First Principle Modeling and Neural Network–Based Empirical Modeling with Experimental Validation...

Amit Kumar Singh*, Barjeev Tyagi, and Vishal Kumar

First Principle Modeling and NeuralNetwork–Based Empirical Modelingwith Experimental Validation of BinaryDistillation Column

Abstract: To get the better product quality and to decreasethe energy consumption of the distillation column, an accu-rate and suitable nonlinear model is crucial important. Inthis work, two types of model have been developed for anexisting experimental setup of continuous binary distillationcolumn (BDC). First model is a theoretical tray-to-tray binarydistillation model for describing the steady-state behavior ofcomposition in response to changes in reflux flows and inreboiler duty. Another model is an artificial neural network(ANN)–based input/output data relationshipmodel. InANN-based model, temperature of first tray, feed flow rate, andcolumn pressures have been taken in addition to reflux flowrate and reboiler heat duty as inputs to give the more accu-rate I/O relationship. The comparison of output of ANNmodel and the equation-based model with the real-time out-put of the experimental setup of BDC has been given for thevalidation of developed models.

Keywords: feed forward neural network, binary distilla-tion column, first principle modeling, black box modeling

*Corresponding author: Amit Kumar Singh, Indian Institute ofTechnology, Roorkee, Uttrakhand, India, E-mail: [email protected] Tyagi: E-mail: [email protected], Vishal Kumar: E-mail:[email protected], Indian Institute of Technology, Roorkee,Uttrakhand, India

1 Introduction

Distillation is one of the most important unit operations inchemical engineering because of its most frequently usedseparation technique in the chemical and petroleum indus-tries. Several models are proposed in the literature that canbe used for distillation column. These models can be cate-gorized under two major groups (i) fundamental models,which are derived from mass, energy, and momentumbalances of the process and (ii) empirical models, whichare derived from input–output data of the process.

Several works have been carried out to implement thefundamental models in the distillation column. The funda-mental dynamic model approach has been used by Canet al. [1] for binary distillation column (BDC). Bansal et al.[2] has developed the dynamic distillation model for separa-tion of benzene and toluene. This model consists of differ-ential–algebraic equations for the trays, reboiler,condenser, and reflux drum. Diehl et al. [3] has developedthe differential–algebraic first principle model for a binarymixture of methanol and n-propanol. This model isdescribed bymeans ofmaterial and energy balances, hydro-dynamic effects, equilibrium relationships for each tray andfor the reboiler, and the condenser. The model reductiontechniques have been used in [4–6] to derive a simplifieddynamic model from a complex higher order model.

Higler et al. [7] applied the nonequilibrium model for acomplete three-phase distillation. The model consists of aset of mass and energy balances for each of the threepossible phases present. The results obtained for the none-quilibrium model are in good match with the experimentaldata for the water-ethanol-cyclohexane system. Bian andHenson [8] have proposed the nonlinear wave model forhigh purity distillation column in separation of benzene–toluene. Two main classes of nonlinear black box modelsFuzzy Models (FM) and Composite Local Linear Models(CLLM) have been proposed by Barroso et al. [9]. The mod-els are estimated directly from experimental data and fromthe simulated data. A new computational mass transfermodel is proposed by Wenbin et al. [10] for distillationprocess. Thismodel is developed by utilizing the fluctuatingmass flux for the closure of turbulentmass transfer equationin order to obtain the concentration profile and the separa-tion efficiency of distillation column. Muntean et al. [11]have proposed a general modeling framework to provide afast and easy solution for modeling distillation columns.

Block oriented models are one of the empirical mod-els, which combine the linear dynamic models with staticor memory less nonlinear function. Pearson andPottmann [12] have given three different model structurescombined by these two model components:

doi 10.1515/cppm-2013-0011 Chemical Product and Process Modeling 2013; 8(1): 53–70

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1. Hammerstein model2. Wiener model3. Feedback block–oriented model

Zhu [13] has studied the process identification ofdistillation column using Wiener model. The considerednonlinear Wiener model has contained linear time-invar-iant transfer function vector followed by static nonlinearfunction. Bloemen et al. [14] have developed the Wienermodel by using the experimental data that have theability to approximate the nonlinearity of distillationcolumn better than linear model and finite impulseresponse model. Nugroho et al. [15] have developed thesimple Hammerstein model for distillation column toidentify the ammonia stripper due to its nonlinearcharacteristic.

