processes are considered for simulation. The PID and fuzzy controllers are designed for both the processes. Incase of multicomponent distillation process, the PID controller is designed with the help of Zeigler-Nichols tuning method andfor reactive process the PID controller is designed using Tyreus-Luyben method. The PID controller is used to control the re-boiler temperature of multicomponent distillation process. In case of reactive process the exothermic reaction takes place be-tween the two feeds and the amount of heat generated depends upon the feed flow rate. Therefore the designed PID control-ler is used for controlling the feed flow rate which controls the temperature indirectly. The fuzzy controllers are designed for both the processes and are used for controlling the reboiler temperature and feed flow rate respectively. The results obtained

from both the controllers are compared. It is observed from the results that the fuzzy controller performs better than the con-ventional PID controller.

Index Terms— Distillation column, Reactive Process, PID controller, Fuzzy controller.

—————————— ——————————

1 INTRODUCTION

ISTILLATION is the separation process of two ormore than two components of a mixture into itscomponent fractions. It is the most widely used

process in chemical industry. Distillation separates twoor more liquid components of a mixture using theprinciple of relative volatility or boiling points. The

greater the difference in relative volatility, the easier itis to separate the mixture using distillation [8], [16].

The quality of distillate product is controlled byusing different control techniques like conventionalcontrol, intelligent control and inferential control [13],[14], [15]. A PID controller [13] is a generic control loop feedback mechanism. The PID controller calculates the"error" as the difference between a measured processvariable and a desired set point. The controller at-tempts to minimize the error by adjusting the processcontrol inputs. The PID parameters used in the control-ler must be tuned according to the nature of the system

to get the desired results [3], [9].The selection of proportional, integral and derivative

constants is decided according to the nature and re-quirement of the process. The weighted sum of thesethree control actions is used by a control element suchas the position of a control valve or the power supplyof a heating element, to adjust the process output. ThePID control scheme is named after its three correctingterms (proportional, the integral and derivative) [6],

whose sum constitutes the manipulated variable (MV)[3].A.M.F. Fileti et al. in [2007][29] developed a PID fuzzyalgorithm for the online control of some processes. PIDfuzzy controllers were compared with conventionalPID controller and found to be most suitable and relia-

ble for the polymerization process. Since the averageproduct flow rate was found to be higher when thebatch column was under PID fuzzy control, theprocess became faster and demanded lesser energy. Inspite of the nonlinear and unsteady behaviour of thebatch process, the fuzzy controller was also able to fol-low variable set point strategies. C.R. Edger et al. in[2000][30] devised a new controller fuzzy-IMC whichis based on internal model control and utilizes a nonlinear crisp consequent Fuzzy relational model at itscore. It was observed that the proposed controller per-formed significantly better than multi-loop PID. Chi-

Huang Lu and Ching-Chih Tsai [31] in 2007 presenteda methodology for predictive control of industrialprocesses via recurrent fuzzy neural networks. Theresults of numerical simulations and experimentsshow that the methodology is capable of controllingindustrial processes with satisfactory performance un-der set point and load changes. The basic structure ofthe process to be controlled is described in the nextsection.

1.1 Multicomponent Distillation Process:The multicomponent distillation column under con-

sideration is having 15 trays, a reboiler to vaporise themixture and a condenser to cool the overhead vapour.Tray 5 is used as feed tray. In distillation, a liquid mix-ture is fed on the feed tray and the mixture is stored inreboiler. The heat is introduced in the reboiler to pro-

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• Asha Rani is with the Netaji Subhas Institute of Technology, University of Delhi, Delhi.

• Vijander Singh is with Netaji Subhas Institute of Technology, Uiversity of Delhi, Delhi.

• JRP Gupta is with Netaji Subhas Institute of Technology, Uiversity of Delhi, Delhi.

D

JOURNAL OF COMPUTING, VOLUME 3, ISSUE 7, JULY 2011, ISSN 2151-9617

HTTPS://SITES.GOOGLE.COM/SITE/JOURNALOFCOMPUTING/

WWW.JOURNALOFCOMPUTING.ORG 48

http://en.wikipedia.org/wiki/Control_loop



http://en.wikipedia.org/wiki/Feedback_mechanism


http://en.wikipedia.org/wiki/Process_variable




http://en.wikipedia.org/wiki/Setpoint_%28control_system%29


http://en.wikipedia.org/wiki/Proportionality_%28mathematics%29



http://en.wikipedia.org/wiki/Integral


http://en.wikipedia.org/wiki/Derivative






















duce vapour. The vapour starts flowing from the re-boiler to top tray and then to condenser through strip-ping and rectifying section. During initial start-up pe-riod, the column operates under total reflux conditionin which vapour from the top of the column is con-densed and returned to the column through refluxdrum. During the column operation under total refluxcondition, the concentration of the lightest componentbuilds-up on the upper trays of the column and theconcentrations of the intermediate component andheaviest component decreases in the top of the columnbut increases in the still pot. When the concentration ofthe lightest component in the distillate reaches its spe-cified purity level, then the distillate product with-drawal begins. The basic structure of distillation col-umn is shown in Fig. 1.

