1MAP lecture, 2003 Hamilton Institute

Two dimensional (2D) System Ideas for Industrial Processes

Peter Wellstead

2MAP lecture, 2003 Hamilton Institute

Examples of Practical 2D Processes

Plastic film extrusion Coating processes (adhesives on paper sheets)

Steel rolling and continuous casting

Spray actuation systems

Paper making

3MAP lecture, 2003 Hamilton Institute

Motivation: Personal Experience

1970-72: real-time image processing for bubble chamber photographs

1975-85: self-tuning control 1980’s: self-tuning filters for 2D images 1980’s: modeling and control of polymer film

extruders 1990’s: algorithms for practical 2D systems

4MAP lecture, 2003 Hamilton Institute

Motivation: Practical (e.g. Paper Making)

Technical - product quality and plant flexibility

Economics – 1% reduction in waste produces a 300,000 Euro saving per year per machine

Environment - EU plant efficiency requirements

5MAP lecture, 2003 Hamilton Institute

Motivation: Research A generic class of 2-D dynamic systems - paper, plastic

film, sheet forming, coating and converting

Opportunity for innovation - 2-D concepts not previously used in sheet forming.

Applications driven research - real 2-D systems as motivation for appropriate 2-D theory.

6MAP lecture, 2003 Hamilton Institute

Idealised Plastic Film Extruder System: Aspects of the Control Problem

aa

Machinedirection, (MD)

Cross direction,(CD)

CD actuatorarray

scanninggauge

gaugepath

material web

Deliverymechanism

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-0.2

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

actuator position

B e

stim

ates

a

scanning frame motion

sensor scan paths

aa

Machinedirection, (MD)

Cross direction,(CD)

CD actuatorarray

scanninggauge

gaugepath

material web

Deliverymechanism

sensors

estimatorscontrollers

sensor signal processing

actuation

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Control Issues: Practical 2D Systems

Models and identification Sensors and sensor signal processing

Control

9MAP lecture, 2003 Hamilton Institute

Models

a

u(1,n) u(2,n) u(i,n) u(MU,n)

Two Dimensional Manufacturing Process

y(i,n) y(MY,n)

y(1,n) y(2,n)

CD actuationpoints

CD outputmeasurementpoints

11MAP lecture, 2003 Hamilton Institute

Models Model for identification: 2D-ARMAX

A(w 1, z 1)˜ y (m, n) z B(w 1,z 1)uCD(m, n)

C(w 1, z 1)e(m, n)

where

w 1 horizontal shift operator

z 1 vertical shift operator

12MAP lecture, 2003 Hamilton Institute

Models Two dimensional data

structures for sheet processes

a

direction of scan

i = -4 -3 - 2 -1 0 1 2 3 4

j = 3

j = 2

j = 1

j = 0

NSHP support for M=4 and N=3

Past Data

Current measurement

Future Data

QP support for M=4 and N=3

direction of scan

i = -4 -3 - 2 -1 0

j = 3

j = 2

j = 1

j = 0

Past Data

Current measurement

Future Data

direction of scan

i = -4 -3 - 2 -1 0 1 2 3 4

j = 3

j = 2

j = 1

j = 0

SHP support for M=4 and N=3

Past Data

Current measurement

Future Data

Structures used in image processing

This structure for2-D control

13MAP lecture, 2003 Hamilton Institute

Identification 2-D identification: 2D-ARMAX estimation

2-D adaptive memory methods

non causal model estimation methods

edge effects

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Identification non causal model

estimation methods uses row-recursive

methods for FIR 2-D filter implementation to generate prediction errors and simulate

a

Past Data

Current data

Future Data

15MAP lecture, 2003 Hamilton Institute

Identification 2-D adaptive

memory methods 2-D forgetting

factors give selected weights to information from all directions

aa

i i

j

(m-i,n-j)

(m,n)

(m+i,n-j)

16MAP lecture, 2003 Hamilton Institute

Identification Structure estimation

Example shows a method for QP support size estimation

a

Past Data

Current measurement

Future Data

layer 1

layer 2

layer 3

layer 4

layer 5

layer 6increasingmodelorder

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Control Issues: Practical 2D Systems

Models and identification

Sensors and sensor signal processing

Control

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Sensors: the requirement Extrusion line speeds move at 300m/min. Paper

machines move at 1000m/min (~30miles/h)

Less than 0.002% of a paper roll is measured

Need for increased density of measurement

19MAP lecture, 2003 Hamilton Institute

Scanning gauge data collection

a

movement of web

scanningframemotion

scanninggaugepath

Data collectedon this path

But what is happening to the product

here?

And here

And here

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How do we get full sheet information?

Hardware for Full Sheet Sensing– sensor arrays

Software for Full Sheet Sensing– Generalised Sampling Theory

21MAP lecture, 2003 Hamilton Institute

Distortion of sheet data using scanning gauges

Collecting data along a zig-zag path scanning gauges are performing a 2-D SAMPLING PROCESS.

2-D spectral analysis shows that the two scans (left scan and right scan) collect sheet data in different ways.

