Study of control actions reveals disturbance patterns for cross directional control of basis weight

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Study of control actions reveals disturbance patterns for cross directional

control of basis weight

Examensarbete utfört i Reglerteknik vid Linköpings tekniska högskola

av Patrik Broman LiTH-ISY-EX-3485-2004

Supervisor: Mats Hiertner, Stora Enso Research Daniel Axehill, LiTH

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Avdelning, Institution Division, Department

Institutionen för systemteknik

581 83 LINKÖPING

Datum Date 2003-03-05 Språk

Language Rapporttyp Report category ISBN Svenska/Swedish

X Engelska/English

Licentiatavhandling

X Examensarbete ISRN LITH-ISY-EX-3485-2004 C-uppsats D-uppsats Serietitel och serienummer _{Title of series, numbering} ISSN

Övrig rapport

____

URL för elektronisk version

http://www.ep.liu.se/exjobb/isy/2004/3485/ Titel

Title Studier av styrutslag avslöjar störningsmönster hos tvärsprofilstyrningen av ytvikt Study of control actions reveals disturbance patterns for cross directional control of basis weight

Författare

Author Patrik Broman

Sammanfattning Abstract

The purpose of this thesis was to examine the demand for cross directional control of basis weight on a board machine. To analyse the demand, changes made by the control system are studied. The significant changes were expected to be present when a major event occurred on the machine. The events classified as major were changes in basis weight, of grade or of coating blade. Break of board and stoppage of the machine were also included. These events can be seen as large disturbances to the machine. In order to identify the disturbances a methodology had to be developed. The methodology developed is to analyse the output from a model with the actuators of the control system as input and measurement of basis weight as output. The analysis of this output was done using the multivariate method of principal component analysis. The data

analysed in this thesis was collected on-line from a board machine operating within the Stora Enso group. Over a period of 3 months, a total of 47 sets of data were collected, each set representing 12-14 hours. The data analysis shows that the variations in the control system are greater than the variation in the measured basis weight. This is a strong indication that the control system is needed and in order to find disturbances in the cross directional profile it is not enough only to analyse the final product, the control signals also have to be analysed. The large disturbances do not

necessarily emerge from the major events as assumed. Other causes might have larger impact to the process then first believed. One of the major obstacles in trying to explain the variations is that the basis weight is controlled by using the centre layer of the board but measured on the final product. This leads to the fact that the errors seen by the measuring system can result from anything on the machine and be compensated by basis weight in the centre layer of the board.

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Abstract

The purpose of this thesis was to examine the demand for cross directional control of basis weight on a board machine. To analyse the demand, changes made by the control system are studied. The significant changes were expected to be present when a major event occurred on the machine. The events classified as major were changes in basis weight, of grade or of coating blade. Break of board and stoppage of the machine were also included. These events can be seen as large disturbances to the machine.

In order to identify the disturbances a methodology had to be developed. The methodology developed is to analyse the output from a model with the actuators of the control system as input and measurement of basis weight as output. The analysis of this output was done using the multivariate method of principal component analysis.

The data analysed in this thesis was collected on-line from a board machine operating within the Stora Enso group. Over a period of 3 months, a total of 47 sets of data were collected, each set representing 12-14 hours.

The data analysis shows that the variations in the control system are greater than the variation in the measured basis weight. This is a strong indication that the control system is needed and in order to find disturbances in the cross directional profile it is not enough only to analyse the final product, the control signals also have to be analysed.

The large disturbances do not necessarily emerge from the major events as assumed. Other causes might have larger impact to the process then first believed.

One of the major obstacles in trying to explain the variations is that the basis weight is controlled by using the centre layer of the board but measured on the final product. This leads to the fact that the errors seen by the measuring system can result from anything on the machine and be compensated by basis weight in the centre layer of the board.

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Acknowledgements

First of all I would like to thank Stora Enso Research for offering me this project and Stora Enso Fors for the support to accomplish it.

There have been a number of people involved in making this thesis possible and first of all I would like to thank my supervisor Mats Hiertner and the department for process analysis and web handling in Falun for taking the time to answer all my “five seconds” questions. Timo Luukas, Karin Oldberg and the development department at Fors for granting me access to the machine and making the collection of data possible. Thanks also to the examiner Inger Klein and supervisor Daniel Axehill, Linköping University for valuable discussions.

I would also like to show my gratitude to all of the staff at Stora Enso Research in Falun for making me feel welcome during my time here.

Falun, February 2004

Patrik Broman

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Notation

Symbols

R Reals.

N M ×

R Real vector space with MxN dimensions. x Vector.

i

x Element i in vector x .

X Matrix.

ij

x Element i,j in matrix X .

[ ]

n

x Vector x in the discrete timen . p Actuator settings, used in Appendix. s Actuator response, used in Appendix. y Basis weight response, used in Appendix.

Operators and functions

× Multiplication. q Time discrete delay operator.

o The Frobenius norm.

{ }

o

E Expectation value.

T

A Transpose of A.

Abbreviations

BL Bottom Layer. The layer of stock lowest placed in the board. CD Cross Directional.

CL Centre Layer. The layer of stock placed in the middle of the board. MD Machine Directional.

MIMO Multiple-Input Multiple-Output.

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1 Introduction

Stora Enso is an integrated paper, packaging and forest products company producing publication and fine papers, packaging boards and wood products, areas in which the company is a global market leader. Stora Enso Research is the shared R&D-resource of Stora Enso. Stora Enso Research has four research centres situated in Falun, Imatra, Karlstad and Mönchengladbach. The organization of Stora Enso Research is product-based. It has three groups: fine paper, packaging board and publication paper. The groups represented at Research Centre Falun are fine paper and publication paper.

The Department of process analysis and web handling within the Publication paper group is located at Research Centre Falun. This department works with the improvement of runnability, product uniformity and production efficiency for winders, printing presses, and paper- and board machines.

In collaboration with Stora Enso Fors mill the department wishes to improve the product uniformity of coated board.

Fors mill located just outside Avesta is one of the top producers of high quality coated board. With its two board machines, Fors mill produces 350 000 tons of board a year. The board produced is spread all over the world and is used in high-demanding packaging applications such as those for cigarettes and special food.

1.1 Background

In order to get as good products as possible from a board machine you have to control the uniformity. Board produced in a board machine is usually wider than the customer wants, thus forcing the mills to cut the product. The changes occurring across the machine are therefore especially important to analyse as different locations must not possess different properties.

