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INFERENTIAL ESTIMATION AND CONTROL OF CHEMICAL PROCESSES

USING PARTIAL LEAST SQUARES BASED MODEL

LIM WAN PIANG

A thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Engineering (Chemical)

Faculty of Chemical and Natural Resources Engineering

Universiti Teknologi Malaysia

JUNE 2005

iii

To my beloved MOTHER and FATHER

iv

ACKNOWLEDGEMENT

First of all, I would like to express my sincere appreciation to my research

project supervisor, Professor Dr. Arshad Ahmad for his invaluable guidance, advice,

support as well as encouragement throughout this research.

I am also indebted to the Ministry of Science, Technology and Environment,

Malaysia for funding my research through National Science Foundation scholarship.

My heartiest appreciations are also for my fellow friends who have directly

and indirectly contribute to the success of this project.

v

ABSTRACT

The use of inferentia l estimation model as a strategy to overcome the lack of efficient on- line measurement for product qualities is proposed. This strategy makes use of easy to measure secondary variables, such as temperature and pressure to infer the value of non-measurable primary variables such as chemical composition. As a case study, a fatty acid fractionation column from a local company was considered. The plant that was simulated using HYSYSTM simulator provided all the required process data throughout the study. To provide the necessary process insights, analyses of dynamic behaviour were carried out. Appropriate secondary measurements with significant relationships with the product composition were then identified for the construction of the inferential estimator within MATLAB environment. A number of models were considered but nested neural network partial least squares (NNPLS) model was found most proficient. The model was tested on-line and reasonable performances were obtained. Further refinements were proposed to improve the accuracy and robustness of the estimator. In particular, the issue of data scaling was elaborately addressed. Following the success implementation of the estimator, inferential control of the product quality was examined. In both regulatory and servo controls, better performances were obtained compared to the indirect strategy of controlling product composition using selected tray temperature. This was further improved by employing cascade control. The results obtained throughout this work have illustrated the potential of inferential control strategy and the capability of the hybrid neural network-PLS model as the process estimator. This should therefore serve as an alternative solution to the lack of measurement in chemical process industry. The model developed from the simulation stage is specified to a particular case and it should be verified against the actual process before practical implementation.

vi

ABSTRAK

Penggunaan model anggaran taabir sebagai satu strategi untuk menyelesaikan masalah pengukuran kualiti produk secara dalam talian yang berkesan telah dikemukakan. Strategi ini menggunakan pembolehubah sekunder yang mudah diukur, seperti suhu dan tekanan untuk meramal nilai pembolehubah utama yang tidak dapat diukur seperti komposisi produk. Sebagai kajian kes, sebuah turus pemecahan asid lelemak dari industri tempatan telah digunakan. Loji yang telah diselaku dengan menggunakan perisian HYSYSTM digunakan untuk membekal semua data proses yang diperlukan dalam kajian ini. Untuk memahami proses tersebut dengan lebih mendalam, analisis sambutan dinamik telah dilaksanakan. Pembolehubah sekunder yang berhubung rapat dengan komposisi produk telah dikenalpasti bagi tujuan pembangunan model anggaran taabir yang dilakukan dengan perisian MATLAB. Penggunaan beberapa model telah dinilai tetapi model rangkaian saraf kuasa dua terkecil separa bergelung didapati paling berkesan. Model tersebut diuji secara dalam talian dan prestasi yang munasabah telah diperolehi. Beberapa pembaikkan telah dikemukakan untuk meningkatkan kejituan dan ketangkasan model anggaran. Secara khusus, isu penskalaan data telah dikaji dengan mendalam. Ekoran dari kejayaan perlaksanan model anggaran itu, kawalan taabir kandungan produk telah diuji. Dalam kedua-dua masalah gangguan dan servo, prestasi yang lebih memuaskan telah dicapai berbanding dengan strategi kawalan kandungan produk secara tidak langsung yang menggunakan suhu dulang. Prestasi tersebut seterusnya dipertingkatkan dengan menggunakan kawalan lata. Keputusan yang diperolehi dalam penyelidikan ini telah menunjukkan potensi strategi kawalan taabir dan keupayaan model hibrid rangkaian saraf kuasa dua terkecil separa sebagai penganggar proses. Kaedah ini seharusnya mampu menjadi salah satu daripada penyelesaian kepada kekurangan alat pengukuran dalam industri proses kimia. Model yang dibina daripada tahap perselakuan adalah terhad kepada kes yang tertentu dan ia harus dinilai dengan process sebenar sebelum diamalkan secara praktikal.