Fig.1. Basic Structure of Distillation Process

Mathematical Modeling:The mathematical model of distillation column, shownin Fig. 1, with the usual assumptions is considered forthe present work. The mass and energy balance equa-tions are obtained by applying conservation laws toeach tray, condenser and reboiler.(a) Component Material Balance Equations(i) Concentration for condenserThe change in reflux drum-level with time at steadystate condition is zero i.e 0 / =dt dM D , because of the

presence of reflux drum level controller, which givesequation (1).

= (1)

Component material balance around condenser is giv-en by

= , , for j=1,…,NC (2)

(ii) Component material balance equation for tray-i isgiven by

= +1+1 , + −1−1 , +

for j= 1,…,NC; i= 1,…,NT (3)

Fig.2. Modelling of general tray-i

Where = �∗ −1 , + −1 ,

for j= 1,…,NC; i= 1,…,NT (4)

(iii) Component material balance for reboiler:

= 11, , (1 ),

for j= 1,…,NC; (5)

, = , 1,, (6)

(b) Total Material Balance EquationFor general tray-i

= +1 + −1 + (7)

for i=1,…,NT

(c) Total Enthalpy Balance Equations:(i) Enthalpy balance for condenser

= ℎ (8)

(ii) Enthalpy balance for general tray-i

ℎ = +1ℎ+1 ℎ + −1+1 + ℎ

for i=1,…,NT (9)

(iii) Enthalpy balance for reboiler

= 1ℎ1 ℎ (1 )ℎ + (10)

At equilibrium the ith tray temperature is found by us-

ing the following bubble point relation:

, , =

=

for j= 1,…,NC; i= 1,…,NT (11)

Mi

Vi

Yi,j

Hi

Li+1

Xi+1,j

hi+1

hFiFiXFi

Vi-1

Hi-1

Yi-1,j

Li

Xi,j

hi






The bubble point above relationship is satisfied by an

iterative procedure.

The feed composition, flow rates, tray temperatures,

column pressure and stage efficiencies are assumed to

be specified for the simulation of distillation column.

Simulation is done following the basic steps of the al-

gorithm reflecting the simplified multi-component dis-

tillation column as in [15]. The second model used for

application of PID and fuzzy controller is the reactive

1.2 Reactive Distillation Process:Reactive distillation shown in Fig. 3 is a process ofchemical reaction and separation of the products in thecommon chamber. It is a highly nonlinear and complexprocess. The chemical industry has already acknowl-edged its significance due to its high gain and compactnature. Pre-installation optimal design of this process

is of great concern because it is a onetime installation, but it requires constant supply of materials like fueland reactants, out of which fuel is very costly. A savingin the design of an ideal reactive distillation column(Ideal RDC) without compromising any of the desiredfeatures would indeed be a great profit to the industry.In the chemical process industries, chemical reactionand purification of the desired products of distillationare usually carried out sequentially. In many cases, theperformance of this classic chemical process can besignificantly improved by integration of reaction anddistillation in a single multifunctional process unit.

This integration concept is called ‘reactive distillation’.RDC is an ideal two-reactant-two-product reactive dis-tillation column proposed by Al-Arfaj and Luyben [20]and later developed into state space model [22]. It con-sists of a reactive section in the middle and non-reactive rectifying and stripping sections at the top and

bottom respectively.

Fig.3. Basic structure of reactive distillation column

The column consists of Reactive Trays (NRX) in themiddle, Rectifying Trays (NR) in the top and StrippingTrays (NS) in the bottom. The trays of the column arenumbered from reboiler to condenser. The reactiontakes place in the reactive zone is exothermic liquid-

vapour in nature and is given by

+ ↔ + (12)

During the process of distillation, the reactant B whichis one of the input feeds is recovered in the rectifyingsection from the output product C whereas the secondfeed i.e. reactant A, is recovered from output product

D in the stripping section. The reactive section com-prises the middle section of the reactive distillationcolumn where the reactants A and B react to produce Cand D. The reaction generates the heat which is thenused for the distillation of the products. The productsare separated to prevent any undesired reaction be-tween reactants A and B and products C and D. Thevolatilities of the products and reactants are such that

> > > (13)

Where is the volatility of the jth component, j=a,b,c,d.