The artificial neural network (ANN) models havebeen used by many researchers to identify the distillationcolumn. The majority of these models have utilized themultilayer feed forward neural network to develop thenonlinear model. A feed forward neural network modelfor distillation column has been developed by Brizuelaet al. [16]. The training data for the network are obtainedfrom the simulation of column during startup, from initialstate to a steady operating state. The neural networkapproach has been used by Savkovic–Stevanovic [17] forlearning nonlinear dynamic model from distillation plantinput–output data. The weight has been adjusted by theback propagation algorithm of the Generalized Delta Rulein a feed forward neural network consisting of severallayers and an output layer. Barrati et al. [18] has used theback propagation algorithm to train the three layer feedforward neural network. Another neural network modelfor distillation column has been proposed byRamchandran et al. [19] to separate the wastewater. Yu[20] used two hidden layers feed forward neural networkapproach to identify the behavior of BDC and found outthat the neural network–based controller performed bet-ter than conventional controller.

Singh et al. [21] have proposed the two topologiesof ANNs, i.e., Feed Forward Neural network andRecurrent Neural Network. Singh et al. [22] have pro-posed the feed forward ANN model for the multicom-ponent distillation column. The neural network modelcontains 17 inputs and 10 outputs. Model is trained bythe data acquired from the rigorous model. The resultsobtained from ANN-based estimator are found out to bein good agreement with the results of simulation asobtained using semi-rigorous model. In another work,Singh et al. [23] developed the neural network estimatorbased on Levenberg–Marquardt (LM) algorithm and

tested it for binary as well as multicomponent mixturecase.

The LM algorithm is found to be more accurate andsensitive as compared to the Steepest Descent BackPropagation algorithm for binary and multicomponent dis-tillation column. The multiple-input multiple-output(MIMO) neural network model is developed by Abdullahet al. [24] to predict the top and bottom product composi-tions of a methanol–water pilot plant distillation column.Li et al. [25] applied the dynamic neural network methodto identify the model and the local optimal controller. Inthis article, modeling of an existing experimental setup ofBDC has been proposed. The experimental setup has beenmodeled by two approaches. In first approach, the equa-tion-based model has been proposed. Vapor–liquid equili-brium based relationship has been utilized to develop theequation-based model. In another approach, an ANN-based model of experimental setup of BDC has been pro-posed. In this work, a three layer feed forward network hasbeen proposed. Reflux flow rate (uR), feed flow rate (uF),first tray temperature (uT1), reboiler heat duty (uQB), refluxdrum top pressure (uPT), and reboiler bottom pressure (uPB)have been selected as inputs to the neural network.

Twelve hidden neurons have been selected in thehidden layer. Distillate composition (xD) has been takenas a single output of the network. The LM-based backpropagation algorithm has been selected to train themodel. The proposed model has been validated by com-paring the results obtained by theoretical model with theactual results obtained from the operation of existingexperimental setup of BDC.

2 Experimental setup of binarydistillation column

The experimental setup of nine-tray continuous BDC unitwith a single feed and two product streams is shown inFigure 1. Mixture of methanol and water is taken as feed tothe column. The BDC contains a vertical column that hasnine equally spaced trays mounted inside of it. Every trayhas one conduit on alternate side, called down comer.Liquid flows through these down comers by gravity fromeach tray to the one below. Every tray has a weir, which ispresent on one side of the tray to maintain the liquid levelat a suitable height. In the present laboratory setup, bub-ble cap trays have been placed; however, flexibility hasbeen provided to change them to sieve trays. A reboiler isconnected to the vertical shell with suitable piping. Itprovides necessary heat for vaporization for distillation

54 A.K. Singh et al.: Modeling and Experimental Validation of BDC



column operation. It has three electric heaters of 4 kW,2 kW, and 2 kW. One condenser that is connected tothe column through another piping so as to condensethe overhead vapors. Water is used as coolant incondenser.

There are two feed tanks for storing and supplyingthe feed to the distillation column whenever required.Three rotameters are provided for measuring the liquidflow rate as well as for controlling the liquid flow of feed,the bottom product, and the cooling water. A pressureregulator is provided to set the pressure in the column.An automatic control valve is provided to fix and controlliquid flow of feed. A compressor is provided to developnecessary pressure for circulating the feed.