vii

TABLE OF CONTENTS

CHAPTER TITLE

PAGE

THESIS STATUS CERTIFICATION FORM SUPERVISORS CERTIFICATION

TITLE PAGE

DECLARATION

DEDICATION

ACKNOWLEDGEMENT

ABSTRACT

ABSTRAK

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

LIST OF APPENDICES

ii

iii

iv

v

vi

vii

xi

xiii

xvii

xxi

1 INTRODUCTION

1.1 Motivation of Study

1.2 Problem Statement

1.3 Objective and Scope of Work

1.4 Contribution of the Work

1.5 Organisation of the Thesis

1

1

2

3

3

4

viii

2 THEORETICAL FOUNDATION AND

LITERATURE REVIEW

2.1 Inferential Estimation and Control

2.1.1 Inferential Control in Process Industry

2.1.2 Techniques of Process Estimation

2.2 Partial Least Squares Regression (PLS)

2.2.1 Structure of PLS Model

2.2.2 Training Algorithm of PLS Model

2.2.3 Validation of PLS Model

2.2.4 Process Estimation using PLS Model

2.2.5 Extension of PLS to Dynamic

and Non-linear Model

2.3 Quadratic PLS

2.3.1 Error-Based Weight Updating

Procedure

2.4 Neural Network PLS

2.4.1 Structure of NNPLS

2.4.2 Improvement of NNPLS

2.5 Artificial Neural Networks (ANN)

2.5.1 Architecture of Feedforward Network

2.5.2 Network Training and Validation

2.6 Nested PLS

2.7 Concluding Remarks

5

5

6

9

10

11

13

15

17

18

19

21

23

23

24

25

26

27

28

34

3 PROCESS DESCRIPTION AND DYNAMIC

ANALYSIS

3.1 Process Description

3.1.1 Column Control Scheme

3.2 Process Simulation

3.2.1 Specification of Light-Cut Column

3.3 Analysis of Dynamic Response

3.3.1 Effect of Changes in Reflux Flow

35

35

37

38

40

41

42

ix

3.3.2 Effect of Changes in Pump-Around

Flow

3.3.3 Effect of Changes in Feed

Temperature

3.3.4 Effect of Changes in Feed Flow

3.3.5 Effect of Changes in Feed

Composition

3.4 Selection of Input Variables

3.4.1 Selection of Stage Temperatures

3.5 Data Generation

43

43

47

47

50

51

53

4 ESTIMATION OF PRODUCT COMPOSITION

4.1 Introduction

4.2 Development of PLS Model

4.2.1 Off- line Estimation Using PLS Model

4.3 Formulation of Non-linear Inferential Model

4.3.1 Results of Off- line Estimation

4.4 Formulation of Nested PLS Model

4.4.1 Results and Discussion

4.5 Formulation of Neural Network Model

4.5.1 Comparison of PLS and Neural

Network Model

4.6 On-line Estimation

4.6.1 On-line Scaling Using Defined Values

4.6.2 Effect of Past Measurements

4.6.3 Modified On-line Rescaling Method

4.7 Effect of Measurement Noise

4.8 Smoothing Filter

4.8.1 Performance of Filter

4.9 Concluding Remarks

55

55

56

59

62

63

65

66

69

70

73

74

76

78

83

85

87

92

x

5 INFERENTIAL CONTROL OF PRODUCT

COMPOSITION

5.1 Introduction

5.2 Ideal Composition Control

5.2.1 Controller Tuning

5.2.2 Results and Discussion

5.3 Indirect Composition Control Using Stage

Temperature

5.3.1 Disadvantages of Indirect Strategy

5.4 Inferential Control

5.4.1 Implementation of Inferential Control

5.4.2 Results and Discussion

5.5 Improvement of Inferential Control

5.6 Concluding Remarks

93

93

94

95

96

98

100

102

102

104

108

113

6 CONCLUSION AND RECOMMENDATIONS

6.1 Summary

6.2 Conclusion

6.3 Recommendations for Future Work

114

114

116

117

REFERENCES

APPENDICES A-B

119

123-150

xi

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 2.2 3.1 3.2 3.3 3.4

3.5 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10

Summary of the steps in non-linear quadratic PLS Summary of the steps in nested PLS Controlled and manipulated variables of the control loops Equipment data of light-cut column Process stream data of light-cut column Output variables of light-cut column Steady state gain and settling time of 12CDx to input variables Training and validation results of PLS model Characteristic of data set for process estimation Training and validation results of QPLS and NNPLS model Off- line estimation results using non- linear PLS Training and validation results of nested PLS model Off- line estimation using nested PLS model Training and validation results of feed forward network Comparison of off- line estimation results using PLS, NNPLS, nested NNPLS and neural network models Characteristic of Data A5 and Data A6 On-line estimation using past measurement

