Multivariable control of a debutanizer column using equation based artificial neural network model inverse control strategies

Author’s Accepted Manuscript Multivariable Control of a Debutanizer Column using Equation Based Artificial Neural Network Model Inverse Control Strategies Nasser Mohamed Ramli, Mohd Azlan Hussain, Badrul Mohamed Jan www.elsevier.com/locate/neucom

PII: DOI: Reference:

S0925-2312(16)00229-0 http://dx.doi.org/10.1016/j.neucom.2016.02.026 NEUCOM16751

To appear in: Neurocomputing Received date: 2 September 2015 Revised date: 29 January 2016 Accepted date: 14 February 2016 Cite this article as: Nasser Mohamed Ramli, Mohd Azlan Hussain and Badrul Mohamed Jan, Multivariable Control of a Debutanizer Column using Equation Based Artificial Neural Network Model Inverse Control Strategies, Neurocomputing, http://dx.doi.org/10.1016/j.neucom.2016.02.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Multivariable Control of a Debutanizer Column using Equation Based Artificial Neural Network Model Inverse Control Strategies

Nasser Mohamed Ramli1,2 Mohd Azlan Hussain2,3* and Badrul Mohamed Jan2

1

Department of Chemical Engineering, Universiti Teknologi PETRONAS, 32610 Bandar Seri

Iskandar, Perak, Malaysia 2

Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603

Kuala Lumpur, Malaysia 3

UMPDEC, University of Malaya

Email : [email protected], [email protected], [email protected]

Corresponding author. Tel : 00603-79675214 Fax : 00603-79675319 email : [email protected] Address : Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

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Abstract

The debutanizer column is an important unit operation in petroleum refining industries as it is the main column to produce liquefied petroleum gas as its top product and light naphtha as its bottom product. This system is difficult to handle from a control standpoint due to its nonlinear behaviour, multivariable interaction and existence of numerous constraints on both its manipulated and state variable. Neural network techniques have been increasingly used for a wide variety of applications where statistical methods have been traditionally employed. In this work we propose to use an equation based MIMO (Multi Input Multi Output) neural network based multivariable control strategy to control the top and bottom temperatures of the column simultaneously, while manipulating the

reflux and reboiler flow rates

respectively. This equation based neural network model represented by a multivariable equation, instead of the normal black box structure, has the advantage of being robust in nature while being easier to interpret in terms of its input output variables. It is implemented for set point changes and disturbance changes and the results show that the neural network based model method in the direct inverse and internal model approach performs better than the conventional PID method in both cases.

Keywords: Debutanizer column, neural network, Equation based, Multivariable control.

1. Introduction

Debutanizer column operation is based on a multi-component, multivariable control strategy which is highly non-linear in nature involving nonlinear dynamics. The column is widely used in process plants and it constitutes a very difficult control problem. The product composition can normally be controlled by two variables, the product split and reflux ratio [1] as the two manipulated variables. However controlling these top and bottom compositions require a number of complex instrumentation which are due to the interactions of the these composition loops which face dynamic stability problems. Its control requires an on-line measurement performance variable directly related to composition, which is normally temperature. Although, temperature-composition relationship is a function of column pressure control, controlling the

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top and bottom temperatures of the column seems to give tight control on product composition despite wide variations in other factors such as the internal reflux ratio [1]. However, application of composition control at both ends of a debutanizer column has shown very little success [1]. The difficulty arises since the two individual control loops tend to interact where the top loop controls the heavy key in the overhead stream while the bottom loop controls the light key in the bottom stream. Slight disturbances in the system can cause the light key concentration in the bottom stream to increase while the lower loop may change the concentration through addition of heat in the reboiler system. At the same time, laboratory measurement procedures for composition measurement are also slow, tedious and time consuming. Therefore, inferential model using linear regression usually encounters co-linearity problem, which adversely affects long-term prediction performance since the outputs of the debutanizer column usually depend on the feed composition which also cannot be determined online. To circumvent some of these problems, the use of software based sensors and controllers incorporating neural network models is proposed in this work. This neural network based system is developed to simultaneously control the top and bottom temperature while at the same time regulating the compositions in a multi-input multi output approach. Since in the real industry large historical data are available, the use of neural network is also appropriate and economical as compared to hardware based instruments. It will also help improve product quality monitoring of the system by predicting the top and bottom compositions and temperatures simultaneously with high accuracy [2]. The software based are also cheap compared to hardware sensors and can be easily integrated on existing hardware controllers in the industry. Previously some work utilizing neural network as a controller have been done which include robust stability analysis with harmonic balance for a multivariable non-linear plant using the neural network controller under generic Lur’e configuration [3]. The neural network controller was applied to describe the sinusoidal input while the linearized model has been derived to represent the nonlinear plant dynamics. The work was applied to a multivariable binary distillation column under feedback neurocontrol and it illustrates the use of a robustness approach to predict the presence of limit cycles subject to restriction of the describing function. In another work, the use of adaptive neural network for composition prediction which was used to control both the composition and inventory for a continuous ethanol-water pilot plant based distillation column has also been proposed [4]. A principal component analysis based algorithm was

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applied to select the input vectors for the soft sensor. The proposed control scheme offers high speed of change which is due to the set point changes with stationary error for composition and inventory control. A multi-loop nonlinear model control strategy has also been proposed for a distillation column using an ARX-NN (Autoregressive Neural Network) cascaded structure incorporated into the PLS (Partial Least Square) inner model [5]. An optimization procedure is provided to identify the set parameter of the ARX-NN PLS in order to minimize the plant model mismatch. The approach was used to demonstrate the control effectiveness for setpoint tracking and disturbance rejection. Neural network has also been applied to handle the nonlinear dynamics of a hydrolyzer [6]. A mathematical model was used to simulate the dynamic response of the temperatures when the controller was applied to the system. Two control strategies implemented include the direct inverse control and internal model control and evaluated for setpoint tracking and disturbances studies. The IMC (Internal Model Control) was found to perform best for temperature control during setpoint and disturbance tests and found to be more stable than the conventional controllers. In a novel implementation of a neural network inverse model based control method on an experimental system, a partially simulated reactor was used to test the neural network based algorithms [7]. The implementation involves the control of the reactor temperature in the face of set point changes and load disturbances which gave acceptable results as compared to the conventional controller. Neural networks for gain prediction within a nonlinear and multivariable system with constraints have also been developed [8]. This strategy was implemented on a lab-scale, non ideal system for a methanol-water distillation column using servo, regulatory and constrained control. The experimental results applied a Generic Model Controller using the neural network as the steady-state model inverse that was developed earlier. A comparative study of these neural network model-based controllers with other advanced controllers such as the dynamic matrix control showed better performance of the proposed controller. A neural network controller design based on the process inverse dynamic modeling was also applied for product composition control of a distillation plant. The algorithm was applied to obtain the dynamic nonlinear relationship between product composition and reflux flow rate [9]. Neural networks model has also been used as the steady state inverse of a process which is then coupled with a simple reference system synthesis to generate a multivariable controller [10]. The control strategy was applied for controlling a