Transducers are interfaced in the BDC to facilitatemonitoring and control of various parameters of the col-umn under consideration. There are totally 12 resistancetemperature detectors (RTD) are used, out of which 9 are

fitted in the trays, 1 in reflux drum, 1 in condenser inlet,and 1 in condenser outlet. Every RTD has attached withan isolator to convert the output of the RTD into currentoutputs for the corresponding temperature. A level trans-mitter is attached with the column to sense the level ofthe reflux drum. There are two pressure transmittersavailable to sense the vapor pressure at the bottom andat the top of the distillation column. A flow transmitter isattached for sensing the feed flow.

3 Equation-based modeling

Dynamic simulation of distillation is characterized by stiffset of differential algebraic equations of material andefficiency equilibrium relationships. The dynamic modelto be developed in this work is expected to meet thefollowing objective: The model should be easy to use

Figure 1 Schematic diagram of distillation column with instrumentation.

A.K. Singh et al.: Modeling and Experimental Validation of BDC 55



for the design of distillation column control schemes,online identification, and optimization purposes.

To develop the equation-based model, the followinginformation has been taken directly from the existingexperimental setup of BDC:(1) Liquid composition on each tray(2) Liquid flow rates from each tray(3) Temperature of each tray(4) Condenser and reboiler duties

To simplify the model, the following assumptionshave been considered [26]:(1) The relative volatility α is constant throughout the

column.(2) The vapor–liquid equilibrium relationship can be

expressed by

y ¼ αx1þ ðα� 1Þx

Whereα ¼ Relative volatilityx ¼ Composition of more volatile component in

liquid, mole fraction,

y ¼ Composition of more volatile component invapor, mole fraction

(3) The overhead vapor is totally condensed in thecondenser.

(4) The holdup of vapor is negligible throughout the

system (i.e., the same immediate vapor response,dV1 ¼ dV2 ¼ � � � ¼ dVNþ1¼ dV), where N ¼ totalnumber of trays

(5) The molar flow rates of the vapor and liquid throughthe stripping and rectifying sections are constant:

V1 ¼ V2 ¼ � � � ¼ VNþ1;

L2 ¼ L3 ¼ � � � ¼ LNþ2

(6) Reboiler and condenser are also considered as atray. Numbering of trays is done from the bottom,i.e., boiler is considered as a first tray and conden-ser is considered as a last tray. This means that ifthere is N number of trays then boiler is first trayand condenser is (N þ 1)th tray.

Distillation column is divided into three differentsections for the modeling point of view as shown inFigure 2. First section is reboiler section, second section

TT LT

LT

TT

Ln-1,xn-1

Vn,yn

Ln,xn

Vn+1,yn+1

Li

MB

VB

Steam

CondensateB

Ist

F IInd

LNT+1NT

VNT

MD

IIIrd

D

Figure 2 Distillation column used in modeling.




is tray section, and third section is condenser section. Thematerial and enthalpy balance equations are obtained byapplying conservation laws to these sections.

3.1 First section

3.1.1 Component material balance equations

The constant molar holdup in reboiler has been consid-ered, i.e., dMB=dt ¼ 0, so by this

B ¼ L1 � VB

Component material balance around reboiler is given by

MBdxB;jdt

¼ L1x1;j � VByB;j � ðL1 � VBÞxB;j ð1Þ

WhereMB ¼ Liquid molar hold up in reboiler, kmolesL1 ¼ Total liquid flow rate from tray-1 entering to reboi-

ler, kmole/hxB,j ¼ Liquid fraction of component j in bottom product,

% mole fractionsVB ¼ Total vapor flow rate leaving reboiler, kmole/hyB,j ¼ Vapor fraction of component j in bottom product,

% mole fractionsB ¼ Total bottom product rate, kmole/h

The vapor fraction of component j from reboiler isgiven by

yB;j ¼ ηv1;j:k1;jxB;j ð2Þ

whereηv1;j ¼ Vaporization efficiency of component j in reboilerk1,j ¼ Equilibrium constant of component j in reboiler

3.1.2 Total enthalpy balance equations

Total enthalpy balance equation for reboiler is given by

MB:dhBdt

¼ L1h1 � VBHB � ðL1 � VBÞhB þ QB ð3Þ

whereh1 ¼ Total molar enthalpy of liquid entering from tray-1

to reboiler, kJ/kmolehB ¼ Total molar enthalpy of liquid leaving reboiler, kJ/

kmoleHB ¼ Total molar enthalpy of vapor leaving reboiler, kJ/

kmoleQB ¼ Reboiler heat duty, kW

3.2 Second section

In the second section, modeling for general ith tray isconsidered. Material balance and energy balance equa-tions are obtained from this section.