It can be observed from the above relation that C is thelightest product with highest volatility, D is the hea-viest product with lowest volatility and volatilities of Aand B lie in between them. This relative volatility en-sures that the products A and B have high concentra-tion in the reactive section, which is typical example ofan Ideal Reactive Distillation column. The three sec-tions consist of trays that have different compositionprofiles, vapour profile, liquid profile and hold up. Asshown in Fig. 3, two inputs are marked as feed A andfeed B at the left side. The two input streams are fed asreactants A and B, the reactant A is lighter as compared

to B, therefore A tries to go up and B being heaviertries to settle in the bottom part of the column. Thequality of products C and D is controlled by manipu-lating the feed flow rates. The controllers in the processare termed as dual end composition control structure.The reflux drum level is controlled by manipulatingthe distillate flow rate. The purity of both products ismaintained at 95%. The general mathematical model-ling of the reactive distillation process is detailed in thenext section.

Mathematical Modelling:The net reaction rate for component j on tray i in the

reactive zone is given by

, = �,, ,, (14)

distillation process and is explained in the next section.The steady-state vapour and liquid rates are constantthrough the stripping and rectifying sections becauseequimolal overflow is assumed. However, these rateschange through the reactive zone because of the exo-thermic reaction. The heat of reaction vaporizes someliquid on each tray in the reactive section; therefore,the vapour rate increases up through the reactive traysand the liquid rate decreases down through the reac-tive trays.






= −1

, (15)

= +1 +

, (16)

The dynamic component balances equations for the

column are as follows:Reflux drum:

(,)

= , (1 + ), (17)

Rectifying and stripping trays:

()

= +1+1 , + −1−1 , , , (18)

Reactive trays:

(,

)

= +1+1 , + −1−1 , , , + ,

(19)

Feed trays:

�, = +1+1 , + −1−1 , , , + , +

, (20)

Column base:

(,)

= 11, , , (21)

The forward and backward specific reaction rates on i th

tray:

, = −/ (22), = −/ (23)

Temperature of the ith tray is calculated by the follow-ing expression:

= /[ ln(/ ∑ ,) ]=1 (24)

With the equimolal overflow mentioned above, all thevapour rates () throughout the stripping section areequal to , and all the liquid rates () are equal to . Analogously, all beginning from the top of the feedtray throughout the rectifying section and total con-denser are and all are equal to .The ideal vapour–liquid equilibrium is assumed. Col-umn pressure P is optimized for each tray. With pres-sure P and tray liquid composition , known at eachtray, the temperature and the vapor composition , can be calculated. This bubble point calculation can besolved by a Newton-Raphson iterative convergence

method.

= ∑ ,=1 (25)

, =

, (26)

The mathematical models of multicomponent distilla-tion column and reactive distillation column describedin this section are simulated in MATLAB and thenused for control and analysis purpose. The controlschemes applied to control the quality of product of

both the processes are explained in next section.

2 CONTROL SCHEMES:

In the present work two types of controllers are de-signed i.e. PID controller and Fuzzy controller. Thesetwo controllers are used for controlling the productquality of multicomponent distillation and reactivedistillation process.

2.1 PID Controller:

A close loop system is used to maintain output withindesirable limits by means of a control action. Any dev-iation of the output from the reference input is de-tected by an error detector. The error signal is the dif-ference between the reference input signal and thefeedback signal obtained from the output. The errordetected is then modified and applied as actuatingsignal to the system. In proportional control the actuat-ing signal of the control action in a control system isproportional to the error signal. This controller is es-sentially an amplifier with an adjustable gain Kp.

() = ∗ () (27)

For the proportional plus derivative control action, theactuating signal consists of proportional error signaladded with derivative of error signal.

() = ∗ () + ∗ (28)

The derivative control action has an anticipatory cha-racter and is effective only during transient periods i.e.it adds damping to the system.For the proportional plus integral control action theactuating signal consists of the proportional error sig-nal added with integral of the error signal. This reduc-

es the offset or steady state error of the system.() = ∗ () + ∫()

(29)

The combination of the three control actions i.e. pro-portional, integral and derivative makes the PID con-troller. In the present work the PID controller is de-signed to control the two processes namely multicom-ponent distillation process and reactive distillationprocess as discussed in the following sections.

2.1.1 PID control of Multicomponent Distillation Process:

The quality of distillate depends upon the temperatureprofile of the distillation column. The temperature pro-file of distillation column may be controlled by feedflow, reflux flow and reboiler temperature. The reboiler






temperature is the main factor which controls the tem-perature profile of the distillation process because thereboiler is the nearest source of heat generation. There-fore the distillate quality can be controlled by regulat-ing the reboiler temperature using PID controller. Theconventional PID controller is designed with the helpof Zeigler–Nichols method. The procedure of design-ing the PID controller is as follows:

1. Turn on the controller to proportional mode i.e. turn

off both integral and derivative mode.

2. Vary the controller gain slowly and observe the out-

put response of the system. When output response

shows sustained oscillations (Fig.4), mark that gain

as Kc and the period of oscillations as T.