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distillation column in the lab and for an industrial-scale high-purity column. An efficient training algorithm based on a nonlinear least-squares technique was used to train the networks. The neural network model based controllers showed better performances for both setpoint and disturbance changes over the conventional feedback controllers. The various works presented so far on the use of neural network models and controllers involve the use of black box models. This is non-versatile and non-robust in nature as well as being difficult to see the correlations between the inputs and outputs to the system, which are important factors for practitioners in many cases. In this work, which lies one of its main novelty and contribution, we have proposed using an equation based inverse neural network models in a MIMO system to control the top and bottom temperature of the debutanizer column simultaneously using the DIC (Direct Inverse Control) and IMC approach. Neural network equation based models have also been used to estimate the compositions in the column. The other contribution of this work is that it utilize a mixture of online close loop and open loop data for data available online and simulation data for data which are not available online, for training the neural network models. The simulation data was validated with the actual loop output to ascertain its accuracy. The paper is organized in several sections. Section 2 describes the column and plant in detail while section 3 outlines the hybrid modeling of the distillation column. Section 4 discusses the methodology for the hybrid model. Finally section 5 covers the overall analysis results using the hybrid model for composition and temperature while section 6 covers the conclusion .

2. Plant and Debutanizer Column Description

The plant under study in this paper is a crude oil processing unit to produce high value petroleum products for domestic and export markets as seen in Figure 1. The plant consists of a refinery process and involves condensate fractionation and reforming of aromatics. The products are petroleum fractions, liquefied petroleum gas, naphtha and low sulfur waxy residue while the feed stock of the refinery is crude oil. There are two main process units for the refinery, which are the CDU (Crude Distillation Unit) and the CRU (Catalytic Reforming Unit) while the Crude Oil Terminal provides the crude oil feed stock. Heat exchangers are used to preheat the crude oil from 1900 to 210 0C. The preheated stream is then further

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heated in a furnace with a temperature range of about 3400 to 342 0C. The crude is then routed to the CDU. The crude oil is split into a number of fractions, which includes the heavy straight run naphtha as overhead vapor, untreated kerosene, straight run kerosene and straight run diesel. From the crude tower, there are three branches of cut streams, which are drawn to a stripper column that consists of naphtha stripper, kerosene stripper and diesel stripper. The hydrogen from the reformer is mixed with the feed of the HSRN (Heavy Straight Run Naphtha) from the CDU and is then heated up to the reaction temperature prior to being fed into a pretreater catalytic reactor. The reactions consist of desulfurisation and denitrification, which protect the reformer catalyst from poisoning. The product from the reactor is then sent to the pretreater stripper. The feed to the reforming unit includes the bottom product of the stripper. The treated naphtha is heated to the reaction temperature and is then fed to the reforming reactors. Effluent from the reactor is cooled and collected in a reformer separator. One part of the gas is sent to an absorber while the other is recycled to the reactor feed stream. In the absorber, hydrogen gas is purged and recycled to the pretreater heater. The raw naphtha feed consists of hydrogen make-up gas while the liquid phase is drawn off and fed into a LPG (Liquefied Petroleum Gas) absorber. The liquid fraction is pumped into a stabilizer and the reformate is withdrawn from the stabiliser bottom and cooled before being sent for storage. The overhead vapour from the stabiliser are cooled, condensed and recovered from the stabiliser reflux drum and part of the liquid stabilizer is sent as raw LPG to the recovery unit. In the current work, the major focus is on the debutanizer column since it produces the major product namely, the LPG. The debutanizer column is located at the CDU section. The feed to the debutanizer column is the De-ethanizer’s bottom product. High boiling point heavy components flow down in contact with vapor produced in the debutanizer reboiler while low boiling point components rise up the tower in contact with the internal reflux. In order to cool the overhead vapor, the debutanizer condenser is used. Part of the collected condensed hydrocarbon is routed to the top of the debutanizer as reflux. At the debutanizer bottom section, the debutanizer reboiler is used to strip the light component. To control the bottom temperature of the column, a debutanizer reboiler control valve is manipulated. On the other hand the reflux flow rate is manipulated to control the top temperature in the column. Hence the control of the debutanizer column is categorized as a MIMO control system. Figure 2 shows the column configuration for

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the debutanizer column. Table 1 outlines the column specifications and Table 2 describes the tag name surrounding the column. A common scheme is to use reflux flow to control top product composition and the heat input is used to control bottom product composition. However, changes in reflux also affect bottom product composition and the top product streams are also affected by changes in heat input and hence several loop interactions can occur in the debutanizer column due to this process design. The present practice for controlling these loops involve conventional controllers controlling the top and bottom temperatures separately with different loops. These are unstable at times due to the nonlinearity and interaction inherently present in the column, which also involves tuning problems for the controller. The main objective of this paper is to develop an advanced equation based neural network control strategies to control the top and bottom temperatures while estimating the top and bottom compositions simultaneously for the debutanizer using a mixture of industrial and simulation data. The proposed approach using neural network controllers and MIMO based controllers for controlling both loops simultaneously, inherently takes into account the interactions within these loops. The proposed method of using equation based NN controllers and estimates add further advantage due to the fact that the relationship between the input and output variables can be represented by equations which can be modified and adapted easily without tedious retraining of the networks, hence is more robust and versatile than the black box NN controllers.

3. Methodology 3.1 Data generation Although most online open loop response from the plant surrounding the column is available, some of the variables in the open loop are not available. In this work, dynamic simulation of the debutanizer column is performed using the plant process simulator HYSYS to obtain the unavailable data sets from the plant.

Unavailable variables include Temp 5 (Reboiler outlet temperature), Pressure 1 (Debutanizer

receiver overhead pressure) and composition at both ends of the column. The simulated close loop response of the composition of n-butane at the top and bottom of the column is also established to compare them with the online close loop data. The steady state for the column needs to be developed in HYSYS before transition of the steady-state to the dynamic state. Steady state simulations can be cast easily into dynamic