Component material balance equation for ith tray isgiven by

dðMixijÞdt

¼ Liþ1xiþ1;j � Lixij � Viyij þ Vi�1yi�1;j þ FixFij

ð4Þyij is calculated as

yij ¼ ηijðy�ij � yi�1;jÞ þ yi�1;j ð5Þ

whereMi ¼ Molar liquid hold up on tray I, kmolexij ¼ Liquid fraction of component j, leaving the tray i, %

mole fractionLi ¼ Total liquid flow rate leaving tray-i, kmole/hVi ¼ Total vapor flow rate leaving tray-i, kmole/hFi ¼ Total feed flow rate injected to tray-i, kmole/hxFij ¼ Liquid fraction of component j in feed on tray i, %

mole fractionsyij ¼ vapor fraction of component j leaving the tray i, %

mole fractionsnij ¼ Murphree stage efficiency based on vapor phase of

component j on tray iyij

* ¼ Equilibrium vapor fraction of component j on tray iLi is an additional variable and it is related to Mi through

Li ¼ 3:33lw Mi= Anet:MDið Þ � hw½ � 3; 6002:204

MDi ð6Þ

wherelw ¼ Length of the weir, ftAnet ¼ Net area of the tray, ft2

hw ¼ Height of the weir, ftMDi ¼ Average molar density of liquid on tray I, kmole/ft3

Total material balance equation for ith general tray iscalculated as

dMi

dt¼ Liþ1 � Li � Vi þ Vi�1 þ Fi ð7Þ

whereLiþ 1 ¼ Total liquid flow rate entering to tray i, kmole/hVi–1 ¼ Total vapor flow rate entering to tray i, kmole/hFi ¼ Total feed flow rate injected on tray i, kmole/h




3.2.2 Enthalpy balance equation for general tray i

Enthalpy balance equation for general tray i is given as

dðMihiÞdt

¼ Liþ1hiþ1 � Lihi � ViHi þ Vi�1Hi�1 þ FihFi ð8Þ

wherehi ¼ Total molar enthalpy of liquid leaving tray I,

kJ/kmoleHi ¼ Total molar enthalpy of vapor leaving tray I, kJ/kmole

Enthalpy on any tray is calculated by mixing rule asgiven by

hi ¼XNCj¼1

hlijxij ð9Þ

Hi ¼XNCj¼1

Hvijyij ð10Þ

wherehlij ¼ Pure component enthalpy of component j in liquid,

kJ/kmoleHvij ¼ Pure component enthalpy of component j in

liquid, kJ/kmoleNext section, i.e., third section produces the modeling of

condenser.

3.3 Third section


Reflux drum level is considered constant. This means atany time D ¼ VNT–R.

Component material balance around condenser isgiven by

MDdxD;jdt

¼ VNTyNT;j � VNTxD;j ð11Þ

whereMD ¼ Liquid molar hold up in the reflux drum, kmole,D ¼ Distillate flow rate, kmole/h,xD,j ¼ Liquid fraction of component j in reflux drum, %

mole fractionsyNT,j ¼ Vapor fraction of component j leaving tray NT, %

mole fractionsR ¼ Total liquid flow rate entering to the tray NT from

reflux drum, kmole/hVNT ¼ Total vapor flow rate leaving the tray NT, kmole/h

3.3.2 Enthalpy balance equation

The enthalpy balance equation for liquid and vapor forcondenser is

MDdhDdt

¼ VNTHNT � VNThD � Qc ð12Þ

wherehD ¼ Total molar enthalpy of liquid leaving the reflux

drum, kJ/kmoleHNT ¼ Total molar enthalpy of vapor leaving the last tray

NT, kJ/kmoleQC ¼ Condenser duty, kW

All the above equations have been used to developthe model. The flow diagram of the simulation algorithmto develop the equation-based model of BDC is given inFigure 3. To simulate open-loop BDC the environment ofMATLAB®/SIMULINK® has been used.

Input data for column size, components,physical properties, feeds and initial

conditions.