One of the many properties continuously measured is basis weight (weight per area). The basis weight is measured by a traversing scanner, crossing the machine in about 25 seconds. This traversing measurement must cross the machine several times in order to predict the true profile of basis weight across the machine. The machine investigated in this thesis is loacted in Fors mill and is about 5.8 metres wide and 75 metres long. To control the cross directional changes in basis weight there are 58 actuators equally spaced across the machine width. The spatial width of the response in basis weight from one actuator is larger than the spatial spacing between the actuators, meaning that a change in one actuator affects several actuators.

1.2 Purpose

This Master’s thesis has two main objectives.

The first purpose is to find out how big the demands for the cross directional control of basis weight are. To analyse the demand, changes made by the control system are to be studied. The significant changes made by the control system are suspected to occur when there is a major event happening on the machine, like a break of board or a change of grade. The major events can be described as disturbances to the control system.

The second objective is to try to identify the sources of the disturbances forcing the control system into making changes.

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Introduction

1.3 Restrictions

The above purpose of the thesis is restricted to identifying and analysing only the slow disturbances present on the machine.

1.4 Thesis

outline

An outline of this thesis is presented below by briefly describing the contents of its chapters and appendixes.

Chapter 2 ‘The making of board’, presentation of the material called board and a description of the different sections in a machine producing it.

Chapter 3 ‘Control of basis weight’, introduction to the term basis weight, how it is controlled across the machine and measured.

Chapter 4 ‘Method for describing control actions’, describes the method used to extract information from the control system.

Chapter 5 ‘Data analysis’, presents the analysis of the extracted information.

Chapter 6 ‘Special case analysis’, describes the search for explanations in two special cases.

Chapter 7 ‘Discussion and recommendations’, summarizes the results and discusses what can be done in the future.

Appendix A ‘Theory of principal component analysis’, the theoretical part of this thesis, explaining the principal component analysis.

Appendix B ‘Bump test analysis’, background to the translation model described in chapter 4.

Appendix C, ‘Tables’, data used for diagrams in the thesis.

Appendix D, ‘Figures’, extracted data from the interesting datasets presented in Chapter 5.

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The making of board

2 The making of board

This chapter will introduce the reader to the board product. When producing board, the mill tries to create a product that consists of several layer of different pulp. Fors mill produces board with up to seven layers of material; three layers of pulp and up to four layers of coating [1]. To get the best performance out of the produced board, the mill tries to work with a technique called I-beam.

When using the I-beam technique you need to place pulp that makes bulkier layers in the middle of the board and stronger in the outer layers. Used in this way, the technique produces a stiff board with low weight. As can be seen in Figure 2.1, the three layers of pulp are applied in the middle, with a couple of coating layers on top.

The pulp used to form the centre layer of the board will be described in Section 2.1. Section 2.2 will describe the mechanical process of making the board.

Figure 2.1 Structure of the board [1]

2.1 Pulp

The main raw material for making the board is cellulose fibres from different types of wood. The pre-processes are intended to break down the internal structure of the raw material so that the fibres can be separated in water. Depending on which properties are desirable in the final product, different methods can be used. These methods can roughly be divided into two different sub-groups: Mechanical wood pulp and Chemical wood pulp. Of course there are many different methods that are a combination of these two. Mechanical wood pulp is also the main pulp used in the centre layer of the board, see Figure 2.1. As will be shown later, the centre layer is the one used to control the basis weight of the board.

Triple layer coating CTMP pulp Matt coating Bleached Chemical pulp Bleached Chemical pulp Centre layer Back layer Top layer

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2.1.1 Mechanical

wood

pulp

There are two main ways of making mechanical wood pulp – by using grindstone or by using refiners. Both these methods break down the wood in a mechanical way, giving it the name mechanical wood pulp. The overall goal of these processes is to heat up the wood so that the lignin, which acts as the glue in wood, softens up. When the lignin has softened, the separation of fibres is relatively easy. Separation of fibres connected with warm lignin is possible by applying only shear stress. One of the main benefits of using mechanical wood pulp instead of chemical wood pulp is that it is relatively cheap to produce and that almost all wood is left in the pulp, about 85 to 95% [2]. Another advantage of these types of pulps is that they produce board with low transparency and are often so bright that they do not have to be bleached, making the process friendly to the environment. These factors combined with good strength make mechanical wood pulp suitable to use in thin printable products such as newspapers but also as armour in board.

2.1.1.1 Groundwood

Pressing debarked logs onto a grindstone is the older of the two main ways of making mechanical wood pulp [2]. This is done by pressing logs onto a big rotating grindstone which lies half way under water, see Figure 2.2. Usually this is done under atmospheric pressure.

Figure 2.2 Mechanical wood pulp produced with a grindstone

2.1.1.2 Thermo Mechanical wood Pulp (TMP)

TMP is the second way of making mechanical wood pulp. In this method heated chips of wood are crushed and transported in between two rotating plates inside a refiner [2]. A schematic description of a refiner ca be seen in Figure 2.3. The heat which is applied before entering the refiner makes he mechanical job easier. The rotation of the plates moves the chips from the centre of the refiner towards the outskirts of the plates. The spacing between the two plates is so small that the chips do not re-enter after exit. This is the most crucial part of the process. This method of refining chips of wood has many advantages if you compare it to the grindstone method above, mainly because the raw material is chips which can be handled more easily than logs. Woodchips of wood can also be bought from sawmills where it is a residue product, thus also an impact on recycling.

Logs

Grindstone

Water

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Figure 2.3 Schematic picture of a refiner build to make TMP and CTMP

This process makes less damage to the structure inside the fibres than the grindstone. After the mechanical process has separated the fibres from each other, screening is necessary to remove unwanted and badly separated material. If the end product demands extra bleaching, this is done by brightening the pulp with oxidizing and reducing agents, mostly hydrogen peroxide. These chemicals though react over time with the lignin in the pulp. This reaction produces a decrease in brightening and can be seen in ordinary newspapers.