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simulations by specifying additional engineering details, including pressure/flow relationships and equipment dimensions. The necessary information such as feed conditions, feed compositions, reflux ratio, condenser pressure and reboiler pressure have to be provided to the selected unit operation in the simulation. The simulation data is performed using similar step tests as in the plant to obtain the fluctuation of the process variables under open loop response, where the manipulated variables are the reboiler and reflux flow rates. Comparison between the close loop responses in simulation to the actual plant data is performed to evaluate the deviation between the simulated and actual composition of n-butane, to ascertain that the simulation data available closely resemble the actual online industrial data. Figure 3 shows the representation of the composition for the bottom of n-butane as an example. The calculated RMSE (Root Mean Square Error) calculated for the top composition is 0.0251 and the bottom composition is 0.008184 respectively. This indicates that there is a small deviation between the online and simulation data which hence can be used in developing the neural network models The data used for the process are obtained online from industry is taken for 540 minutes with 1-minute sampling interval, which amounts to a total data of 5410 as seen in Figure 4. It could seen that there is some noise in the actual data collected as seen in Figure 4. Section 4.1 describes in detail how the data are generated. The available data from the plant are large and need to be screened by performing PCA (Principal Component Analysis) and PLS to determine the significant variables affecting the top composition, bottom composition and the top and the bottom temperatures of the column which determine the inputs for the neural network model. From these analysis, the main inputs to the forward neural network model temperature are obtained i.e Overhead pressure flow rate, the Feed flow, Temp 2 (Bottom temperature), and Temp 1 (Top temperature), reflux flow rate and the reboiler flow rate. These variables are the necessary inputs to the neural network model where 2 of these i.e Temp 2 and Temp 1 are the measured controlled variables and reflux flow rate and reboiler flow rate are the manipulated variables. Details of these analysis can be seen in [11].

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3.2 Application of Artificial Neural Network

ANN (Artificial Neural Network) is a popular and reliable tool when dealing with problems involving prediction of variables in engineering problems at the present age. Details of the ANN and its applications can be found elsewhere [12, 13, 14, 15, 16, 17]. In essence, the main advantage of ANN is in its ability to approximate an arbitrary function mechanism that learns from observed data. However, it is not a straightforward step to apply neural network for control. A relatively good understanding of the underlying theory is essential. The first criterion is the model selection which depends on the representation of data and its application. Selecting and tuning an algorithm for training on an unseen data requires a significant number of experiments. The other criterion involves the robustness of the selected model. If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can be robust but otherwise not. Neural network has been extensively used for a number of chemical engineering applications involving prediction, control and nonlinear process identification. A review of various applications utilizing neural network for control both in simulation and online implementation for chemical processes can be seen elsewhere [12]. Today FANN (Feed Forward Neural Network) architecture is the most studied and used neural network architecture. It models a global approximation of a multi-input multi-output function in a similar manner as fitting a low order polynomial through a set of data points. A rich collection of different network and learning algorithms are available in the literature [18, 19] but the network is selected as the basic building block to be used in this study. The mathematical formula describing the networks takes the following form:

é n æ nj ç ê k ç ê y=F ê W .f ç w j +w i i, j j j ,l l j.0 ç ê ç l =1 = 1 j ê è ë

å

å

ù ö ÷ ú ÷ ú ÷ + Wi.0 ú ÷ ú ÷ ú ø û

(1)

where j is the external input, nj is the number of input in an input layer, nk is the number of hidden neurons in a hidden layer, W and w are the weights, f and F are activation functions for hidden layer and output layer respectively.

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In order to model the dynamics of a system, either ELMAN (Recurrent Neural Network) or neural network with ARX are used. However, in this work, Neural network with NARX (Non-linear Autoregressive Network with exogenous inputs) structure is applied to model the dynamic system based on time-series data since it gives better result than the ELMAN type network as will be seen later in section 4.1.1 The equations describing the NARX structure can be expressed as follows:

(

Y = f Y ,Y ,........ Y ,U ,U ,..... U 1

2

n

1

2

m

)

(2)

where:

[ ] = [y (k ), y (k - 1),......y (k - ny )]

Y = y (k + 1) y (k + 1) T 1

Y

1

2

1

1

1

1

.............

[

Yn = y n (k ), y n (k - 1)......., y n (k - nyn )

[ = [u

U = u (k ), u (k - 1),......u (k - nu ) 1

U

m

1

1

m

1

1

]

]

(k ), u (k - 1),.....,u (k - nu ) m

m

m

]

and m is number of input variables, n is number of output variables and ny and nu are the history length for output variables and input variables, respectively. The procedure for obtaining the past values done by first setting all ny and nu to be 1 and calculating the RMSE values, after which, we gradually increased until some maximum value of k, normally 5. The combination ny and nu which gives the least RMSE values is chosen as the best values for the delayed inputs, which corresponds to one delayed time in this study. This approach follows that of the previous work in [20, 21]. These past values is very important in term of the performance of the model, too many past values may increase the complexity of the system or for less past values, the model may not be able to capture the dynamics of the process. However, all applications before have utilised neural network as a black box model, which has its own disadvantages and limitations especially in respect to the robustness problems. In this work, we have shown that by proper choice of the activation function, the neural network can be represented by an algebraic

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equation. The general equation for the output from the neural network can be given as (for a 2 layer network)

ö æ y = f 2 ç LW 2,1 f 1æç IW 1,1 p + b1 ö÷ + b 2 ÷ è ø ø è

IW 1,1 = weight at layer 1

b1 = bias value at layer 1

LW 2,1 = weight at layer 2 (hidden layer)

b2 = bias value at layer 2

p

(3)

= inputs to the neural network

y = outputs from the neural network f = activation function at layer i

1 2 The f and f are simplified by multiplying the matrix input layer and the biases value with the matrix

hidden layer, If we choose the activation function to be linear, we can simplify the equation to be in the form of;

é y1 ù é ù y = ê ú = ê LW 2,1 éê IW 1,1 p + b1ùú + b 2 ú y ë û êë 2 úû ë û

(4)

where the matrix definition LW2,1 , IW1,1 , b1 and b2are given as;

IW 1,1 = weight at layer 1 (input layer) b1 = bias value at layer 1

LW 2,1 = weight at layer 2 (hidden layer) b2 = bias value at layer 2

These representations can then be utilized in this work as an estimator to ascertain the top and bottom compositions and multivariable controllers to control the top and bottom temperatures simultaneously as

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will be shown in the next sections.

3.3 Neural Network based control strategies

Two types of Neural Network based control strategies are implemented in the inverse model based control schemes for the debutanizer column under study in this paper i.e. the DIC (Direct Inverse Control) and the IMC (Internal Model Control) methods as described next.

3.3.1. Direct Inverse Control method

This strategy consists of a plant which is placed in a series with the neural network inverse models that act as the controller. In this scheme, the outputs predict the desired current system input, while the desired set-point acts as the desired output which is fed to the network together with the past plant inputs. The structure of the DIC is in multi-input multi output form and appropriate control parameters for the desired target will be predicted based on the inputs by the neural network model acting as the controller as shown in Figure 5. The variables to be controlled are the top and bottom temperatures while the manipulated variables are the reflux and the reboiler flow rates for this case.