Calculate initial holdups and the pressureprofile of the column

Calculate the temperatures and the vaporfraction from the vapor liquide quilibriumdata on each tray including reboiler and

condenser

Calculate liquid and vapor enthalpies on alltrays, reboiler and condenser using

equations 9 and 10

Calculate vapor flow rates on all trays,start ingin the column base,using the

algebraic form of energy equations 12,8 and 3

Evaluate all derivatives of the componentcontinuity equations for all components on

all trays plus there flux drum and the columnbase using equations 11,4 and 1

Integrate all ordinary differential equations(ODEs) (usingode15s)

Calculate new total liquid holdups from thesum of the component holdups. Then

calculate the new liquid molefraction fromthe component holdups andthe total holdup

equations (4,5)

Calculate new liquid flow rates from the newtotal holdups from all trays using equation 7

Go

to s

tep

3 fo

r nex

t ite

ratio

n

Step 1

Step 2

Step 9

Step 8

Step 7

Step 6

Step 5

Step 4

Step 3

Figure 3 Simulation algorithm.




4 Neural network modeling

In chemical process, parameter variations and uncertaintyplay an important role on the system dynamics and aredifficult to be accurately modeled. In such cases, modelingstrategies of various kinds by means of input–output mea-surements are commonly used. Such methods do notrequire a deep mathematical knowledge of the systemunder study, but it is sufficient to predict the system evolu-tion. This is often the case in control applications, wheresatisfactory predictions of the system are the only require-ment. In this article, a neural network model has beenproposed to estimate the dynamic behavior of BDC.

A neural network is composed of simple elements(artificial neurons) operating in parallel. The networkfunction is determined by the connections (weights)

between the elements. Adjusting the values of the con-nections between elements, the neural network is trainedto approximate a given function.

These are the steps of neural network model devel-opment. The flow diagram of neural network algorithmcan be seen in Figure 4.Step 1. Select proper neural network architecture.Step 2. Vary the input variables (manipulated variables),

collect the input and output data from process setup,or simulators that are normally available for any plant.

Step 3. Start training, based on standard neural networktraining algorithm such as the LM optimization algo-rithm. The optimal number of hidden layers is selectedbased on the minimum mean square error (MSE) value.

Step 4. Update weights between input-hidden as well ashidden output layers until stopping condition is reached.

Figure 4 Flow diagram of neural network algorithm.




The stopping condition may be number of epochs, mini-mum mean square error, and so forth. To design the neuralmodel of BDC, first step is to determine the manipulatedinputs. In the previous section, description of first princi-ple–based BDC model is given. In that model two manipu-lated variables, i.e., reflux flow rate and reboiler heat dutyhave been taken as inputs. In case of any disturbance such asfeed flow and reflux flow, the pressure in reboiler changesand the temperature profile of the column and hence thecomposition of distillate. To overcome such type of problems,the reboiler duty, reflux flow, and pressure along with thecolumn temperature profile are used as inputs in neural net-workmodeling to estimate the distillate composition tomakethe estimator more sensitive. Therefore, the distillate compo-sition is considered as the function of column top and bottompressure, reboiler heat input, feed flow rate, reflux flow, andtray temperature of the column and can be expressed as:

XDðkÞ ¼ f ðuRðk � 1Þ; uFðk � 1Þ; uT1ðk � 1Þ; uQBðk � 1Þ;uPTðk � 1Þ; uPBðk � 1ÞÞ;

whereuR(k–1): Reflux flow rateuF(k–1): Feed flow rateuT1(k–1): First tray temperatureuQB (k–1): Reboiler dutyuPT (k–1): Reflux drum top pressureuPB (k–1): Reboiler bottom pressure

The proposed estimator has six input neurons. Theoutput consists of methanol composition. An input vectorof six elements (reflux flow rate, feed flow rate, first traytemperature, reboiler duty, reflux drum top pressure, and

reboiler bottom pressure of the column) is given to theinput layer of the network. Weights are initially rando-mized when the net undergoes training the errorsbetween the results of the output neurons and the desiredcorresponding target values are propagated backwardthrough the net. The backward propagation of error sig-nals is used to update the connection weights. Finally, anetwork is achieved which can predict the output for anyinput vector.