22MAP lecture, 2003 Hamilton Institute

Sampling theory reminder One dimension

0 T 2T 3T 4T 5T 6T 7T

0 1/T 2/T-1/T-2/T

t

f

time domain

frequency domain

Data spectrumData spectrum

0

Two dimensions

T 2T 3T 4T 5T

f1

f2

1/T

-1/T

time/space domain

2-D frequency domain

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Spectra of scanninggauges

The scans are NOT in the CD,

Alternate scans are in opposite directions

a

Time Domain Frequency Domain

left scan

right scan

f1

2T

f1

f2

f2 RESULT: the two sets of spectra are distorted and

in different ways

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Scan averaging interpretation

In a basic scannerthe results of adjacent scans are averaged

25MAP lecture, 2003 Hamilton Institute

Result of basic gauge signal processing

Data spectrumleft scan

Right scanspectrum added

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How to avoid distortion and get full sheet information

Use Generalised Sampling to reconstruct the MD signal.

Get the full sheet information by assembling the reconstructed MD signals

27MAP lecture, 2003 Hamilton Institute

Generalised Sampling By considering

reconstruction along an MD line, the Generalised Sampling Theorem can be used to reconstruct the full 2-D sheet and double the bandwidth.

a

T 3T 5T

a a

a aaaa a

28MAP lecture, 2003 Hamilton Institute

2T

Signal processing interpretation

Sampling along the MD as a generalised

sampling process

Signal processing

block diagram

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MD reconstruction results

Reconstruction of MD data

using generalised

sampling

Reconstruction of MD using conventional

signal processing

Actual MD data

Results using conventional

methods

31MAP lecture, 2003 Hamilton Institute

Summary

Conventional averaging of scanner data gives a distorted view of the sheet variations, and has an aliassing bandwidth of 1/2T.

Generalised sampling reconstructs full sheet data by compensating for the scanning geometry. The bandwidth is DOUBLED to 1/T.

32MAP lecture, 2003 Hamilton Institute

How do we get full sheet information?

Hardware for Full Sheet Sensing– sensor arrays.

Software for Full Sheet Sensing– use 2-D sampling theory find out how and under what

conditions full sheet information can be reconstructed from scanning gauge data.

34MAP lecture, 2003 Hamilton Institute

a

movement of web

scanningframemotion

scanninggaugepaths

Multi-gauge scanning array

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Practical 2D Systems: Scanning Sensor Array Research System

36MAP lecture, 2003 Hamilton Institute

Multi-gauge scanning arrays Calibration of sensors across the web/sheet done

by special ‘calibration transfer’ trick

Only one expensive gauge is required

Gauge technologies can be mixed (e.g. beta gauge and infrared)

Generalised sampling is applicable to multiple gauges

37MAP lecture, 2003 Hamilton Institute

Control Issues: Practical 2D Systems

Models and identification

Sensors and sensor signal processing

Control (Courtesy of Honeywell)

38MAP lecture, 2003 Hamilton Institute

CD Profile Control Loop

The pursuit of better paper quality has placed new demands on Cross Directional (CD) control systems– smaller zone sizes

– faster response

– lower CD spreads

CD Controller CD Process

40MAP lecture, 2003 Hamilton Institute

Tuning: just right!!!

smooth paper!

active, but not picketing

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-0.2

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

actuator position

B e

stim

ates

a

scanning frame motion

sensor scan paths

aa

Machinedirection, (MD)

Cross direction,(CD)

CD actuatorarray

scanninggauge

gaugepath

material web

Deliverymechanism

sensors

estimatorscontrollers

sensor signal processing

actuation

42MAP lecture, 2003 Hamilton Institute

NEW DIRECTIONS: 2D Scanning Actuators Consider Mass Deposition Processes

– eg spray painting Source of mass is spray gun that is moved over

surface– manipulation usually done by robot

Aim to deposit specific mass profile on surface– for most applications, desired profile is uniform (ie

flat)

43MAP lecture, 2003 Hamilton Institute

Scanning Actuators Given “footprint” of

mass flow rate from gun

What track should the gun follow over the surface to achieve desired mass profile?

Scanning actuator is “dual” of scanning sensor

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Raster Pattern Results from 2D

scanning theory tell you:

– how close to put the tracks

– how far off edges you need to scan to avoid edge effects

Robot Path

Part being Sprayed

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More Complex Paths Generalised Scanning

Theory also shows that this path is also valid

Path is suitable for thermal spray processes– aim to achieve specific

temperature profile

– more difficult problem because heat flows

Robot Path

46MAP lecture, 2003 Hamilton Institute

Example of 2D Spray Actuation

SPRAY FORMATION OF METAL– Spray forming of metal as an alternative to casting– 2D generalised sampling ideas from sensing are

DUALISED to get dual results for actuation.– Metal is sprayed in a special pattern to optimise spray

cast metal quality

47MAP lecture, 2003 Hamilton Institute

Benefits of spray-forming

Reduced cost Costs US$ 100Million to provide tooling for new

car model

Reduced time Takes >18 months to produce tooling for big parts

(bumpers, bonnets, door panels etc) Freeze design long before production

48MAP lecture, 2003 Hamilton Institute

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Typical sprayed steel “flat”

53MAP lecture, 2003 Hamilton Institute

2D Spray Actuation

Painting. Spray coating Metal deposition And many more

For example………..

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And 2D Sensing again:

Sub-sea profiling

55MAP lecture, 2003 Hamilton Institute

Acknowledgements

Greg Stuart of Honeywell: Greg supplied the information and slides of his profile control system.

Steven Duncan of Oxford University: Steven supplied slides of his 2D actuation systems

Final photograph from ‘CropDusters’