3.3.2. Internal Model Control method

Neural network based IMC method incorporates both the inverse and the forward models in the control scheme. The dynamic of the process is modeled by the forward model, which is placed in parallel with the system to cater for mismatches of the model with the plant during implementation [22]. The inverse neural network model acts as the controller as in the DIC strategy. In this scheme, the error between the neural network forward model and the plant output is subtracted from the set- point before being fed into the inverse model, as seen in Figure 6. With a mismatch detection feature, the internal model based controller can be used to drive the controlled parameter to the desired set-point even when noise and disturbances are present in the system. The error produced by the process can be minimized and compensated by the error

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produced by the neural network forward process model [22]. In most cases, the IMC performs better when disturbances are present which is the reason for implementing both strategies in this case study.

3.3.3. Neural networks models

Before applying the inverse model neural network control strategies for the debutanizer column, it is crucial to discuss the development and configuration of the forward and inverse neural network models which is fundamental in these model based control strategies. The details of the neural network model used are given in Tables 3 and 4. The LM (Levenberg-Marquardt) algorithm method is used to train the neural network in the NARX structure designed for second order training. The inverse neural network model that has been developed to control the top and bottom temperatures, there are 12 inputs (p inputs as given in next section) and 2 outputs, which are the reflux and reboiler flow rates. These outputs are the manipulated variables used to control top and bottom temperatures respectively. For the composition prediction, the forward neural network model that has been developed to estimate the top and bottom composition, contains 10 inputs and 2 outputs which are the top and bottom composition respectively.

3.3.3.1. Forward models

The procedure of training a neural network to predict the outputs by giving the required inputs is called forward modeling and the model obtained from this method is referred to as the forward models. The most straightforward and popular approach is to augment the network inputs data signals in real number form, from the model or system being identified [23]. Other fundamental state variables can also be fed into the network and considered as part of the inputs. In this method, the network is fed with the present inputs, past inputs as well as the past outputs to predict the necessary outputs. The neural network is placed in parallel with the model or system. The error between the network output and system output, which is the prediction error is used as the training signal for the neural network. In this work, the equation based models are used to replace the black box neural network modeling and the forward model is used both in the IMC strategy and as the neural network estimator to predict the top and bottom composition. The matrix

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of the weights and biases values are extracted from the network developed in the neural network training and these weights are used to obtain the neural network model as given by the general form of equation (4). The forward model for temperature is then given as;

éT1 ù é ù ê ú = ê LW 2,1 é IW 1,1 p + b1ù + b 2 ú ê ú ë û êëT 2 úû ë û In this case, p is the inputs to the neural network temperature given by the vector

[mv1(k) mv1(k -1) mv2(k) mv2(k -1) mv3(k) mv3(k -1) f (k) f (k -1) Ttop(k) Ttop(k -1) Tbot(k) Tbot(k -1)]T After pruning the neural network structure (simplifying the weights and biases values) the equation above can be further simplified to give the equation below;

éT1 ù é- 0.16 - 0.14 0.04 - 0.002 - 0.094 - 0.95 1.03 - 0.61 - 0.71 0.81 0.16 - 0.049 ù é- 0.28ù y=ê ú=ê úp+ ê ú êëT 2 úû ë0.42 0.07 0.04 0.20 - 0.30 - 0.19 0.12 - 0.28 0.35 - 0.29 - 0.48 0.168 û ë- 0.22û

(5)

where T1, T2 are the output for the top and bottom temperature of the column.

This forward model for temperature is used in the IMC approach described in section 3.3.2. If the activation function used is logsig instead of linear in the output layer, the equation obtained from this is given in equation A1, Appendix 1. If the activation function used is logsig instead of linear in the hidden layer, the equation obtained is given in equation A2, Appendix 1. But if the activation function for both layers, using logsig transfer function the equation, it will be more complex and meaningless to be used in the model control strategy. However our initial study shows that the linear activation function gives better results than logsig transfer function [11].

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The forward model for composition is given by;

é y1 ù é ù ê ú = ê LW 2,1 é IW 1,1 p + b1ù + b 2 ú ê ú ë û êë y 2 úû ë û where in this case, p is the inputs to the neural network composition given by the vector

[mv2(k ) mv2(k - 1) mv3(k ) mv3(k - 1) f (k ) f (k - 1) ptop (k ) ptop (k - 1) pbot(k ) pbot(k - 1)]T After pruning the neural network structure (simplifying the weights and biases values) the equation above can further be simplified to give the composition equation below;

é y 1 ù é- 0.26 0.15 0.37 0.23 0.38 0.40 - 0.50 0.97 0.12 - 0.31 é- 0.28ù ù ê ú=ê ú úp + ê êë y 2 úû ë- 0.09 0.006 0.31 - 0.10 0.02 0.02 - 0.42 - 0.12 0.36 - 0.085û ë- 0.21û

(6)

where y1 and y2 are the output for the top and bottom composition predictions.

3.3.3.2. Inverse models

Inverse models are basically the neural net structure representing the inverse of the system dynamics at the completion of training. The method for obtaining the inverse models is achieved by switching the inputs with the required outputs. The purpose of the switching is to enable the predictions of the manipulated variables for control in the MIMO fashion. In this case the manipulated variables that is the reboiler and reflux flowrates are switched with the future predictions of top and bottom temperatures which are basically the set points of the top and bottom temperatures. The sequence of the inputs of the network needs to be maintained as in the forward models. The training procedure in this case is called inversed modeling and y(k+1) corresponds to the required reference signal or set-point. The final network representation of the inverse is given in the general form;

u(k ) = f -1[ y p (k + 1), y p (k ), y p (k - 1), u(k ), u(k - 1)]

(7)

where, f -1 represents the inverse map of the forward model

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The prediction of the control output i.e. mv2(k) and mv3 (k) is performed for a one-step ahead prediction, in conformity with that of the forward model and also the one-step ahead control action is applied in the control strategies since this is an inverse model based approach which need a one step immediate control action to give good results. The one step ahead is due to using the inverse model control strongly which need immediate action. Our previous work also shows that the network with multiple outputs prediction are not as stable as single output prediction which is very critical for control implementation studies [23, 24]. The training and validation data set generated for the networks are similar to that used for forward modeling but with different input and output configurations.

The inverse neural network model to predict the reboiler and reflux flow rates is given as;

émv2(k )ù é 2,1é 1,1 1ù 2ù ê ú = ê LW ê IW p + b ú + b ú ë û û ëmv3(k ) û ë In this case, p is the inputs to the neural network inverse temperature given by the vector

émv1(k ) mv1(k - 1) mv2(k - 1) mv3(k - 1) f (k ) f (k - 1) Ttop (k + 1) Ttop (k )Ttop (k - 1) Tbot (k + 1) Tbot (k ) ù ê ú êëTbot (k - 1) úû After pruning the neural network structure (simplifying the weights and biases values) the equation above can further be simplified to give the equation below as;

émv2(k )ù é-0.16 0.14 0.039 - 0.004 - 0.09 - 0.951.03 - 0.61 - 0.72 0.81 0.17 - 0.05ù é-0.79 ù ê ú=ê úp + ê ú (8) ëmv3(k ) û ë0.42 0.077 0.039 0.20 - 0.30 - 0.19 0.13 - 0.27 0.34 - 0.28 - 0.47 0.16û ë- 0.008û

where mv2(k) and mv3(k) are the manipulated reflux and reboiler flow rates respectively and p

is the

inputs to the neural network inverse model.