The developed neural network has two layers, one isinput or hidden layer and another is output layer.Number of neurons in the hidden layer affects the perfor-mance of the training. There is not a definite method toselect the number of neurons in hidden layer. Neurons inthe input layer have been decided by trial and errormethod. Hidden neurons have been selected since onthis value the mean squared error between the trainedoutput and desired target output is minimum. In the two-layer network, a hyperbolic tangent sigmoid function hasbeen chosen as activation function in the first layer,whereas a pure linear function has been taken in thesecond layer. Pure linear function in the output layerhas been used to model most nonlinearities.

In chemical engineering, the most widely used neuralnetwork is the Feed forward neural network (FFNN). Inthis work, a three-layer feed forward network has beenselected. The layers are the input layer, a hidden layer,and an output layer. The structure of the proposed net-work to model the dynamic behavior of BDC is shown inFigure 5. The output of the neural network model is xD,the distillate output composition. The relationshipbetween s1, the output of the first layer, and the inputvariables is given by eq. (13)

Figure 5 Feed forward neural network model of BDC.




s1 ¼ IWf1; 1guR þ IWf1; 1guF þ IWf1; 1guT1 þ IWf1; 1guQB

þ IWf1; 1guPT þ IWf1; 1guPB þ bf1gð13Þ

Where s1 is the weighted sum of the input variables,which is fed to hyperbolic tangent sigmoid transferfunction. The output of the hyperbolic tangent sigmoidfunction is x1, which is given by eq. (14)

x1 ¼ tan sigðs1Þ ¼ 21þ e�2s1

� 1� �

ð14Þ

x1 multiplies with the weight and sum up with the bias. Itgives s2 as shown in eq. (15).

s2ðFNNÞ ¼ LWf2; 1gx1 þ bf2g ð15Þ

Now s2ðFFNNÞ goes to the activation function of secondlayer. A pure linear function is chosen to be the activationfunction of the second layer. The output of the activation

Function is the distillate composition xD as shown ineq. (16).

xDðFNNÞ ¼ purelinðs2ðFNNÞÞ ð16Þ

The data for training of the neural network model arereal data acquired from the operation of existing setup ofBDC in laboratory. Input–output data sets with differentvalues of uR, uF, uT1, uQB, uPT, and uPB are used as thetraining data sets. These data samples have beenacquired by the changes between the defined ranges inthe manipulated variables at every 60 s and record theoutput methanol composition on these input samples.Each input vector consists of 579 data samples. Eachinput variable vary in a range as given below

uR: 0.82 to 1.41 kmole/huF: 2.5–3.5 kmole/huT1: 80–99°CuQB: 0.019 � 106 (5.5 kW) to 0.0241 � 106 kJ/h (7.0 kW)uPT: 101.42–106 kPa,uPB: 115.21–120 kPa

For output data set, there is one output xD, i.e., outputdistillate composition. xD is varied from 0.84 to 0.92%.Overall, 3,447 data samples are used to train the neuralnetwork model for the BDC. The LM back propagationalgorithm [27, 28] is used for training, which is performedusing the neural network tool box of MATLAB®.

Table 1 shows the gradient value and the MSE ofFFNN with the different number of hidden neurons.These two characteristics represent the performance ofthe model and are used for validation and testing of thedeveloped neural network model. The numbers of hiddenneurons considered are 6 to 22 because the neural net-work did not converge when the numbers of neuronswere taken less than six. Training the network withmore than 22 neurons produces the non-convergence.

Table 1 shows that the optimal number of hiddenneurons for FFNN model is 12 because gradient andMSE both are minimum for these number of hidden neu-rons. One can understand by analyses from Table I thatfurther increment or decrement in the number of neuronswill not help in the optimization.

The developed neural network model will be used ina manner that first a PID controller will be designed tocontrol the temperature of tray uT1 in SIMULINK environ-ment. Designing of PID means to know the parametersKp, Ki, and Kd. To know these parameters, the developedneural model will be used. The inputs other than the traytemperature will be fixed to the nominal values. The

Table 1 Gradient and MSE of the FFNN model with different number of neurons.