3. The settings of Kp T i and Td for different types of

controller suggested by Zeigler-Nichols [22] are

shown in table 1.

Table-1: Zeigler-Nichols method

Type ofController

Kp T i Td

PI controller 0.45Kc 0.83T 0

PID control-ler

0.6Kc 0.5T 0.125T

With the help of above chart the following values are

obtained for proportional, integral and derivative con-

trollers [21].

= 0.069, = 49 = 12.25

These values of Kp , T i and Td are then used for control-

ling the temperature of reboiler. The controlled reboiler

temperature is shown in Fig. 5. The set point for the

process is 202 ˚F. It is observed from Fig. 5 that the re-

boiler temperature reaches at steady state after 164 it-

erations. It is also observed that the transient response

of the process is oscillatory. The PID controller is also

applied to control the distillate quality of the reactive

distillation process and is explained in the next section.

2.1.2 PID control of Reactive Distillation Process:

Several control structures have been proposed for reac-tive distillation process. The appropriate control struc-ture depends on the flow sheet and on the type of reac-tions occurring in the column. If two reactants are in-volved and desired to operate the process without the

excess of reactants then it is necessary to manage thefresh feed streams so that the stoichiometry is exactly balanced.To control the distillate quality, it needs to bemeasured which can be done with the help of compo-sition analyser. However, if there are two products, itmay be possible to avoid the use of an analyser by us-ing inferential control. In this scheme the compositionis inferred from the temperature profile of the process.The temperature profile is controlled by manipulatingfeed flow rate. This control structure is known as “TheEastman structure” shown in Fig. 6.

Fig. 6 Eastman Control Structure

The temperature profile of the process can be con-trolled by regulating the temperature of the most sen-sitive tray. The suitable tray is selected by the gainanalysis. In this case the feed flow rate is changed by asmall amount and corresponding change in the tem-perature is measured. The gain is defined as the ratioof the change in the temperature to the change in feedflow rate. The tray which shows the maximum gaincorresponding to change in feed flow is considered asthe most sensitive tray. A small disturbance in the feed

of A-component is provided and it is observed fromFig. 7 and Fig. 8 that the 6th tray is most sensitive cor-responding to change in the feed of A-component andthe 14th tray is most sensitive tray corresponding to

Fig.4. Sustained oscillation with period

Fig. 5 Reboiler temperature control using PID controller

200.5

201

201.5

202

202.5

203

1 34 67 100 133 166 199 232

T B

( ° F )

iterations

201.20

201.40

201.60

201.80

202.00

202.20

1 1 6

3 1

4 6

6 1

7 6

9 1

1 0 6

1 2 1

1 3 6

1 5 1

1 6 6

1 8 1

1 9 6

2 1 1

2 2 6

T B

( ˚ F )

iterations






change in the feed of component-B respectively. There-fore 6th and 14th tray temperatures are required to becontrolled to regulate the product quality. As the reac-tion is exothermic and depend on the two feeds, therespective tray temperature can be controlled by varia-tion in feeds of component A and B to get the desiredpurity of the product.The feed flow rate is controlled to achieve the desiredproduct quality with the help of PID controller. ThePID controller is designed using Tyreus-Luyben tun-ing method. The values of gain Kc and sustained oscil-lations period T are obtained using the same proce-dure as for Zeigler-Nichols method. Kp, T i and Td cal-culated using Tyreus-Luyben chart (table-2) are as fol-lows.

Table-2: Tyreus-Luyben ChartType of controller Kp T i Td

PI controller Kc/3.2 2.2T

PID controller Kc/2.2 2.2T T/6.3

Fig. 7 Gain A = ∆T/∆FoA

Fig. 8 Gain B = ∆T/∆FoB

Table-3: Tuning parameters

Tray No. Kp T i Td

6 1.235 122.27 42.698

14 2.94 113.182 39.524

The tuned PID controllers are used to control the

process. The set point for 6th tray is 390.54 K. It is ob-

served from Fig. 9 that the steady state temperature,

390.534K is obtained after 400 iterations. Thus the

steady state error obtained is 0.006 K. Fig. 10 shows the

temperature control of 14th tray using the PID control-

ler. The set point of tray 14 is kept at 392.12 K. It is ob-

served from Fig. 10 that the transient response is oscil-

latory and steady state obtained after 400 iterations has

the offset error.

Fig.9. Temperature of 6th

tray (With PID controller)

As observed from the above results for the twoprocesses, the PID controller is sluggish and there areoscillations in the transient response. The results alsodepict that a finite steady state error exists which must

be reduced to zero. To obtain the precise control of dis-tillate quality, it is desired to control the tray tempera-ture in a more efficient manner and for that purpose anadvanced control technique i.e. fuzzy controller is pro-posed which is discussed in the next section.