The equation is implemented in SIMULINK (MATLAB) by having the system with more than one control loop in a MIMO strategy. Figure 7 shows the forward and inverse models used in the multivariable control strategies in this work.

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T

4. Results and Discussion

4.1. Step test for reboiler flow rate and reflux flow rate to generate input-output data

In order to generate the input-output data for the neural network training, various step changes are applied to the input data to obtain the corresponding outputs. The inputs for the system in this case are the reboiler flow rates and reflux flow rates while the outputs are the top and bottom temperatures respectively. The step test for these inputs, which are the manipulated variables, is generated by using a multi amplitude, multi step rectangular pulse as seen in Figure 4. This figure shows the step tests for the reboiler flow rate and the reflux flow rate data sets. The step test is important to see the effect and the fluctuations of the various important process variables when performing changes to the reboiler flow rate and as can be seen in this case the fluctuations of the temperatures of the top and bottom of the column changes dynamically as the reboiler flow rate changes. The step test for the reflux flow rate is also conducted in the same way. However only the step test results for the reboiler flow rate are shown in this paper for brevity. The data generated are partitioned according to the training; validation and testing data sets as shown in Figure 8.

4.1.1 Comparison between NARX and ELMAN network

As mention before, the type of dynamic network used for training, validation and testing in this work is the NARX inputs with series-parallel architecture. However to compare the NARX with the ELMAN network and justify the use of the NARX model, we have simulated the output for both results for the bottom composition of n-butane as seen in Figure 9. The same results are obtained for the temperature which is not given here for brevity. From these results it can be concluded that the NARX network gives better prediction than the ELMAN network, hence justifying its use for our control purposes. 4.2 Neural network control implementation

In order to develop and analyze the controller performance for the debutanizer column, two typical test criteria are implemented which are the set point changes and disturbance changes for the column. The set

17

point changes have been performed to check the performance of the neural network control under different required conditions and the disturbances are introduced by changing the column feed temperature. As mentioned before, the control is done in MIMO fashion where the top and bottom temperatures are controlled simultaneously by manipulating the reboiler and reflux flow rates. The top and bottom compositions are monitored by the use of the forward neural network model as the estimators to ensure that the compositions regulate closely to their set point values. There are 3 types of control strategies implemented for the control strategies, which are the IMC, DIC and the conventional PID controller for comparison purposes.

4.2.1 Set point changes

. Figures 10 and 11 show the fluctuations for the top and bottom temperatures which are due to the set point changes. First the top temperature is increased from 30 to 58oC while the bottom temperature is increased from 40 to 137oC. The starting point for the top temperature is 30 oC and for bottom temperature is 40oC where these starting point temperatures are based on the nominal temperatures used in the industry. The one step prediction is used since this is an inverse model control based strategy that demands fast control action, without the need for multiple predictions as in the optmization method for the top and bottom temperatures.

It can be seen that the IMC and DIC show similar trend with small error, no

overshoot and fast settling times to the set point of about 200 minutes. The IMC and DIC method also give less fluctuations for step up tracking of the set point. The fluctuations during step up for the conventional PID controller give unacceptable results because it exhibits very large overshoot with small decay ratio while the settling time for PID is also larger compared to the IMC and DIC methods. The PID controller also gives offset for the set point changes applied and Table 5 shows the parameter of the PID controller which is obtained from the normal Ziegler Nichols method with fine tuning [11]. Table 6 summarizes the performance of these controllers to control the top and bottom temperatures. In terms of the results, the IMC controller gives the best performance as the IAE, ISE values and ITAE values are the smallest compared to the other controllers. Figures 12 and 13 also show the fluctuation of the manipulated variable to control the top and bottom temperatures for the neural network and PID controllers respectively . The neural network based controller is able to predict the manipulated variable for reboiler and reflux more

18

accurately compared to the PID controller and hence the performance of these neural network based controllers show better performance than the conventional PID method. The fluctuations of these manipulated variables for the reboiler and reflux is very important to see how the final control element reacts to the changes in controller actions and hence on the long term effect and performance of the control valves. The MV for the IMC is a bit static due to the way it was trained before, step change pattern with constraint maximum and minimum values while the PID had no training and is flexible in its valve movement.

4.2.2 Disturbances tests

Figures 14 and 15 show the fluctuations for the top and bottom temperatures as a result of the disturbances test. The disturbances introduced to the debutanizer column is the feed temperature with a magnitude increase of 10%, which is introduced after 140 minutes and fix at that value throughout the process onwards. The major control objective is to keep the top and bottom temperatures as close as possible to the set points in spite of fluctuations in the feed temperatures which affect the top temperature significantly as can be seen in Figure 14. The disturbance of the system is chosen as the feed temperature because one of the inputs to the neural network model is also the feed temperature and hence any change in the magnitude of the feed temperature will definitely affect the system behavior . Similar trends were observed for the DIC and IMC methods for the top and bottom temperatures as a result of these disturbances. The neural network control performs well compared to the PID controller with small overshoot, fast settling time and small error. The PID controller gives unacceptable results as they generate high overshoot, offsets and large error. Table 7 shows the performances of these controllers to control the top and bottom temperatures. The results indicate that IMC based method gives slightly better performance than the DIC and its values for the IAE, ISE and ITAE are the smallest compared to other controllers and can be seen by the enlarge partition in Figure 14. Figures 16 and 17 show the fluctuations of the manipulated variables for the different type of controllers respectively. The neural network is able to predict the manipulated variable for reboiler and reflux accurately as compared to the PID controller hence giving better performance from this approach. 4.2.3 Neural network estimator

19

The neural network estimator used in the IMC and DIC method is to monitor and estimate the top and bottom compositions. Figures 18 and 19 show the fluctuations for the top and bottom compositions when there are due to set point changes. For the top composition for the neural network controller using the IMC and DIC methods, it can be concluded that the IMC approach shows optimum result compared to DIC. This is due to, fast settling time to the required set point for the composition. However both IMC and DIC methods are superior compared to the conventional PID controller which gives large overshoot, large error and longer settling time. For the bottom composition fluctuations, the IMC and DIC methods show similar trend as both methods show less fluctuation compared to that using the PID controller. Figures 20 and 21 show the fluctuations for the top and bottom compositions that are due to the disturbance changes. For the top composition for neural network controller for using IMC and DIC method, it can be concluded that the IMC trend shows similar results to the DIC method but both IMC and DIC methods are superior in comparison to the conventional PID controller. The results for PID controller are unacceptable because of the large overshoot, large error and longer time to settle. For the bottom composition fluctuations, the IMC and DIC methods show similar trend but less fluctuations compared to the PID controller.