Architecture Gradient MSE for feed forward network

Training Testing Validation

6-6-1 7.08754e-007 5.38178e-007 8.0423e-007 1.2104e-0076-8-1 4.40621e-006 1.12582e-007 4.4063e-006 4.0231e-0066-10-1 6.63989e-007 6.50383e-007 9.5467e-007 5.2435e-0076-12-1 7.19207e-008 2.7823e-008 5.55703e-008 4.3213e-0086-14-1 1.13615e-007 4.19688e-007 1.13728e-007 1.1256e-0076-16-1 3.13599e-006 3.86997e-006 4.3219e-006 2.3251e-0066-17-1 4.64871e-007 3.00008e-006 4.6488e-007 3.0412e-0076-18-1 1.08061e-005 2.10534e-007 2.13081e-005 1.9229e-0056-20-1 5.53205e-007 1.52098e-007 3.64351e-007 2.6511e-0076-22-1 5.63932e-006 6.98418e-006 5.63980e-006 4.8965e-006




neural model will give the methanol composition corre-sponding to the tray temperature. To set a referencetemperature, a methanol composition to tray temperatureestimator will be used after the neural model. After know-ing the PID parameters by simulation, the known para-meter will be fixed in the hardware PID controller. By thisthe validation will be done of the designed PID controller.

5 Results and discussion

The BDC has been used to separate the mixture of metha-nol and water. This mixture is used as a feed to BDC. Thecomposition of the feed is 90% water and 10% methanol.This mixture is fed at fifth tray of BDC. In BDC, methanolis separated from water. Methanol is collected at theupper part of the column as distillated output.

To simulate the equation-based model, the inputsreflux flow rate and reboiler heat duty varied between0.82–1.41 kmole/h and 0.019 � 106 (5.5 kW) to 0.0241 �106 kJ/h (7.0 kW), respectively. To validate the equation-based model, the results obtained from this model havebeen compared with the results obtained from the experi-mental setup.

The existing experimental setup parameters havebeen set as given below:

Liquid feed rate 2.5 kg-moles/hLiquid feed temperature 34.5°C

Pressure in the bottom 115.21 kPaPressure in the reflux drum 101.42 kPaMurphree vapor efficiency 0.60

In experimental setup, reflux flow rate and reboilerheat duty have been varied similarly as in case ofequation-based model. As change in reflux flow rateaffects top composition more effectively than thechange in reboiler heat duty, three different step valuesof reflux flow rate have been take into consideration.The step values are between the minimum and max-imum range of reflux flow rate. As the working range ofreflux flow rate is 0.82 kmole/h to 1.41 kmole/h here sothe step values are chosen between this range. Firstvalue is 0.82–0.92 kmole/h, second value is 1.02–1.12kmole/h, and third value is 1.31–1.41 kmole/h. Thesethree step values are applied to experimental setupand to both the equation-based model and neuralmodel. After application of these changes, distillatecomposition is measured and compared. The distillatecomposition output from equation-based model andexperimental setup is shown in Figures 6, 7 and 8 atthe above three step values, respectively. The errorbetween the experimental output and equation-basedmodel output is shown in Figures 9, 10 and 11respectively.

It is observed from the results that the proposedequation-based model closely match with the experimen-tal results and this model can be used as a equivalentmodel for the experimental setup of distillation column.

Figure 6 Comparison of experimental output and equation-based model output at reflux rate step values 0.82–0.92 kmole/h.




The temperatures of first tray, feed flow rate, toppressure, and bottom pressure have also included inaddition to reflux flow rate and reboiler duty as inputsto give the more accurate I/O relationship for the devel-opment of neural network model. This means that totalsix inputs have been taken into consideration. The dataused for training the neural network model are acquiredby the operation of the experimental setup of BDC.

Input–output data set consists of 579 data samplesof each input variable. The LM back propagation algo-rithm is used for training, which is performed using theneural network toolbox of MATLAB/SIMULINK. The con-vergence criterion for training the model is set to 1e-10.After training the model for 77 epochs, the meansquared error observed is 7.19207e-008. Mean squarederror is the average squared difference between outputs






and targets. The training performance is shown inFigure 12.

Another way to judge the performance of neuralmodel is regression R values. R values measure the cor-relation between outputs and targets, an R values close to1 means the output is close to target. R values obtained

for training, testing, and validation are 0.99962, 0.9993,and 0.9999 as shown in Figures 13 , 14 and 15 respec-tively. It is a very good correlation among simulationresults and experimental data.

To obtain the distillate output from neural networkmodel, four inputs, feed flow rate, first tray temperature,

Figure 9 Error between experimental output and equation-based model output at reflux rate step values 0.82–0.92 kmole/h.