2.1.1.3 Chemical Thermo Mechanical wood Pulp (CTMP)

Producing CTMP is actually almost the same as producing TMP. The only difference is that in this process chemicals are added to the heated chips before putting them into the refiner. The wooden chips are impregnated with chemicals and heated. After separation of fibres in the refiner, the pulp needs to be separated from dissolved wood substances and residual chemicals. The fluid separated from the pulp is reused or burned as fuel in the mill. With the use of chemicals more kinds of wood chips can be refined. Chemical add-ins used in this process give the pulp more strength but reduce transparency of light compared to TMP. One of the greatest advantages with the use of chemicals in thermo mechanical wood pulp is that the fibres are more easily separated from each other, meaning that the damage to each fibre will be reduced. By reducing the damage, the average length of the fibres will increase, giving the board more strength as the contact area between each fiber increases. Compared to TMP and Groundwood, CTMP has a lower percentage of wood left in the pulp, about 85-90% [2].

2.2 Process

description

A board machine has since the beginning of twentieth century been divided into five separate sections [3]. The sections are:

1) Headbox 2) Wire 3) Pressing 4) Drying 5) Coating Heat Wood chips Plates

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These different sections each have a unique task to perform if the machine is to produce board of high quality. When entering the machine the pulp has been mixed with a lot of water. This mixture is called thin stock and has a concentration of fibres around 0.05% and 99.95% water. All sections except the headbox and the coating dewater the thin stock to get the concentration of fibres in the final product up to around 90-95%. At the end of the machine, the board is wound onto big reels. These reels contain approximately 50 tons of board.

The length of the machine used in this thesis is about 75m and the board travels around 600m.

2.2.1 Headbox

The first part of a board machine is the headbox, as can be seen in Figure 2.4. In order to produce board with three layers of pulp there have to be three headboxes. You can measure the headboxes performance by the ability to produce the same quality of each layer, time after time. These devices are therefore the most important tool to adjust and control the uniformity of board properties. Each headbox has three main functions: flow transforming, blending and distribution of thin stock onto the wire section [4].

Flow transforming The headbox must transform a stream of thin stock from a pipe to a rectangular jet as wide as the machine. This must be done so that the thin stock has a completely uniform thickness, concentration and speed across the jet. The consistency of thin stock approaching the headbox must be very accurate in both concentration and speed; any pulsation can lead to uncontrollable variations in basis weight.

Blending

At the level of concentration in the thin stock coming into the headbox, thin stock fibres have a tendency to build up networks called flocks. This is a natural behaviour of the fibre, as they collide in the thin stock. If this happens, the uniformity of the thin stock may be destroyed and can in worst cases lead to dramatic changes in basis weight in the board. To prevent this, the headbox is built so that the flow is always turbulent. The turbulence has a tendency to break up weak flocks and to try and make sure that a consistent flock will never appear. Distribution

To achieve uniform basis weight on the reel of the machine, the headbox jet needs to be constant both in flow rate and speed, all the way across the lip. This leads to the conclusion that the pressure and lip opening should be constant across the machine. This means that a small change in either of the above-mentioned factors would result in a greater change at the reel. To be able to accelerate thin stock to the desired speed, a reduction of opening and pressure is applied across the headbox. The landing angle of the jet must be controlled in

Press section Drying section

Coating Section

Wire section _Reel

Head box

75m

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2.2.2 Wire

section

The second part of the board machine is the wire section; this section receives the jet coming from the headbox and tries to increase the fibre separation to prevail clogging of fibres. The wire also dries out water from the thin stock. When leaving the wire section the thin stock consists of about 80% water [3]. One main part of the wire section is the recirculation of water coming from the wire. This water is collected and reused when mixed with new pulp in order to produce new thin stock. This is called the short circulation of water.

There are generally two different types of wire sections, the twin wire and the traditional fourdrinier, when using a fourdrinier the thin stock drains downwards through a single wire. The higher the machine speed, the longer this section has to be because dewatering takes time. On twin-wire machines, the headbox jet impinges into the nip between two converging wires, draining the thin stock both upwards and downwards. The twin-wire solution is thus more appropriate for high-speed machines.

Figure 2.5 Schematic picture of the wire section with the headboxes. [1]

Figure 2.5 shows the wire section of the machine. The wire section is constructed as a fourdrinier. Figure 2.5 also shows how the partly dewatered furnish is put together into a homogeneous web before entering the press section.

2.2.3 Press

section

When the web enters the press section of the machine, it is exposed to mechanical actions that will transport water from the thin stock into the felt [2, 5]. This section is also where the dewatered thin stock starts to look like board. Pressing is performed in a series of nips formed by rolls pressing together. Each press nip is constructed so that the product will have certain desired properties.

The Press section is important because it is cheaper and faster to drain the web by pressing than by drying with steam. The pressure in the nip has to be very high because the fibres themselves consist of water that is difficult to remove. Leaving this section the product will consist of 50-65% water. Wire Wire Centre layer Top layer Back layer Headbox Centre layer Headbox Back layer Wire Wire Wire Headbox Top layer

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2.2.4 Drying

section

The drying section receives the wet board web from the press section mentioned above. Here the process of drying the board continues until the moisture level is about 5-10%. If the machine uses a lot of coating, a situation may occur where the drying reduces the water level even further and lets the coating section re-moisturise the board. Drying is also one of the most expensive parts in the making of board. About two thirds of the mills energy consumption goes to heat in the drying section on a board machine.

Today almost all board mills dry their products on a wrapping series of steam cylinders [5], as seen in Figure 2.6.

Figure 2.6 Drying section of the board machine [1]

The steam heats up the cylinders from inside and lets moisture in the board evaporate. If there is any inconsistency in the basis weight of the board it will have a large effect on this section, because water bound inside the fibres is harder to remove. This results in slower drying in places with high thickness and/or basis weight. If this difference in drying time across the web is large it will affect the board negatively and in the end different properties may become apparent.

2.2.5 Coating

section

The coating section of the machine is used to produce board with extraordinary properties. Properties affected by coating are smoothness and several of the measurable optical properties, and indirectly the printing ability of the product. When coating a product, a liquid of pigment particles is applied onto the surface [2, 3].

This liquid also contains binders and other additives. It is most commonly used on high quality board products used in packaging, where the surface is very important. When applied, the coating fills the empty space between fibres, and hopefully the fibres are covered with a layer of pigment particles. On the machine used in this study blade coaters apply the coating to the board. This method operates by applying more coating than desired and later scrapes off the excess coating with trailing blades.

Fors mill has four coating sections because they produces board with up to four layers of coat as could be seen in Figure 2.1.