5. Conclusions Established control system design techniques rely on the availability of non-linear system models. Multivariable and nonlinear systems such as the debutanizer column must first be modeled using a set of differential equations to describe their behaviors to an assumed structure of the process. However the resulting control strategy performance depends on the accuracy of the model for the debutanizer column. There is a high degree of uncertainty about its process behavior. Hence in this work, with the large amount of online data available, MIMO equation based neural network based controllers with NARX structure is proposed and developed to control the debutanizer column top and bottom temperature for set point and disturbance changes. It is observed that the neural network equation based method gives good performance and better than the PID controller for all the cases. Future work will include the neural network models in an online optimization approach.

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Acknowledgement The authors would like to acknowledge PETRONAS for providing the required data and information for the research. I would like to acknowledge University Malaya for providing the grant for the research (PS107/2010B)

Refereces [1] L. Smith Cecil, Industrial process control, Proceedings AIChe Continuing Education Department, American Institute of Chemical Engineers (1979). [2] N. Mohamed Ramli, M. A. Hussain , Badrul Mohamed Jan , B Abdullah, Composition prediction of a debutanizer column using equation based artificial neural network model, Neurocomputing 131 (2014) 59-76. [3] J. Fernandez de Canete, S. Gonzalez, P del Saz-Orozco, I Garcia , A harmonic balance approach to robust neural control of MIMO nonlinear processes applied a distillation column, Journal of Process Control 20 (2010) 1270-1277. [4] J. Fernandez de Canete , P. del Saz-Orozco, S. Gonzalez, I. Garcia-Moral , Dual composition control and soft estimation for a pilot distillation column using a neurogenetic design, Computers and Chemical Engineering 40 (2012) 157-170. [5] B. Hu, Z. Zhoa, J. Liang, Muiti-loop nonlinear model controller design under nonlinear dynamic PLS framework using ARX-neural network model, Journal of Process Control 22 (2012) 207-217. [6] J. S. Lim, M. A. Hussain M. K. Aroua, Control of a hydrolyzer in an oleochemical plant using neural network based controllers, Neurocomputing 73 (2010) 3242-3255. [7] M. A. Hussain, L S. Kershenbaum, Implementation of an inverse model based control strategy using neural networks on a partially simulated exothermic reactor, Chemical Engineering Research and Design IChemE 78 (2000) 299-311. [8] P. Dutta, R. R. Rhinehart, Application of neural network control to distillation and an experimental comparison with other advanced controllers, ISA Transactions 38 (1999) 251-278.

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[9] J. S. Stevanovic, Neural Net controller by inverse modeling for a distillation plant, Computers and Chemical Engineering 20 (1996) 925-930. [10] S. Ramchandran, R R Rhinehart, A very simple structure for neural network control of Distillation, Journal of Process Control 5 (1995) 115-128. [11] N. Mohamed Ramli, Development of Neural Network Based Models to control temperature and estimate composition of a debutanizer column, PhD thesis, University of Malaya, 2015. [12] M. A .Hussain, Review of the application of neural networks in chemical process control – simulation and online implementation, Artificial Intelligence in Engineering 13 (1999) 55-68. [13] M. A. Greaves, I.. M. Mujtaba, M. Barolo, A. Trotta and M. A. Hussain, Neural network approach to dynamic optimization of batch distillation application to a middle vessel column., Trans IChemE 81 (2003) 393-401. [14] M. S. Rahman ,M.M. Rashid, M.A. Hussain, Thermal conductivity prediction of foods by neural network and fuzzy (ANFIS) modeling techniques, Food and Bioproducts Processing 90 (2012) 333-340. [15] M. A. Hosen, M..A. Hussain, Farouq S Mjalli, Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): An experimental investigation, Control Engineering Practice 19 (2011) 454-467. [16] A. Arpornwichanop, P. Kittisupakorn, M A Hussain, Model based control strategies for a chemical batch reactor with exothermic reactions, Korean Journal of Chemical Engineering 19 (2002) 221-226. [17] N. M. Ghasem, S A Sata, M A Hussain, Temperature control of a bench scale batch polymerization reactor for polystyrene production, Chemical Engineering Technology 30 (2007) 1193-1202. [18] M. Norgaad, N. Poulsen, L. Hansen L,Neural Networks for Modeling and Control of Dynamic Systems, Springer-Verlag, London, 2000. [19] S. Haykin, Neural network - a comprehensive foundation, Prentice Hall Inc, New Jersey, 1999. [20] G Chen, T J McAvoy, M J Pivoso, A multivariable statistical controller for online quality improvement, Journal of Process Control 8 (1998) 139-149.

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[21] H. V. H. Ayala, L S Coelho, Cascaded evolutionary algorithm for non-linear system identification based on correlation functions and radial basis functions neural networks, Mechanical System and Signal Processing (2016) 378-393. [22] I M. Mujtaba, N. Aziz, M A Hussian, Neural network based modeling and control in batch reactor, Chemical Engineering Research and Design 84 (2006) 635-644. [23] Ng C W, M A Hussain,Hybrid neural network prior knolwledge model in temperature control of a semi batch polymerization process, Chemical Engineering and Processing 43 (2004) 559-570. [24] P Kittisupakorn, P Thitiyasook, M A Hussain, W Daosud, Neural network based model predictive for a steel pickling process, Journal of Process Control 19 (2009) 579-590.

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List of figures

Fig. 1. Flow chart for the refinery process Fig. 2. Debutanizer column configuration Fig 3. Bottom composition of n-butane simulation versus online Fig. 4. Changes in top and bottom temperature with manipulated variable Fig 5 Control loop of neural network based Direct Inverse Model Control (DIC) strategy Fig 6 Control loop of neural network based Internal Model Control (IMC) strategy Fig 7 Forward and inverse model to control temperature Fig.8 Partition of data sets for manipulated variable Fig 9 Actual and simulated n-butane bottom composition validation for NARX and ELMAN network Fig 10 Set point changes for top temperature Fig 11 Set point changes for bottom temperature Fig 12 Manipulated variable top temperature Fig 13 Manipulated variable bottom temperature Fig 14 Control of top temperature with disturbances in feed temperature Fig 15 Control of bottom temperature with disturbances in feed temperature Fig 16 Manipulated variable top temperature disturbances Fig 17 Manipulated variable bottom temperature disturbances Fig 18 Neural network estimator for the top composition with set point changes Fig 19 Neural network estimator for the bottom composition with set point changes Fig 20 Neural network estimate for top composition with disturbances Fig 21 Neural network estimate for bottom composition with disturbances