22 32 38 40 41 42

51 58 60 64 64 66 67 69 71 75 78

xii

4.11 5.1 5.2 5.3

Comparison of prediction results using on- line estimator with and without smoothing filter Parameters of composition controller Parameters of temperature controller at stage 7 Results of regulatory and servo control using various control strategies

88 98 100 112

xiii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 2.2 2.3 2.4 2.5 2.6 2.7 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

General scheme of inferential control system Inferential control of compositions of the distillation column Schematic of the PLS model A schematic illustration of NNPLS model Basic structure of artificial neural networks A typical feed forward network with one hidden layer Illustration of the nested non- linear PLS structure Schematic diagram of light-cut column in a fatty acid fractionation plant Control scheme of light-cut column The main flowsheet of the light-cut column in HYSYS environment The internal view of the light-cut column in HYSYS environment Dynamic response of changes in reflux valve opening Dynamic response of changes in pump-around valve opening Dynamic response of changes in feed temperature Dynamic response of changes in feed flow rate Dynamic response of changes in C-12 feed composition

6 7 11 24 26 27 29 36 37 39 39 44 45 46 48 49

xiv

3.10 3.11 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 5.1

Gain matrix plot of stage temperatures Response of output data (C12 fatty acids in mole fraction) Algorithm of developing PLS-based model MSE of training and validation data using PLS model Training and validation results using PLS model Off- line estimation results using PLS-based model Off- line estimation results using non- linear nested PLS model (neural network) Training and validation results of feed forward network Off- line estimation results using feed forward network On-line implementation of process estimation using DDE driver On-line estimation using nested NNPLS model Prediction error of on- line estimation using past measurement Scatter plot of actual and predicted outputs On-line estimation using modified rescaling method On-line estimation of excited data Effect of measurement noise to on- line estimation Filtering predicted output using bias MSE of prediction using bias values at different past time MSE of prediction using various tuning values Performance of filter in on-line estimation for Data A1 to A6 Performance of filter in on-line estimation for Data B1 to B4 Ideal composition control of light-cut column

52 54 56 57 59 61 68 70 72 73 75 77 79 81 83 84 85 86 87 89 91 94

xv

5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11

5.12 5.13 5.14

5.15 5.16 B1 B2 B3

Close- loop response of C12 purity with different tuning parameters Performance of ideal composition control scheme with a step increase (solid line) and decrease (dotted line) of disturbances Performance of ideal composition control in set point tracking Indirect composition control scheme Close- loop response of overhead composition respect to the changes in the set point of temperature controller Performance of indirect temperature control scheme with a step change in the feed flow rate Inferential control of light-cut column Communication between HYSYS and MATLAB using DDE interface Response of product composition to unit step change in feed flow rate Close- loop response of 12CDx with respect to the fluctuation in feed composition using inferential control Close loop response of 12CDx with respect to the fluctuation in feed flow rate using inferential control Performance of inferential control in set point tracking Inferential cascade control scheme Close loop response of 12CDx with respect to feed disturbances using inferential cascade control Performance of inferential cascade control in set point tracking Off- line estimation results us ing quadratic PLS model Off- line estimation results using neural network PLS model Off- line estimation results using linear nested PLS model