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Control of basis weight

3 Control of basis weight

This chapter will introduce the reader to the term basis weight. The first section, 3.1 is an introduction to basis weight. The measuring method will be described in Section 3.2. Collection and variation of the data from the measurements of basis weight will be explained in Section 3.3. Based on the collection and variation in the data, there has to be some sort of control of the basis weight, how this control is performed across the machine is explained in Section 3.5.

3.1 Introduction

to

basis

weight

Basis weight is the most important property to be measured on the board. Basis weight, also called grammage in the literature, is a measure of mass per unit area. It is usually expressed as the non SI-unit [g/m2_{]; this unit comes from the early years of making board when the only} method to investigate basis weight was to cut out sheets of board with a given area and weigh them. The performance of board is strongly connected to basis weight; it has a direct or indirect affect on most of the measurable properties of board. When basis weight of the board is raised, different properties are affected in different directions and some not at all [3], for example:

– Transmission of light through the board decreases. – Bending stiffness is increased.

– Tensile stiffness is increased. – Roughness is not affected.

When the board is passes through a board or printing machine stress is forced upon the web. If the basis weight varies a lot there are some places in the board sheet that have less fibre than others. Those places in the material that consists of more fibres can of course take more stress, making the intersection between areas with lesser amount of fibres more vulnerable. This, combined with the changes in properties mentioned above, can result in difficulties with the runnability on the machines.

By applying changes only to the basis weight of the product, manufacturers are able to change the performance of the board. In this way, the mill is able to meet new demands from the customers. Nevertheless, an economic approach to basis weight significance is that it should be kept as low as possible and thereby using less thin stock, water and drying energy in the production.

3.2 Measurement

The characteristics of board can be measured in more than a thousands different ways. This section will describe how most of the manufacturers measure basis weight on-line, namely by beta gauge [3, 4]. The beta gauge measurement operates by using beta radiation. One of the biggest problems using radiation is the divergence of rays: the radiation source has to be constructed in such a way that the radiation rays are as close to parallel as possible. Recent development in this area has almost eradicated this problem of divergence. The divergence that is left is an important factor, as the resolution is heavily dependent on it. In the receiving end an ion chamber is placed to detect the intensity of the transmitted rays. The source is usually placed above the web and the ion chamber below

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When material of any kind is placed in the spacing between the source and the chamber, radiation is absorbed and the ion chamber detects a difference in intensity of the beta rays. The area that the gauge is sending rays through on the web is normally about one to two square centimetres which is the absolute resolution of the measurement. The amount of transmitted beta rays differs considerably between different materials, but the difference between water and fibre is very small, which is why this method is regularly used in board making. This may sound easy but specific calibration is still needed for different board qualities. This is caused by the difference in furnish and treatment in the process. To calculate basis weight from the measurements, exponential reduction of intensity is assumed [4], as seen in (3.1). ρ τ µ ** 0* * − =I B e I (3.1) Where 0 I = Intensity of source

I = Intensity measured by the ion chamber B = Constant that depends on the energy of the

source, ρ and τ, the amount of scattering between source and chamber is concluded here.

ρ_{= Specific gravity of the material.} τ = Thickness of the material. µ_{= Absorption coefficient.}

Beta radiation from the source is somewhat random which is why this method of measuring is not entirely precise. By averaging over a small amount of time this randomness disappears and the measurement is approximately constant. This method however reduces the beta gauges response time.

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3.3 Collection of basis weight measurements

The measurement of basis weight on-line with a beta gauge is performed by a measure head, described in Section 3.2. This measure head is placed inside a scanning device. The scanner moves at a speed of about 12 metres per minute and has a resolution of about 100 samples per metre. The effective measurement area is approx. 1 square centimetre [6].

The scanning movement across the web, seen in Figure 3.1 makes the interpretation of the samples from the measurement interesting. For example: the machine operates at around 480 metres per minute MD (which is the common speed for this specific board machine used in this thesis) and the scanner has a CD resolution of 100 samples per metre. With the speed of 12 meters per minute this means that about 1200 samples will be taken from 480 metres of board MD. Each sample is then an average from measurement in 40 centimetres of board MD and approximately 1 centimetre CD, seen in Figure 3.2.

Travel direction of Board

Machine Direction (MD)

Cross Direction (CD) Moving Scanner

Headbox

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This problem gets more interesting if we look at the distances for one complete scan across the machine. The machine used in this study is about 5.8 metres wide. This means that it takes the scanner approximately 25 seconds to complete one scan. During this period of time 200 metres of board MD have passed beneath the scanner. The exiting thing is that there now exist a set of values from the scanner. This set of values is the basis weight measurement across the machine, but each value represents an average of 40 centimetres of MD measured at different times. Consider the first and the last measurement in the scan: between those two measurements we have more than 190 metres of board.

MD

CD

5.8m First and last

measurement 200m MD CD 40 cm 1cm

Figure 3.2 The amount of paper representing one sample.

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Control of basis weight The sampling period of CD profile data is precisely the time it takes for the scanner to pass the machine once. With the scanning speed of 12 metres per minute the sampling rate becomes nearly 25 seconds. This is a pretty slow sampling rate, all events with time constants lower than this cannot be seen in the data collected by the scanner.

Other problems facing the instrument collecting these types of data are that the board is not as wide as the machine. When drying the thin stock it shrinks, making the web of board less wide than the headbox and wire sections. The scanning gauge has to traverse the entire machine width, also collecting data where there is no board. This can be seen if we look at the data from one single scan, seen in Figure 3.4.

Figure 3.4 Single scan of basis weight.

3.4 Variations in Basis Weight measurements

Variations in basis weight measurements are usually split into two components [7]; Cross Directional (CD) and Machine Directional (MD). If there are variations left in the measurements these are referred to as residual variations. In order to define these variations, the data received from each complete scan is put into a matrix, B where each cell represents a measurement of basis weight. Each column is a single scan and each row a position across the web (CD position). Data collected when the scanner is outside the web is removed.

0 116 232 348 464 580 0 50 100 150 200 250 CD-position [cm] Ba si s W eig ht [g /m 2]

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The matrix B shown in Figure 3.5 can be presented in a very powerful way by translating each basis weight measurement to a colour and drawing a figure showing each cell as a colour pixel. This is shown in Figure 3.6

Figure 3.6 Basis weight measurement matrix with 300 scans # CD-column 1 2 --- M-1 M # MD- row 1 b11 b12 --- b1(M-1) b1M 2 b21 b22 --- b2(M-1) b2M 3 b31 b32 --- b3(M-1) b3M 4 b41 b42 --- b4(M-1) b4M | | | | | | | | | | | | | | | | | | | | | | | | | | | | | N-1 b(N-1)1 b(N-1)2 --- b(N-1)(M-1) b(N-1)M N bN1 bN2 --- bN(M-1) bNM

Figure 3.5 Scans of basis weight, sorted into a matrix denoted B .