24

Fig. 1. Flow chart for the refinery process

P res s ure 1

T emp 1

D ebutanizer to other column

E 3

F low 3 L evel 2

C ondens er

F low 2

F eed flow

L P G to s torage R eflux flow

P ump T emp 3

D ebut feed

D ebutanizer column C V feed flow

Control loop involving neural network based control strategies

L evel 1

T emp 6 T emp 5 F low 1 E 2 L ight Naphtha to s torage E 1 T emp 2 T emp 4

Fig. 2. Debutanizer column configuration

25

Bottom composition n-butane

Composition (mole fraction)

0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0

2000

4000

6000

8000

10000

12000

Time (min)

simulation

online

Fig. 3 Bottom composition of n-butane-simulation versus online

26

22.5

61

22

60

21.5

59

21

58

20.5

57

20

56

19.5 19 1

51

101

151

201

251

Temperature (0C)

Refluxflow flowrate Reflux rate 3 (m /hr) (m3/hr)

Step test Tem p 1

55 301

Time (min) Reflux.flow rate

Temp 1

Step test Tem p 2

Reboiler flowrate (m3/hr)

144

144

142

143

140

142

138 136

141

134

140

Temperature (0C)

146

145

132 1

51

101 151 201 251 301 351 401 451 501 Time (min)

Reboiler.Flow

Temp 2

Fig. 4. Changes in top and bottom temperature with manipulated variable

27

Z-1

mv2(k)

Neural network Inverse model

Z-1

Tset_top

T_top(k+1)

Plant mv3(k)

Tset_bot

T_bot(k+1)

Z-1 Z-1

C_top(k+1) Z-1

Z-1

Z-1

Z-1

Composition estimator

Neural network estimator

C_bot(k+1)

Fig 5 Control loop of neural network based Direct Inverse Model Control (DIC) strategy

Z-1

Tset_top Tset_bot

+

Neural network Inverse model

Z-1

T_top(k+1)

mv2(k)

Plant T_bot(k+1)

mv3(k)

-1

Z

Z-1 Z-1

Z-1

Z-1

Z-1

Z-1

+

Z-1

Z-1

-

Neural network Forward model

Neural network estimator

T_nn(k)

C_top(k+1) C_bot(k+1)

Fig 6 Control loop of neural network based Internal Model Control (IMC) strategy

28

mv1 1 (k) mv1 1 (k-1)

mv 1 (k) mv 1 (k- 1)

mv 2 (k) mv2 2 (k-1)

mv 2 (k-1) mv 3 (k-1) Ttop(k+1)

Neural network Forward model

f (k) f (k-1) T top(k) T top(k-1) T bot(k) T bot(k-1)

T

f (k) f (k-1) T set top(k+1)

bot(k+1)

T

Neural network Inverse model

mv2(k)

mv3(k)

top(k)

T

top(k-1) T set bot(k+1) T bot(k) T bot(k-1)

Fig 7 Forward and inverse models to control temperature

Manipulated variable reboiler and reflux 22.5

145 144.5

Training

MV (m3 /hr)

144

Validation Testing

143.5

22 21.5

143 21

142.5 142

MV (m3 /hr)

mv3 (k) mv 3 (k-1)

20.5

141.5 141

20 0

50

100

150

200

250

300

T ime (min) Reboiler

Reflux

Fig.8 Partition of data sets for manipulated variable

29

Bottom composition (mole fraction):Validation

Actual and simulated plot compostion n-butane: Validation 0.075 0.07 0.065 0.06 0.055

Actual

0.05

NARX

0.045

ELMAN

0.04 0.035 0.03 0.025 0

10

20

30

40

50

Time (min)

Fig 9 Actual and simulated n-butane bottom composition validation for NARX and ELMAN network

Top tem perature

100 90

Temperature (0C)

80 70 60 50 40 30 20 10 0 0

50

100

150

200

250

300

Time (min)

pid

imc

dic

Fig 10 Set point changes for top temperature

30

Bottom tem perature 200 180

140 120 100 80 60 40 20 0 0

50

100

150

200

250

300

Time (min)

pid

imc

dic

Fig 11 Set point changes for bottom temperature

Manipulated variable top temperature 23

40 35

22.5 22

25

21.5

20 15

21

MV (m3/hr)

30 MV (m3/hr)

Temperature (0C)

160

10 20.5

5

20 0

50

100

150

200

250

300

0 350

Time (min) reflux imc

reflux pid

Fig 12 Manipulated variable top temperature

31

Manipulated variable bottom temperature 144

60

143.5

50 40

142.5 142

30

141.5

MV (m3/hr)

MV (m3/hr)

143

20

141 10

140.5 140 0

50

100

150

200

250

0 350

300

Time (min)

reboiler imc

reboiler pid

Fig 13 Manipulated variable bottom temperature

Top temperature disturbances 60 59 58

56 55 54 53 52 51 50 0

50

100

150

200

250

300

350

Time (min)

pid

imc

dic

Top tem perature disturbances

59 58.5 58 Temperature (0C)

Temperature (0C)

57

57.5 57 56.5 56 55.5 55 54.5 54 135

145

155

165

175

185

195

205

215

Time (min)

imc

dic

Fig 14 Control of top temperature with disturbances in feed temperature

32

Bottom temperature disturbances 150

Temperature (0C)

145 140 135 130 125 120 0

50

100

150

200

250

300

350

Time (min)

pid

imc

dic

Fig 15 Control of bottom temperature with disturbances in feed tempearture

Manipulated variable top tem perature disturbances

23

70 60

22.5

50 40 21.5 30

MV (m3/hr)

MV (m3/hr)

22

21 20 20.5

10

20 0

50

100

150

200

250

300

0 350

Time (min) reflux imc

reflux pid

Fig 16 Manipulated variable top temperature disturbances

33

Manipulated variable bottom temperature disturbances 300

144 143.5

250 200

142.5

150

142 141.5

MV (m3/hr)

MV (m3/hr)

143

100

141 50

140.5 140 0

50

100

150

200

250

300

0 350

Time (min)

reboiler imc

reboiler pid

Fig 17 Manipulated variable bottom temperature disturbances

Top composition 0.2

Composition (mole fraction)

0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 15 0

65 50

115 100

165 150

215 200

265 250

315 300

Time(min) (min) Time pid

imc

dic

Fig 18 Neural network estimator for the top composition with set point changes

34

Bottom composition

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 10 0

60 50

110 100

160 150

210 200

260 250

310 300

Time Time (min) (min) pid

imc

dic

Fig 19 Neural network estimator for the bottom composition with set point changes

Top com position disturbances

0.14

0.138

Composition (mole fraction)

Composition (mole fraction)

0.08

0.136

0.134

0.132

0.13 0

50

100

150

200

250

300

350

Time (min) pid

imc

dic

Fig 20 Neural network estimate for top composition with disturbances

35

Bottom com position disturbances

Composition (mole fraction)