95 97 98 99 100 101 103 104 105

106

107 108 109

111 112 144 145 146

xvi

B4 B5 B6

Off- line estimation results using non- linear nested PLS model (quadratic) On-line estimation results using non- linear nested PLS model (neural network) On-line estimation using past measurement values at 15 minutes

147 148 149

xvii

LIST OF SYMBOLS

SYMBOLS

a - Last dimension in PLS

b - Regression coefficient in PLS

b0 - Bias weight of neuron model

akb - Regression coefficient in inner PLS

ci - Coefficients of polynomial function.

d - Weight vector in QPLS

e - Matrix of mismatch between the u and u

E - Residue matrix of X blocks in PLS

F - Residue matrix of Y blocks in PLS

f - Residual matrix of inner PLS

gak - Loading scores of e-block in inner PLS

hak - Loading scores of Z-block in inner PLS

k - Last dimension in the inner PLS

Kc - Controller gain

Kp - Steady state gain

N - Non-linear function in NNPLS

p - Input loading factors matrix in PLS

q - Output loading factors matrix in PLS

rak - Latent scores of e-block in inner PLS

s - Column matrix in QPLS

sak - Latent scores of Z-block in inner PLS

xs - Standard deviation

t - Input latent scores matrix in PLS

xviii

ts - Settling time

u - Output latent scores matrix in PLS

u - Predicted output latent scores matrix in PLS

v - Column vector in QPLS

vak - Weight in the inner PLS

w - Input weights matrix in PLS

wi - Neuron weight

X - Independent variables matrix in PLS

x - Input variables

x - Average value

xi - Neuron input

xms - Mean-scaled data

12CDx - Composition of C12 fatty acid in the distillate product

Y - Dependent variables matrix in PLS

y - Neuron output

cty - Filtered output

ty - Predicted value at current time

ct f

y - Previous corrected predicted value at time tf

Z - Weight matrix in QPLS

GREEK SYMBOLS

- Prediction coefficient in PLS

- Residual matrix of inner relation in quadratic PLS

- Weight of neural network model

- Bias of neural network model

? w - Increment weight in QPLS

s - Activation function in neural network

tD - Derivative time constant

t I - Integral time constant

xix

ABBREVIATIONS

ANN - Artificial neural networks

ARMA - Autoregressive moving average

CC - Composition controller

CSTR - Continuous stir tank reactor

DDE - Dynamic data exchange

DNNPLS - Dynamic neural network partial least squares

EBWU - Error-based weight updating procedure

EKF - Extended Kalman filter

EOS - Equation of state

EPV - Explained prediction variance

FC - Flow controller

FFN - Feed forward networks

FPM - First principle method

LC - Level controller

LCC - Light-cut column

LM - Levenberg-Marquardt method

MIMO - Multiple input multiple output

MISO - Multiple input single output

MLR - Multiple linear regressions

MSE - Mean squared error of prediction

NIPALS - Non-linear iterative partial least squares

NNPLS - Neural network partial least squares

PCA - Principal component analysis

PCR - Principal component regression

PIC - Pressure indicator

PI - Proportional-Integral

PID - Proportional-Integral-Derivative

PLS - Partial least squares regression

QPLS - Quadratic partial least squares

RBFPLS - Radial basis function partial least squares

SISO - Single input single output

SSE - Sum Squared Error

xx

TC - Temperature controller

UNIQUAC - Universal Quasi Chemical

xxi

LIST OF APPENDICES

APPENDIX TITLE PAGE

A1 A2 A3 A4 A5 A6 B

Cross-validation code of inferential estimator (off- line estimation) MATLAB Code of Feed Forward Network Off- line Estimation Code of Feed Forward Network On-line estimation code using defined value The Matlab code of on- line estimation (final model) The Matlab code of inferential model during inferential control Graphical results of estimation

124 127 132 135 137 140 143

CHAPTER 1

INTRODUCTION

1.1 Motivation of Study

Stringent product specifications, stiff competition among manufacturers and

increasingly strict regulation from local authority in the face of full capacity

operation with zero accidents and emissions have forced many existing plants to

revamp their existing control system. More advanced control schemes have been

introduced, and although small in numbers, real-time optimisations have also been

implemented.