[g/m2] 194 196 198 200 202 204 206 208 Number of scan CD pos ition [c m ] 50 100 150 200 250 50 100 150 200 250 300 350 400 450 500 Number of scan CD position

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3.4.1 Cross Directional variations

One problem with the type of measuring system described in 3.3 is that changes in both MD and CD on the machine show themselves in each scan, this being due to the zigzagging motion of the scanner. If we were to get the true CD behaviour of the machine in each scan, we must get rid of the simultaneous changes in MD. The biggest problem in getting rid of these variations is that we have a value measured over time, meaning that every sample is a combination of change in CD and MD.

Trying to filter out one component from another in one stored value is impossible. One assumption often made is that the MD change between each scan is faster than the change in CD, making the separation possible by using a low pass filter. This low pass filtering can be made as a simple exponential filter, seen in (3.2).

[

cd_ki

]

= CD ,_CD_∈_RN ×M ) 1 ( ) 1 ( − ₋ + = _ki _k_i ki b cd cd α α ,b_ki∈R (3.2)

Where b is the raw value from current scan in CD position k, _ki cdk(i−1)the filtered value from last scan andcd the filtered value from current scan in CD position k. _ki αis called the filter factor and decides the importance of each new scan. The normal filter factor used in this type of application in around 0.2 [7]. This filter factor is enough to get acceptable independence from MD variations in the CD profiles.

All that is left after the influence from variations in MD has been reduced is to remove the mean from each scan.

              − − − − =

∑

= = = = N k kM NM N k k N N k kM M N k k CD N CD CD N CD CD N CD CD N CD 1 1 1 1 1 1 11 1 1 1 1 L M O M L P ,_P_∈_RN ×M

The CD basis weight profile is now defined as the columns in matrix P and is shown in Figure 3.7. 0 100 200 300 400 500 -2 -1 0 1 2 3 4 CD position [cm] B as is W eight [g/m 2]

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In order to put a value on the CD variation, Q is defined below. _i Q is called two-sigma value i

and is twice the ordinary one-dimensional standard deviation. With this definition, seen in (3.3), each scan performed by the beta gauge has a unique variation.

( )

2 1 2 1 1 1 2 _       − × =

∑

= N k ki i _N p Q (3.3)

The CD basis weight profile produced in each machine is fairly stable over time. Averaging the CD profiles from a couple of scans indicates that this is true. To show how consistent the CD profile is, two different sections from the matrix P are examined. Both sections include ten scans of basis weight. In Figure 3.8 the average CD profiles from the two sections are shown.

Figure 3.8 Two CD profiles. Created by averaging 10 scans.

3.4.2 Machine

directional

variations

The Machine directional profile, DM observed by the scanning gauge is found by removing the mean CD profile, defined in (3.4). The mean CD profile is the average of all CD profiles described in 3.4.1.

[ ]

md

_i

=

D

M

,∀i∈

{

1...M

}

∑

= = N k ki i _N b md 1 1 (3.4) As can be seen in (3.4) MD variation is the changes between each scan. By using this

definition we get a good picture of the changes occurring in the basis weight over time. The data presented above gives us the following MD profile.

-2 0 100 200 300 400 500 -1 0 1 2 3 4 5 CD position [cm] Ba si s Weight [g/m 2]

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Figure 3.9MD profile of basis weight.

To calculate the variations in MD, S is defined. As can be seen in (3.5), there have to be a couple of sampled rows. If there is only one row in the matrix, the MD variation is zero per definition.

{ }

(

)

2 1 2 1 1 1 2 _       − − × =

∑

= M k i E md M S MD (3.5)

3.4.3 Residual

variations

As mentioned above, variations in basis weight do not always have to be in CD or MD: there may for example be diagonal variations across the machine. All variations not in CD or MD directions are referred to as residual variations. One of the definitions of residual variations is presented in equation (3.6) below.

(

)

(

)

2 1 1 1 2 1 1 1 * 1 2               − − − − × =

∑ ∑

∑

= = = N j M k N j jk jk jk jk p _N b p b N M R (3.6)

To put a single value on the residual variations, shown in (3.6), is not completely satisfying. In order to get extensive knowledge of the residual variations, (3.6) combined with a study of the all-means-removed basis weight matrix is necessary.

3.5 Cross

directional

control of basis weight

The control of basis weight is performed by two system acting in different directions: Cross directional and Machine directional. The residual variations in basis weight described in 3.4 are not controlled at all.

0 50 100 150 200 250 300 199 199.5 200 200.5 201 201.5 Number of scan Basi s W eig ht [g/m 2]

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This thesis is about the slow disturbances in the control of the cross directional basis weight profile. Therefore there will be no discussion about the other control system. The entire focus will be upon how the cross directional (CD) profile of basis weight is analysed and controlled. Control of the CD basis weight profile is performed by a control system acting in a closed loop. The system is a multiple input multiple output system (MIMO) and can be described with a block scheme seen in Figure 3.10.

Figure 3.10 Schematic depiction of CD control of basis weight.

The control system is divided into three separate blocks [6]; the machine, pre-processing of data and the controller. The control of basis weight uses only the centre layer of the board, therefore only the centre headbox will be considered here. The other two headboxes used for outer layers in the board are controlled manually by the operator and are only set to deliver a constant amount of thin stock.

3.5.1 The machine block

The machine block can be divided into three separate parts, shown in Figure 3.11. The dimension of the input signal to this block is 58, which is the same as the numbers of actuators in the headbox. These actuator settings are generated by the controller. The array describes the new settings for each of the headbox actuators. The output signal from this block is of dimension 580, where each dimension is a measurement of basis weight across the machine.

Figure 3.11 Schematic depiction of the machine block.

The different physical parts of the process have already been described in Section 2.2 and for that reason there will be no further discussion here. The measurement and collection of basis weight data is described in Sections 3.2 and 3.3.