0.055 0.054 0.053 0.052 0.051 0.05 0.049 0

50

100

150

200

250

300

350

Tme (min)

pid

imc

dic

Fig 21 Neural network estimate for bottom composition with disturbances

36

List of tables Table 1 : Column specification Table 2 : Tag name description of the column Table 3 : Neural network architecture for n-butane composition prediction Table 4 : Neural network architecture for temperature prediction Table 5 : PID tuning Table 6 Controller performance during set point changes Table 7 Controller performance during disturbance changes

37

Table 1 : Column specification Number of tray of the column

35

Feed tray - stage number

23

Type of tray used

Valve

Column diameter

1.3 m

Column height

23.95 m

Condenser type

Partial

Feed mass flowrate

44106 kghr-1

Feed temperature

113 0C

Feed pressure

823.8 kPa

Overhead vapor mass flowrate

11286 kghr-1

Overhead liquid mass flowrate

5040 kghr-1

Condenser pressure

823.8 kPa

Reboiler pressure

853.2 kPa

Table 2 : Tag name description of the column Tag Temp 1 Temp 2 Temp 3 Temp 4 Temp 5 Temp 6 Level 1 Level 2 Flow 1 Flow 2 Flow 3 Pressure 1

Description Debutanizer top temperature Debutanizer bottom temperature Debutanizer receiver bottom temperature Light Naphtha temperature after condenser E 1 Reboiler outlet temperature to column

Units o C o C

Debutanizer feed temperature Debutanizer level Debutanizer condenser level Light Naphtha flow to storage LPG flow to storage Reflux flow rate Debutanizer receiver overhead pressure

o

o

C

o

C

o

C

C % % m3/hr m3/hr m3/hr kPa

38

Table 3 Neural network architecture for n-butane composition prediction Parameters Network Training function

Description NARX series parallel network (newnarxsp) Levenberg Marquardt

Performance function

MSE

Epochs

1000

Goal

1e-6

Number of layers

2

Layer 1: Number of Neuron

10

Transfer function Layer 2: Number of Neuron

PURELIN 2

Transfer function

PURELIN

Table 4 Neural network architecture for temperature prediction Parameters Network Training function

Description NARX series parallel network (newnarxsp) Levenberg Marquardt

Performance function

MSE

Epochs

1000

Goal

1e-6

Number of layers

2

Layer 1: Number of Neuron

12

Transfer function Layer 2: Number of Neuron

PURELIN 2

Transfer function

PURELIN

39

Table 5 PID tuning Parameter Top temperature Bottom temperature Top composition Bottom composition

Kc 0.71 1.76 13.73 8.74

Ti 1.41 3.25 3.26 3.26

Td 20 15 10 5

Table 6 Controller performance during set point changes

IAE top IAE bottom

ISE top ISE bottom

ITAE top ITAE bottom

IMC eq 830.76 3809

IMC eq 2.10E+04 1.21E+05

IMC eq 4.25E+04 1.92E+05

DIC eq 912.78 4289

DIC eq 2.23E+04 2.67E+05

DIC eq 4.48E+04 2.16E+05

PID 1219.70 4666

PID 2.69E+04 3.06E+05

PID 1.44E+05 4.45E+05

Table 7 Controller performance during disturbance changes

IAE top IAE bottom

ISE top ISE bottom

ITAE top ITAE bottom

IMC eq 817.21 2811.80

IMC eq 6.02E+03 1.14E+05

IMC eq 7.78E+04 1.28E+05

DIC eq 836.95 2876.00

DIC eq 6.63E+03 1.23E+05

DIC eq 7.90E+04 1.30E+05

PID 1736.30 7891.20

PID 3.37E+04 1.75E+06

PID 1.78E+05 4.64E+05

40

éT1 ù é6.12 0.31 7.47 6.48 - 0.05 6.43 5.53 - 0.45 7.46 5.75 5.81 0.18 ù é7.24 ù y=ê ú=ê úp + ê ú êëT 2 úû ë14.64 - 0.38 15.36 14.48 - 0.32 15.28 16.12 0.72 15.68 16.06 15.61 0.79û ë15.94û

1 f1 = If the f is given by the logsig transfer function, 1 - exp(n) , the equation can be simplified in the form;

1

éT1 ù é0.68 - 1.14 - 1.01- 0.48 - 1.30 - 1.03 0.02 - 0.65 - 0.86 1.29 0.57 - 0.04ù é1.02ù y=ê ú=ê ú úp + ê êëT 2 úû ë0.56 - 0.59 0.87 0.74 0.11 0.29 1.47 0.34 0.35 - 0.17 0.57 - 0.04 ë1.34û û

2 f2= If the f is given by the logsig transfer function, 1 - exp(n) , the equation can be simplified in the form;

1

2 1 where f is the activation function in the output layer and f is the activation function in the hidden layer

ö æ y = f 2 ç LW 2,1 f 1æç IW 1,1 p + b1 ö÷ + b 2 ÷ è ø ø è

The general equation for the output from the neural network can be given as (for a 2 layer network)

Appendix 1

(A2)

(A1)

41

Prof Mohamed Azlan Hussain joined the Department of Chemical Engineering, University of Malaya in 1987 as a lecturer and obtained his Ph.D in Chemical Engineering from Imperial College, London in 1996. He is a member of the American Institute of Chemical Engineers and British Institute of Chemical Engineers. At present he is holding the post of Professor in the department of chemical Engineering. His main research interests are in modelling, process controls, nonlinear control systems analysis and applications of artificial intelligence techniques in engineering systems. He has published more than 250 papers in book chapters, journals and conferences within these areas at present. He has also publish and edited a book on “Application of Neural Networks and other learning Technologies in Process Engineering” published by Imperial College Press in 2001.

Nasser Mohamed Ramli is a PhD student in the Chemical Engineering Department, Faculty of Engineering, University of Malaya. He obtained his bachelor’s degree in chemical engineering from Loughborough University, United Kingdom and his master’s degree from University of Queensland, Australia. His area of research is in artificial intelligence, process modeling and control.

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Badrul Mohamed Jan, SPE is a researcher and academic lecturer attached to the Department of Chemical Engineering, University of Malaya, Malaysia. He holds a BS, MS and PhD degrees in petroleum engineering from New Mexico Institute of Mining and Technology. Jan’s research areas and interest include the development of super lightweight completion fluid for underbalance perforation, ultra low interfacial tension microemulsion for enhanced oil recovery, and conversion of palm oil mill effluent into super clean fuel for diesel replacement. He has worked closely with industry in oil and gas project such as 3M Asia Pacific and BCI Chemical Corporation. He has also published numerous technical conference and journal papers. Jan is the deputy director of University Malaya Center of Innovation & Commercialization. His responsibilities include providing an environment at the University of Malaya conducive to researchers bringing their research outputs to a commercialization-ready level.

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