Despite these successful implementations, many issues remained as

hindrances to efficient process control. For example, the success in the

implementation of any optimisation scheme requires adequate performance of all

control loops. This is however, sometimes hampered by two issues. The first is

related to inadequacy of conventional controllers used since chemical process

dynamics are typically non-linear whilst the controllers are based on linear theory.

The second issue is associated with process measurements, the accuracy of which is

a prerequisite to successful process control.

Since measurement devices are one of the main factors in achieving effective

process control, selection of appropriate sensors and their location should be properly

considered. However, not all variables in a process plant are readily to be measured

on- line. Product quality variables such as chemical composition and molecular

2

weight distribution of polymer are rarely available on-line, and are usually obtained

by laboratory sample analyses. This is usually performed at long intervals and is

therefore not practical to be used for process control.

Over the years, various on- line measurement devices have been developed.

However, many of these on- line devices are still suffering from problems due to the

availability, reliability, complexity and large delays. For example, on- line gas

chromatograph is a common instrumentation for the on- line measurements of

product compositions. However, in many applications this measurement device is

not reliable enough to be used for on-line control due to low sampling rate and

sometimes inconsistency of results. High operating and maintenance costs add to the

disadvantages of such implementations. For some quality variables, existing

analytical tools used are simply unavailable for on-line applications. Hence, the

development of inferential estimation and control has been advocated as one of the

alternative solution to deal with measurement difficulties.

1.2 Problem Statement

A fatty acids fractionation column from a local industry is faced with the

product compositions control problems. Currently, indirect control of product

compositions is achieved by controlling temperature at selected location in the

column. At times, this control scheme cannot cope with disturbances and process

uncertainties in the plant. This scenario has created some difficulties in the

composition control and occasionally, off-specification products have been produced.

This work is proposed to untangle some of these difficulties. An inferential

model, which is built based on partial least squares (PLS) regression is employed for

estimating the product composition in the light-cut column to facilitate process

control.

3

1.3 Objective and Scope of Work

The aim of this work is to develop an inferential model using PLS modelling

approach and to investigate its application in composition control. The scopes of the

study are as follows.

i. Dynamic simulation and analysis of a fatty acid fractionation column

using HYSYS process simulator.

ii. Development of a base-case inferential model using PLS modelling

approach in MATLAB environment.

iii. Improving the inferential model using a modified PLS model, namely

nested PLS model.

iv. Development of inferential control strategy to regulate the product

composition using the established estimation model by linking both

software packages using DDE interface.

1.4 Contribution of the Work

Successful development of the inferential estimator using PLS modelling

approach is the main contribution of this work. Dealing with the issue of on- line

implementation of the inferential model, on- line post-processing or rescaling of the

predicted values was solved using polynomial regression method. After several

refinements, the inferential estimator was therefore able to produce predictions with

reasonable accuracy under various operating conditions. The work has also

demonstrated the use of neural networks in a hybrid PLS modelling structure as a

means of extending the PLS model capability to nonlinear process estimation.

Another contribution of this work is on- line monitoring and controlling of the

product composition of a fatty acid fractionation in the simulation platform using the

inferential model. Two inferential configurations were investigated in this work and

the inferential cascade control showed better performance in both regulator and servo

control.

4

1.5 Organisation of the Thesis

The thesis is organised as follows. Chapter 2 includes literature review and

some theoretical background about inferential estimation and control. Previous

development and application of PLS-based models are reviewed. The theory and

implementation requirements for the proposed method are also discussed. Chapter 3

commences with the description of the selected case study. This is followed by

relevant analysis for inferential model development. Chapter 4 then elaborates the

development of process estimation model and some proposed improvements to the

model. Chapter 5 demonstrates the application of inferential model in process

control. The thesis is then concluded with the overall findings and some

recommendations for future work.

119

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INFERENTIAL ESTIMATION AND CONTROL OF CHEMICAL PROCESSES USING PARTIAL LEAST SQUARES BASED MODEL LIM WAN PIANG A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Engineering (Chemical) Faculty of Chemical and Natural Resources Engineering Universiti Teknologi Malaysia JUNE 2005
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