Headbox actuators Process Measurement & Data collection Actuator settings Dim. 58 Measurement Dim. 580 Reference profile

_–

Pre-processing Controller Machine Actuator settings Measurements CD profile Error profile

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3.5.1.1 Headbox actuators

The control array, denoted actuator settings, is received by the actuators in the headbox. There are mainly two different kinds of actuators used by the industry; screw jacks and injection [4].

The screw jacks are typically placed 10 – 15 cm apart all the way across the machine. These jacks act individually upon a thin beam. The regulation is performed by bending this lip. The bending change in the lip opening is in the order of micrometres. The jacks are controlled individually by motors or thermal expansions. A change in one jack produces a result which is wider than the actuator spacing. This implies that the nearby neighbours have to react upon changes. The method also consists of a built-in resistance towards big changes in lip movement; you cannot move a screw jack as far as you want without nearing the bending limits of the lip. This also means that two jacks placed next to each other cannot move completely freely.

The other way of controlling basis weight across the machine is by injecting or spraying water into the thin stock before it leaves the headbox. By doing this, the actuator causes a local change in concentration, which implies changes in the basis weight. This type of regulation has some major advantages compared with the screw jacks; each injector can be placed closer to each other, about 3.5 – 7 cm. This can be achieved because the injectors’ only change the amount of water entering the thin stock, nothing can be broken if we put every second in minimum flow and the rest in maximum. The injectors are also controlled individually and the response is of course quicker than for the jacks.

The headbox on the machine used in this thesis has screw jacks placed with 10 cm spacing making the numbers of jacks across the machine 58.

3.5.2 The

pre-process

block

The second step in the process of analysing the CD basis weight profile is to pre-process the data collected from the scanning beta gauge measurement. The big part in this block is to reduce the noise level and to resample the data so that the dimensionality is the same as the actuator settings.

The pre-process block consists of three separate parts: MD separation, anti alias and finally alignment and mapping. The separation of MD influence is described in 3.4.1.

The output signal from this block is directly compared with the reference profile in order to receive an error profile accessing the control block.

MD

separation _aliasAnti

Alignment & Mapping Measurement Dim. 580 CD profile Dim. 58

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3.5.2.1 Anti Alias

When reducing the dimensionality in the signal from 580 to 58 by resampling, a filter is needed in order to avoid aliasing. The frequencies needed to be removed are those greater than half of the sampling frequencies following the Nyqvist sampling theorem. This is done with a simple low pass filter. The filter has to cut off frequencies higher than 0.5 cycle/actuator, which in this case are 29.

3.5.2.2 Alignment and Mapping

The board that ends up on the reel do not have the same width as the headbox, as can be seen in Figure 3.4. This is a result of two things: shrinking and “cutting”. First of all to avoid major problems in edge defects, the machine “cuts” off some of the board width before it enters the drying section. Secondly, the board shrinks when it is dried out.

These two factors mean that the actuator responses are not equally spatial spaced in high resolution domain. This in turn means that the beginning of the first actuator and the end of the last are not the start and end of the measurement. This problem is solved in the control system by something called alignment, which tells us where in the high resolution measurement the start and end of each actuator zone is.

Figure 3.13 Graphical presentation of alignment. The alignment tells us which of the data boxes from the measurements corresponds to each actuator in the headbox. The alignment tells us which of the data boxes from the measurements corresponds to each actuator in the headbox. When the alignment has been calculated, the control system knows which of the measurements that is connected to each headbox actuator. It is now fairly easy to resample the measurement data down to the dimension of headbox actuator. The resampling procedure is called mapping and can be performed in a number of different ways.

3.5.3 The

Controller

The controller block receives an error profile which is the difference in pre-processed CD profile and reference profile. This block has to translate the error profile into actuator settings. In order to do so a so-called bump test has to be performed.

Headbox actuators

Measurements

High edge of board

1 2 57 58

1 2 3 4 5 6 7 8 9 10 11 570 571 572 573 574 575 576 577 578 579 580

Low edge of board

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Control of basis weight The bump test is a MIMO version of an ordinary step response. What happens is that open loop control with constant actuator setting is applied. When the process is in steady-state a couple of actuators are “bumped” by changing their settings. The actuators used in the test are changed equally at the same time. To verify the uniformities in responses, a couple of actuators across the headbox are changed at the same time.

Figure 3.14 Change in actuator settings and measured basis weight.

Analysing a test like this gives a picture of what the CD spatial response from actuator setting to basis weight looks like. As we can see in Figure 3.14, the response in basis weight is clearly wider than the spacing between two actuators.

When the response has been calculated, it is applied on to the error profile. By using the response in this way the actuators are decoupled and can be treated individually. There is also a time delay between actuator change and response that the controller has to compensate for. This delay is present because of the measurement is carried out on the reel at the end of the machine.

The control law most common for this type of application is the Dahlin feedback controller [6]. This controller can be seen as a special case of the Otto Smith controller, described in [8]. An example of what a control law using the Dahlin controller looks like is presented in equation (3.7) below. 1))] -(n (e K -(n) [e K d)] -(n c * K -d) -(n c ... 1) -(n [c K (n) ci = 1 i + + i 2 i + 3 i 4 i (3.7)

Where ci (n) is the change in actuator setting for actuator i, ei (n) the error profile for actuator i.

d is an integer that expresses the ratio between the time delay and scan time. K1 and K3 are machine-dependent constants.

K2 is the correction between d and the exact ratio between time delay and scan time. K4 is a time constant that expresses importance of earlier error.

-4 CD position [cm] [g/m 2] 0 100 200 300 400 500 600 -2 0 2 4 0 10 20 30 40 50 60 0 50 100 150 200 Actuator position [µ m]

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As can bee seen in (3.7) above, each new scan results in updated settings for the actuators, filtered with earlier settings and errors. This makes the update rate for the controller the same as the sampling rate of CD profiles.

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Method for describing control actions

4 Method for describing control actions

The first objective of this master thesis was to study the demand for cross directional control of basis weight. The need is connected to the changes made by the control system. If the control system does not change at all, there is no need for control. The changes can be seen as results from disturbances present on the machine. In order to detect when and how these disturbances occur, the output from the control system is studied.

The control output describes how much the current cross directional profile of basis weight has to be compensated in order to make uniform board. A method for describing the output therefore indirectly describes how much the control system is needed.