2.2 Fuzzy Controller:Fuzzy control provides a formal methodology forrepresenting, manipulating, and implementing a hu-man’s heuristic knowledge to control a system. To de-sign the fuzzy controller, the control engineer mustgather information on how the artificial decision mak-er should act in the closed-loop system. Sometimes this

information can be obtained from heuristics, while atother times from the knowledge base and a set of rulesare written for controlling the system. The fuzzy con-troller block diagram is shown in Fig. 11, where a

Fig. 10 Temperature of 14th

tray (With PID controller)






fuzzy controller is embedded in a closed-loop controlsystem. The plant output is denoted by y(t), its input isdenoted by u(t), and the reference input to the fuzzy controller is denoted by r (t).

The fuzzy controller has four main components:

1. The fuzzification interface simply modifies the in-

puts so that they can be interpreted in the form of

fuzzy sets.

2. The “rule-base” holds the knowledge, in the form ofa set of IF-THEN rules to control the system.

3. The inference mechanism finds the relevant control

rules at the current time and provides the fuzzified

output.

4. The defuzzification interface converts the fuzzy

output concluded by the inference mechanism into

the actuating input to the plant.Fuzzy control system design involves following steps.

1. Choose the fuzzy controller inputs and outputs.

2. Choose the pre-processing that is needed for the

controller inputs and possibly post processing that

is needed for the outputs.

3. Design each of the four components of the fuzzy

controller shown in Fig. 11. The main part of the

fuzzy controller design is the rule-base.In the present temperature control problem, a controlengineer regulates the plant output manually and usesthis information for designing the rule base. For in-stance, one rule that a human expert may use is “IF theproduct quality is lower than the set-point, THEN cor-rect the heat input”. A rule that would represent more

detailed information to regulate the output would be“IF the output is lower than the set-point AND theoutput is approaching the set-point very fast, THENdecrease the heat input by a small amount”. Thesecond rule characterizes the knowledge to make surethat response does not overshoot the desired goal (theset-point temperature). Generally if a very detailedexpertise into the rule-base is obtained, one can en-hance its chances of obtaining better performance. Thefuzzy controller described above is used to control thedistillate quality of the distillation process.

2.2.1Fuzzy Control of Multicomponent Distillation Process:The simulations of the mathematical model of the mul-ticomponent distillation process are used to design thefour components of fuzzy controller. The error, changein error and output are fuzzified using 13, 9, and 8

membership functions respectively. The plot of thesemembership functions are shown graphically in Fig.12, Fig. 13 and Fig. 14 and in the form of tables in Table4, Table 5 and Table 6. The rule base is selected basedupon the error, change in error and output results ofsimulation as shown in Table 7. The Mamdani infe-rence technique is used to infer the results from rule

base and centroid method is used for defuzzification ofthe inferred output of the controller. Then the fuzzycontroller is tested for the distillation process.

Fig.12. Membership function of error for fuzzy controller

Table 4: Error limitsName Lower limit Medium Higher limit

VVESP ------- -0.005 -0.0025

VESP -0.005 -0.0025 0.00

ESP -0.0025 0.00 0.0025

VVSP 0.00 0.0025 0.005

VSP 0.0025 0.005 0.0075

SP 0.005 0.0075 0.01

NP 0.0075 0.01 0.0125

LP 0.01 0.0125 0.015VLP 0.0125 0.015 0.0175

VVLP 0.015 0.0175 0.02

ELP 0.0175 0.02 0.0225

VELP 0.02 0.0225 0.025

VVELP 0.0225 0.025 -----

Fig.13. Membership function of rate of change of error

Table 5: Table for change in errorName Lower limit Medium Higher limit

VESD -------- -15x10-3 -12.5 x10-3

ESD -15 x10-3 -12.5 x10-3 -10 x10-3

VSD -12.5 x10-3 -10 x10-3 -7.5 x10-3

SD -10 x10-3 -7.5 x10-3 -5.0 x10-3

ND -7.5 x10-3 -5.0 x10-3 -2.5 x10-3

LD -5.0 x10-3 -2.5 x10-3 0.0

VLD -2.5 x10-3 0.0 2.5 x10-3

ELD 0.0 2.5 x10-3 5.0 x10-3

VELD 2.5 x10-3 5.0 x10-3 ----

Fig.11. Fuzzy controller architecture






Fig.14. Membership function of change in temperature

Table 6: Change in temperature for fuzzy controllerName Lower limit Medium Higher limit