Figure 12 Training of the neural network model.

Figure 13 Training outputs vs. targets.




Figure 14 Test outputs vs. targets.

Figure 16 Comparison of neural model output with experimental output and equation-based model output at reflux rate step values0.82–0.92 kmole/h.

Figure 15 Validation outputs vs. targets.




reflux drum top pressure, and reboiler bottom pressure,are fixed at the values 2.5 kmole/h, 90°C, 101.42 kPa, and115.21 kPa, respectively.

Two inputs reflux flow rate and reboiler heat duty arevaried similarly as in case of equation-based model andin operation of experimental setup.

To validate the neural model, same step values ofreflux flow rate that are used for the validation of equa-tion-based model are considered. For first step valuereflux flow rate is between 0.82 kmole/h and 0.92kmole/h. The neural model output is compared with

experimental output and equation-based model outputas shown in Figure 16.

The error between the neural model output and equa-tion-based model output is given in Figure 17. Figures 164and 17 illustrates that neural model closely trace theexperimental output.

The second step value of reflux flow rate is between1.02 kmole/h and 1.12 kmole/h. For this value, the com-parison of neural model output with equation-basedmodel output and experimental output is shown inFigure 18. Figure 19 illustrates the error between the

Figure 18 Comparison of neural model output with experimental output and equation-based model output at reflux rate step values1.02–1.12 kmole/h.

Figure 17 Error between neural model output and equation-based model output at reflux rate step values 0.82–0.92 kmole/h.




models. Results show that neural model works fine alsofor this value of reflux flow rate.

Figure 20 shows the comparison of the models whenthe step value of reflux flow rate is between 1.31 kmole/hand 1.41 kmole/h. Error between the models is shown inFigure 21. Result shows that both the models closelymatch the experimental output.

After comparison it can be concluded that equation-based model and neural model closely match with the

experimental setup and can be used as an alternatemodel for simulation purposes.

6 Conclusions

In this work, the equation-based modeling and neuralnetwork modeling of the existing experimental setup ofcontinuous nine-tray BDC have been presented. In the

Figure 20 Comparison of neural model output with experimental output and equation-based model output at reflux rate step values 1.31–1.41 kmole/h

Figure 19 Error between neural model output and equation-based model output at reflux rate step values 1.02–1.12 kmole/h




equation-based modeling, a model of a continuous bin-ary distillation was constructed based on mass balanceand constant relative volatility. The model was then usedto simulate the dynamics of the column. Experiments onthe real plant have also been carried out in order tovalidate the model. The simulation results show that thecomposition outputs are close to the response of existingexperimental setup of BDC. Even though fundamentalmodels are generally far more accurate, these modelstend to involve many equations. The models obtainedmay be too complex to be used for nonlinear model–based control design and will increase the computationalburden of the controller. So to remove out this problem,this article reveals that neural network models are the

most popular framework for empirical model develop-ment. The neural network model was found to be ableto predict the top product composition precisely. Theresults showed that the developed neural networkmodel was in good agreement with the experimentaldata. The results obtained in this study proved that thisneural network model could be used to represent theexisting experimental setup of BDC.

Acknowledgement: The authors wish to acknowledge thefinancial support of the Ministry of human resource anddevelopments (MHRD), India under faculty initiationgrant scheme with grant no. MHRD-03-29-801-108(FIG).

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Barjeev Tyagi received B. Tech. degree in Electrical Engineering fromUniversity of Roorkee (India) in 1987 and Ph.D. degree from IIT Kanpur in2006. Presently, he is Associate professor in Electrical EngineeringDepartment at Indian Institute of Technology, Roorkee (India). Hisresearch interests include control system, power system deregulation,power system optimization and control.

Vishal Kumar received the Ph.D. degree in power system engineeringfrom the Indian Institute of Technology, Roorkee, India, in 2007.Currently, he is Assistant professor in the Department of ElectricalEngineering, Indian Institute of Technology,Roorkee, India. His researchinterests include power distribution system operation and protection,and digital design and verification.

Amit Kumar Singh is currently working towards his Ph.D. degree inDepartment of Electrical Engineering at Indian Institute of Technology,Roorkee (India). His research interests include control system, processcontrol and application of evolutionary techniques to chemicalprocesses.




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First Principle Modeling and Neural Network–Based Empirical Modeling with Experimental Validation...

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