In order to explain how the output from the control system control system changes over time, a large amount of data must be analysed. Section 4.1 will describe collection of the data used in this study. A translation between low-resolution actuator settings and high-resolution basis weight measurement was created to express the changes in basis weight. This translation model was made as a linear transformation and is described in Section 4.2 and Appendix B. The output data from the model will show how the error in the measured profile is corrected. The next step is to explain the changes seen in the output from the translation model in as simple way as possible. The solution will be a pair of vectors; one which describing the behaviour of the actuators across the machine and a one which shows how it changes over time. The method for extracting these vectors are explained in Section 4.3 and Appendix A.

4.1 Collection of data

The collection of data was made on-line on board machine number 3 in Fors mill during autumn 2003. Measured profile, calculated control output and error profile was stored into a log together with constants used by the control system. The log system was active during 1833 scans making the total time at least 12 hours. If something happened on the machine during the collection that forced deactivation of the control and measuring system, the computer storing the data had to wait. This meant that in some cases there were considerable time gaps between two scans, making the total time for the dataset longer.

Normally each log was started in the morning and collected the next day simultaneously starting a new one. Each log is from here on denoted dataset or set of data. The datasets were received over a period of 3 months between September 8th and December 4th 2003. During this period of time, a total of 47 sets were collected.

4.2 Translation

model

In order to translate low-resolution control output (58 actuators) into high-resolution basis weight (580 measurements), a bump test was performed. Based on this test, a model is build as a linear transformation. This transformation is based on the assumption that the response for each actuator is the same across the machine.

The bump test is actually a MIMO version of an ordinary step response analysis. What happens is that closed loop control is turned off, with constant actuator setting. When the process is in steady-state, some actuators are forced to do a “bump” by changing their settings. To verify the uniformities in responses, more than one actuator has to be used. All of the actuators used in the test are changed equally and at the same time.

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Based on this test, a profile which is the translation from actuator setting to basis weight in the CD profile can be presented. The profile is called the CD response and has been identified by Fors mill. It is currently used by the control system as described in Section 3.5. Figure 4.1 shows the response profile.

Figure 4.1 The CD response profile.

The width of the response profile is a lot more then the spatial spacing between two actuators (~140cm compared to 10cm). The total response in basis weight from the headbox actuators can now be modelled as the superposition of responses from each actuator [9, 10]. Calculations made in order to receive the complete model are described in Appendix B.

4.2.1 Cross

Validation

0 100 200 300 400 500 600 -5 0 5 10 15 20 x 10 -3 CD position [cm] [g/m 2] 0 100 200 300 400 500 -15 -10 -5 0 5 10 15 20 CD position [cm] Measurement Model Model x 0.7 Ba si s Weig ht [g/m 2] 600

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Method for describing control actions Cross validation of the translation model is presented in Figure 4.2. The correlation coefficient between model and the measurement is very good, 0.967. This indicates that the shape of the CD response vector is accurate enough to describe the major changes across the machine but tells nothing of the magnitude.

Figure 4.2 also shows that the result of the model is not complete satisfying. The translation model is overreacting compared with the measurement and we receive a response that is too great. The measured profile is about 70 percent of the modelled profile, meaning that the maximum model error is about 30 percent. Analysis based on data from the translation model has to take this in consideration. The good part of all this is that we have a value of how big the model error is, in a worst-case scenario.

4.3 Information extraction

In order to describe the changes seen in the output from the translation model, principal component analysis is used, see Appendix A. The goal is to explain the variation in two dimensions; time and CD position. The extraction is made according to Figure 4.3. Each set of data represents about 1800 control outputs. The control outputs from the complete dataset is placed in a matrix the same way as presented in section 3.4 and translated. The translation output gives information of how the control outputs looks like in terms of high-resolution basis weight profiles

As can be seen in Figure 4.3, the information extraction is performed in three major steps: removal of mean profile, extraction of principal components and calculation of projection vectors. In order to express the CD profiles in basis weight, there has to be performed a normalization with the largest values found in each of the projection vectors.

4.3.1 Mean

profile

If the changes occurring over time are to be examined, the mean profile has to be withdrawn. The mean profile is the general compensation that the control system has to perform and is

Averaging Calculation of the covariance matrix Principal components Projection Score vectors CD profiles Multiplication Projection vectors Subtraction Mean profile Control outputs from dataset

representing 12-14 h Translation model Separate the largest values

Figure 4.3 Schematic description of the calculations from control output to CD profiles, score vectors and mean profiles

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4.3.2 CD

profiles

Data left after removal of the mean profile is the changes during the day. In order to describe these changes, principal component analysis is used. The theory of principle component analysis is presented in Appendix A.

The principal components are those vectors that best describes the variation across the machine in the specific dataset. The CD profile is calculated by multiplying the principal components with a single value.

Figure 4.4 shows an example of what the CD profiles can look like after the multiplication has been made. The profiles are numbered in descending order of description of variation, the first one describing most.

The extracted CD profiles will show how the control system has been working relative the mean profile. The CD profiles therefore give a direct picture of how the disturbances across the machine looked like during the collection of data. If the CD profile shows large changes across the machine it means that the control system had to work a lot in order to compensate for disturbances relation the mean profile.

4.3.3 Score

vectors

The score vectors are created from the projection vectors and describe the changes over time. According to Appendix A, each value in the projection vector is the one that minimizes the difference between the corresponding principal component and the mean removed translated control outputs.

By using principle component analysis, the projection vectors multiplied with the principle components is the approximation of the mean removed translated control outputs. This also means that neither the projection vector or the principle component will alone be expressed in basis weight. 0 100 200 300 400 500 600 -6 -4 -2 0 2 4 6 [g/m 2] CD-position [cm] First Second

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Method for describing control actions By identifying the largest value of each projection vector and perform normalization, score vectors are created. The corresponding principle components are also multiplied with this value in order to construct the CD profile.

The CD profile will now express basis weight. Each value in the score vector tells how much the corresponding CD profile has to be multiplied with in order to describe each mean removed translated control output, between -100% and + 100%. This is why the score vector expresses the presence.

Score vector multiplied with corresponding CD profile is the approximation of the mean removed translated control outputs.

A change in presence from negative to positive makes the CD profile flip. As an example of a flip the first CD profile seen in Figure 4.4 can be considered. This CD profile is a “Happy mouth” if multiplied with positive presence but a “Sad mouth” if multiplied with negative presence.

The score vector is therefore very interesting to examine. Seen in Figure 4.5 is a good example of things that can be analysed. First there is the flat area around the time 20:24. The control outputs have not been changed around this time; this means that the control has not been active. The change in presence from negative to positive after the flat area indicates that the control is reacting to a large disturbance.