VESC ----- -10 x10-3 -7.5 x10-3

ESC -10 x10-3 -7.5 x10-3 -5.0 x10-3

VSC -7.5 x10-3 -5.0 x10-3 -2.5 x10-3

SC -5.0 x10-3 -2.5 x10-3 0.0

NC -2.5 x10-3 0.0 2.5 x10-3

LC 0.0 2.5 x10-3 5.0 x10-3

VLC 2.5 x10-3 5.0 x10-3 7.5 x10-3

ELC 5.0 x10-3 7.5 x10-3 ----

Table 7: The rule baseek

dek

VVESP VESP ESP VVSP VSP SP NP LP VLP VVLP ELP VELP VVELP

VESD VESC VESC VESC VESC VESC ESC ESC VSC VSC NC NC VLC ELC

ESD VESC VESC VESC VESC VESC ESC ESC VSC VSC NC NC VLC ELC

VSD VESC VESC VESC VESC VESC ESC ESC VSC VSC NC NC VLC ELC

SD VESC VESC VESC VESC VESC ESC ESC VSC VSC NC NC VLC ELC

ND VESC VESC VESC NC LC ESC ESC VSC VSC NC NC VLC ELC

LD VESC LC SC NC LC ESC ESC VSC VSC NC NC VLC ELC

VLD ESC LC NC NC VLC ESC ESC VSC VSC NC NC VLC ELC

ELD VSC LC LC ELC ELC ESC ESC VSC VSC NC NC VLC ELC

VELD SC LC VLC ELC ELC ESC ESC VSC VSC NC NC VLC ELC

Comparison of Results: The designed PID and fuzzy controllers are applied tocontrol the reboiler temperature and results are com-pared. The variations reboiler temperature using fuzzycontroller is shown in Fig. 15. It is observed fromFig.15 that the reboiler temperature reaches at steady

state after 41 iterations where as in case of PID control-ler the reboiler temperature settles after 164 iterations.It is observed from Fig. 16 that in case of fuzzy control-ler there is no overshoot and the settling time is highlyreduced as compared to PID controller.

Fig.15. Reboiler temperarure using fuzzy controller

Fig.16. Reboiler temperature using PID and Fuzzy Controller

The distillate and bottom product quality of the proc-

ess is controlled by manipulation of the reboiler tem-

perature. The distillate composition obtained after ap-

plication of two controllers is shown in Fig. 17-21. The

set point of reboiler temperature is 202℉ to obtain 98%

of distillate quality of component, XD2. It is observedfrom the results of distillate product that by using

fuzzy controller peak overshoot is reduced thus de-

creasing the settling time.

Fig. 17. Liquid composition of distillate XD1 with iterartion

Fig. 18. Liquid composition of distillate XD2with iterartion

201.20

201.40

201.60

201.80

202.00

1 9 1 7

2 5

3 3

4 1

4 9

5 7

6 5

7 3

8 1

8 9

9 7

1 0 5

1 1 3

T B

( ̊ F

)

Iterations

201.2

201.4

201.6

201.8

202

202.2

1 21 41 61 81 101 121

T B

( ̊ F

)

iterationsPID Fuzzy controller

0.0171

0.0172

0.0173

0.0174

0.0175

0.0176

0.0177

0.0178

1 1 3

2 5

3 7

4 9

6 1

7 3

8 5

9 7

1 0 9

1 2 1

1 3 3

1 4 5

1 5 7

1 6 9

1 8 1

1 9 3

X D 1

( %

m o

l e f r a c t i o n s

)

iterations

PID FUZZY

0.9814

0.9816

0.9818

0.982

0.9822

1 1 5

2 9

4 3

5 7

7 1

8 5

9 9

1 1 3

1 2 7

1 4 1

1 5 5

1 6 9

1 8 3

1 9 7

X D 2

( %

m o


)

iterationsPID FUZZY






The fuzzy controller thus provides the best controlled

output with minimum transient time and less oscilla-

tion as compared to conventional PID controller.




Fig. 22. Liquid composition XB2 with iteration

The liquid composition of bottom product correspond-ing to the reboiler set point of 202 ˚F is shown in Fig. 22to Fig. 25. The quality of bottom product is observedusing conventional as well as intelligent controller. Thecomposition of first component of bottom product is

not shown as its composition is negligible. It isobserved from the results of the bottom products (Fig.22 –Fig.25) that the fuzzy controller acts much fasterthan the conventional (PID) controller and reaches atthe steady state earlier than the conventiaonalcontroller. Fuzzy controoller designed for reactivedistillation process is explained in the next section.




2.2.2 Fuzzy Control of Reactive Distillation Process:The quality of product C and D is controlled by thePID controller but the response achieved is not up tothe mark. Therefore a fuzzy controller is designed withthe help of the simulated mathematical model of thereactive distillation process as discussed earlier. Here,the error, change in error and output are fuzzified us-ing 3, 7 and 3 membership functions for the 6th trayand 10, 7 and 7 membership functions for the 14 th trayrespectively. These membership functions are shownin tables 8, 9, 10, 12, 13 and 14. The rule base is se-lected for the temperature control of the 6th tray andthe 14th tray with the help of the simulation results.