15:36 16:48 18:00 19:12 20:24 21:36 22:48 00:00 01:12 02:24 03:36 -100 -80 -60 -40 -20 0 20 40 60 80 100 HH:MM Pr es en ce [ % ] First Second

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Data analysis

5 Data

analysis

When analysing datasets collected over long periods of time, like in this thesis, some days are more interesting than others. In this thesis more interesting is the same as when the control system has to work hard. The more disturbances present in or around the machine, the harder the control system has to work. How the detection of interesting datasets was made is described in Section 5.1. The analysis of these datasets is made in Section 5.2.

The assumption made in the purpose to this thesis was that the big changes occurred when a major event happened on the machine. This assumption is analysed in Section 5.3.

Section 5.4 describes how the analysis of the mean profiles extracted from each dataset was made.

5.1 Detection of interesting datasets

The mean variance in error profiles and mean removed translated actuator settings were chosen to study in order to attain a value on how much the control system had to work. The error profile, seen in Figure 3.10 is calculated as the difference between the CD profile described in Section 3.5.2, and the reference profile. In perfect conditions this error profile will be zero.

Figure 5.1Mean variance in error profile and translation model for each collected dataset The difference between the translation model and the error profiles, shown in Figure 5.1, is a good value of how much the control system has had to work. Figure 5.1 also shows that nearly half of the datasets have mean variance in the translation model that is close to that of the error profile.

To show the correctness of this approach, Figure 5.2 presents the CD profile extracted from the datasets from 16/9 and 14/11.

09/06 09/16 0 09/26 10/06 10/16 10/26 11/05 11/15 11/25 12/05 1 2 3 4 5 6 MM/DD M ean v arianc e [g/ m 2] 2 Error Profile Translation model

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Data analysis

Figure 5.2 CD profiles corresponding to the first principal component of the two different datasets

As can be seen in Figure 5.2, the differences are enormous. The changes made during 14/11 were nothing compared to the changes in the data from 16/9. This means that the errors that the control system had to compensate for were much smaller on 14/11, that is to say, the disturbances were smaller. This confirms that the usage of mean variance in order to detect the presence of large changes made by the control system is correct. The datasets having a mean variance of 1 (g/m2₎2_{or more were chosen for further investigation. The dates chosen} are presented in Table 5-1.

Table 5-1 Datasets worth further investigating Day/Month 8/9 8/10 11/11 10/9 14/10 12/11 12/9 21/10 24/11 16/9 29/10 27/11 6/10 30/10 2/12 7/10 6/11

The complete background material for Figure 5.1 and in Table 5-1 can be found in Table C-2.

5.2 Analysis

of

interesting datasets

The first thing to be done with the datasets chosen for further analysis is to investigate how much of the changes made in each set of the mean removed data that can be described by two components. This is done by comparing the two largest eigenvalues of the covariance matrix with the total sum of all eigenvalues.

0 100 200 300 400 500 600 -6 -4 -2 0 2 4 6 CD position [cm] [g/m 2] 16/9 14/11

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Data analysis 0 10 20 30 40 50 60 70 80 90 100 2003-09-08 2003-09-10 2003-09-12 2003-09-16 2003-10-06 2003-10-07 2003-10-08 2003-10-14 2003-10-21 2003-10-29 2003-10-30 2003-11-06 2003-11-11 2003-11-12 2003-11-24 2003-11-27 2003-12-02 YYYY-MM-DD % of t o ta l s u m

First eigenvalue Second eigenvalue

Figure 5.3 The two largest eigenvalues as percentage of the total sum of all eigenvalues Figure 5.3 shows a very good result. The conclusion that can be drawn from this is that nearly all of the variance is described by the principal components corresponding to the two largest eigenvalues. The complete background material for Figure 5.3 can be found in Table C-3.

5.2.1 CD

profiles

The principal components forming those CD profiles describing the changes have to be examined one by one in order to get a feeling for how the control system has had to work in order to compensate for the disturbances. The CD profile corresponding to the first principal component is the one that describes most of the changes and the second describes second most.

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Data analysis

Figure 5.4 The two different types of CD profiles found in the datasets As can be see in Figure 5.4, some days the control system has to compensate considerably on both sides of the machine (smiling mouth). The other profile, the slope, can be described as a continual increase in applied basis weight from left to right. The different types of CD profiles described above can be found in each of the datasets. The first and second CD profiles are placed in a group, described in Table 5-2.

0 100 200 300 400 500 600 -5 0 5 CD position [cm] Slope 0 100 200 300 400 500 600 -5 0 5 [g/m 2] [g /m 2] Smiling mouth CD position [cm]

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Data analysis

Table 5-2 Summary of CD profiles in interesting datasets

First CD profile Second CD profile

Smiling mouth Slope Smiling mouth Slope

8/9 10/9 10/9 8/9 16/9 12/9 12/9 16/9 14/10 6/10 6/10 21/10 21/10 7/10 7/10 12/11 8/10 8/10 24/11 29/10 14/10 30/10 29/10 11/11 30/10 27/11 11/11 2/12 12/11 24/11 27/11 2/12

The complete background for Table 5-2 can be found in Appendix D.

The next thing to investigate is how large the changes made by the control system were, expressed in basis weight. Maximum amplitude of each CD profile is an indication of this. This value is also the maximum amplitude of the changes, indirectly the maximum amplitude of the disturbances. The value is somewhere in between 70 and 100% correct, as has been discussed in Section 4.1. 0 2 4 6 8 10 12 20 03-09 -0 8 20 03-09 -1 0 20 03-09 -1 2 20 03-09 -1 6 20 03-10 -0 6 20 03-10 -0 7 20 03-10 -0 8 20 03-10 -1 4 20 03-10 -2 1 20 03-10 -2 9 20 03-10 -3 0 20 03-11 -0 6 20 03-11 -1 1 20 03-11 -1 2 20 03-11 -2 4 20 03-11 -2 7 20 03-12 -0 2 YYYY-MM-DD B asi s Wei g h t [g /m 2] Uncertainty

Figure 5.5 Maximum amplitude of the CD profiles corresponding to the first principal component

Figure 5.5 shows the maximum amplitude of the CD profiles corresponding to the first principal component, together with the uncertainties. The lower part of each bar is the

Study of control actions reveals disturbance patterns for cross directional control of basis weight