0.0065

0.0066

0.0067

0.0068

0.00690.007

0.0071

0.0072

0.0073

1 1 3

2 5

3 7

4 9

6 1

7 3

8 5

9 7

1 0 9

1 2 1

1 3 3

1 4 5

1 5 7

1 6 9

1 8 1

1 9 3

X B 2

( %

m o


)

iterationsPID FUZZY

0.1078

0.1079

0.108

0.1081

0.1082

0.1083

0.1084

1 1 5

2 9

4 3

5 7

7 1

8 5

9 9

1 1 3

1 2 7

1 4 1

1 5 5

1 6 9

1 8 3

1 9 7

X B 5

( %

m o


)

iterations

PID FUZZY

8.23E-058.23E-058.23E-058.23E-058.24E-058.24E-058.24E-058.24E-05

1 1 5

2 9

4 3

5 7

7 1

8 5

9 9

1 1 3

1 2 7

1 4 1

1 5 5

1 6 9

1 8 3

1 9 7

X D 3

( %

m o


)

iterationsPID FUZZY

4.92E-05

4.92E-05

4.93E-05

4.93E-05

4.93E-05

4.93E-05

1 1 4

2 7

4 0

5 3

6 6

7 9

9 2

1 0 5

1 1 8

1 3 1

1 4 4

1 5 7

1 7 0

1 8 3

1 9 6

X D 4

( %

m o l e

f r a c t i o n s

)

iterations

PID FUZZY

6.57E-10

6.58E-10

6.59E-10

6.6E-10

6.61E-10

6.62E-10

1 1 4

2 7

4 0

5 3

6 6

7 9

9 2

1 0 5

1 1 8

1 3 1

1 4 4

1 5 7

1 7 0

1 8 3

1 9 6

X D 5

( %

m o


)

iterations

PID FUZZY

0.04720.04740.04760.0478

0.0480.04820.04840.04860.0488

0.049

1 1 3

2 5

3 7

4 9

6 1

7 3

8 5

9 7

1 0 9

1 2 1

1 3 3

1 4 5

1 5 7

1 6 9

1 8 1

1 9 3

X B 3

( %

m o


)

iterations

PID FUZZY

0.8355

0.836

0.8365

0.837

0.8375

1 1 3

2 5

3 7

4 9

6 1

7 3

8 5

9 7

1 0 9

1 2 1

1 3 3

1 4 5

1 5 7

1 6 9

1 8 1

1 9 3

X B 4

( %

m o


)

iterations

PID FUZZY






The corresponding rule base for the trays is shown intables 11 and 15 respectively. Mamdani inference tech-nique is selected for inferring the results and centroidmethod is used for defuzzification. The designed fuzzycontroller is tested and results are obtained.

Table 8: Membership functions and rule base defined

for 6th tray

Membership

function

Lower limit Middle

limit

Higher limit

SP -0.019 0 0.019

NP 0 0.019 0.039

LP 0.019 0.039 0.058

Table 9:Membership

function

Lower limit Middle

limit

Higher limit

ESD -0.0256 -0.0100 0.0048

VSD -0.0100 0.0048 0.0204

SD 0.0048 0.0204 0.0352

ND 0.0352 0.0508 0.0656

LD 0.0508 0.0656 0.0812

VLD 0.0656 0.0812 0.0960

ELD 0.0812 0.0960 0.1116

Table 10:Membership

function

Lower limit Middle

limit

Higher limit

SC -0.05 0 0.05

NC 0 0.05 0.1

LC 0.05 0.1 0.15

Table11: Rule BaseMem.

Funcions

ESD VSD SD ND VND LD VLD ELD

SP SC SC NC NC NC NC LC LC

NP SC SC NC NC NC LC LC LC

LP SC NC NC LC LC LC LC LC

Table 12: Membership functions and rule base defined

for 14th tray

Membership

function

Lower limit Middle limit Higher limit

ESP -0.0150 0 0.0150

VVSP 0 0.0150 0.03

VSP 0.0150 0.03 0.045SP 0.03 0.045 0.06

NP 0.045 0.06 0.075

VNP 0.06 0.075 0.09

LP 0.075 0.09 0.105

VLP 0.09 0.105 0.12

VVLP 0.105 0.12 0.135

ELP 0.12 0.135 0.15

Table 13:

Membership

function


ESD -0.1 -0.05 0VSD -0.05 0 0.05

SD 0 0.05 0.1

ND 0.05 0.1 0.15

VND 0.1 0.15 0.2

LD 0.15 0.2 0.25

VLD 0.2 0.25 0.3

Table 14:

Membership

function


ESC -0.1 -0.05 0

VSC -0.05 0 0.05SC 0 0.05 0.1

NC 0.05 0.1 0.15

VNC 0.1 0.15 0.2

LC 0.15 0.2 0.25

VLC 0.2 0.25 0.3

Table 15: Rule BaseMem

Functions

ESP VVSP VSP SP NP VNP LP VLP VVLP ELP

ESD ESC ESC ESC VSC VSC VSC VSC SC SC NC

VSD VSC NC VSC VSC SC SC NC NC NC VNC

SD LC LC VLC VLC VLC VLC VLC VLC LC LC

ND NC NC LC LC VLC VLC LC LC LC LC

VND NC NC VNC VNC LC VLC VLC VLC LC LC

LD NC NC NC VLC VLC VLC VLC VLC VLC LC

VLD VLC VLC VLC VLC VLC LC LC VNC VNC NC

Comparison of Results:

In case of reactive distillation process the temperatureof 6th and 14th tray is controlled separately by using theconventional PID and fuzzy controllers to achieve thedesired product quality. The controlled temperature of6th and 14th tray using the controllers is shown in Fig.

26 and Fig. 27. It is observed from Fig. 26 and Fig. 27that the fuzzy controller controls the temperature moreefficiently as the steady state error is negligibly small.The steady state error in case of PID controller is of

order of 0.144 and while in case of fuzzy controller it isorder of 0.0001, hence fuzzy controller gives more ac-curate results. It is also observed that in case of fuzzycontroller the settling time is less as compared to con-ventional PID controller.






Fig.26. Comparison of results for 6th

tray

Fig.27. Comparison of results for 14th

tray

3 CONCLUSIONS

The generic mathematical models of multicomponent

distillation and reactive distillation process are consid-

ered in the present work. These mathematical models

are simulated with the help of MATLAB. The PID and

fuzzy controllers are designed for both the processes.

In case of multicomponent distillation process, the PID

controller is designed with the help of Zeigler-

Nicholas chart and for reactive process the PID con-

troller is designed using Tyreus-Luyben method. In

the multicomponent distillation process, the PID con-troller is used to control reboiler temperature and

hence the distillate quality. In case of reactive process

the designed PID controller is used to regulate the feed

flow rate which in turn controls the temperature indi-

rectly. The fuzzy controllers are also designed for the

control of multicomponent distillation and reactive

distillation process. The results obtained from PID and

fuzzy controllers are compared for multicomponent

distillation and reactive process. It is observed from

the comparison of the results that fuzzy controllerprovides fast response, negligibly small offset error

without much oscillation. Thus, the fuzzy controller

outperforms the conventional PID controller.

Abbreviations:

yB,j Vapour composition of reboiler of component(%mole Fraction)Hl Liquid enthalpy on 1st tray (Btu/lbm)HBv Vapour enthalpy in reboiler (Btu/lbm)L1 Liquid flow rate leaving 1st tray (lb-mole/h)Q

RReboiler heat (Btu/h)

VB Vapour flow rate leaving reboiler (lb-mole/h)x1,j Liquid composition on 1st tray of component

(%mole Fraction) Activation energy for backward reaction (Btu/mole) Activation energy for forward reaction (Btu/mole) Input feed flow rate (lb-mole/h)−1 Vapour enthalpy on ( 1) tray Liquid enthalpy on tray (Btu/lbm) Vapor enthalpy on tray (Btu/lbm)+1 Liquid enthalpy on ( + 1) tray (Btu/lbm) Liquid flow rate leaving tray (lb-mole/h) Molar holdup on tray (lb-mole)

, Rate of reaction on the tray Temperature on ith tray ( °F) Vapour flow rate leaving tray (lb-mole/h)−1 Vapor flow rate leaving ( 1) tray (lb-mole/h) Backward specific reaction rate on tray Forward specific reaction rate on tray Stoichiometric coefficient of component j Liquid composition in reflux drums of component, Liquid composition on tray in component, Mole fraction of component A on tray (%mole Frac-tion), Mole fraction of component B on tray (%mole Frac-

tion), Mole fraction of component C on tray (%mole Frac-tion), Mole fraction of component D on tray (%mole Frac-tion), Vapour composition on tray in component

(%mole Fraction)−1,Vapour composition on (NT-1)th tray of component

(%mole Fraction)

Avp Antione constant for component AB Bottom flow rate (lb-mole/h)

Bvp Antione constant for component B

D Distillate flowrate (lb-mole/h)L Liquid flow rate (lb-mole/h)

NC Number of componentNT Total number of traysP Pressure in the column (psia) Pure vapour pressure of components j (psia)R Reflux flowrate (lb-mole/h)V Vapour flow rate (lb-mole/h)α Relative volatility

Heat of vaporization (Btu/lbm) Heat of reaction (Btu/lb-mole)

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