Two dimensional (2D) System Ideas for
Industrial Processes
Peter Wellstead
MAP lecture, 2003
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Examples of Practical 2D Processes
 Paper
making
 Plastic
film extrusion
 Coating processes (adhesives on paper sheets)
 Steel
rolling and continuous casting
 Spray
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actuation systems
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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
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Motivation: Practical (e.g. Paper Making)
 Technical
- product quality and plant flexibility
– 1% reduction in waste produces a
300,000 Euro saving per year per machine
 Economics
 Environment
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- EU plant efficiency requirements
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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.
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Idealised Plastic Film Extruder System: Aspects
of the Control Problem
CD actu ator a rray
m aterial w eb
Cross d irection,
(CD)
gau ge p ath
Machine d irection, (MD)
Delivery
m echanism
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scann ing
gau ge
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CD actu ator a rray
sensors
m aterial w eb
Cross d irection,
(CD)
gau ge p ath
Machine d irection, (MD)
Delivery
m echanism
sensor signal
processing
scann ing
gau ge
actuation
1
0.8
controllers
B estimates
0.6
estimators
0.4
0.2
0
-0.2
0
5
10
15
20
25
actuator position
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Control Issues: Practical 2D Systems
 Models

and identification
Sensors and sensor signal processing
 Control
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Models
u(i,n)
u(1,n) u(2,n)
u(MU,n)
CD actuation
points
Two Dimensional Manufacturing Process
CD output
measurement
points
y(i,n)
y(MY,n)
y(1,n) y(2,n)
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Models
 Model
for identification: 2D-ARMAX
1
1

1 1
˜
A(w , z )y(m, n)  z B(w ,z )u CD (m, n)
1
1
 C(w , z )e(m, n)
where
w
1
 horizontal shift operator
z 1  vertical shift operator
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Future Data
Models
Current measurement
direction of scan
j=0
j=1
j=2
j=3
 Two
dimensional data
structures for sheet
processes
i = -4 -3
-2
-1
0
1
2
3
4
Past Data
NSHP support for M=4 and N=3
Future Data
Curr ent mea sure ment
dir ection of sc an
j=0
j=1
j=2
j=3
Structures used in
image processing
i = -4
-3
-2
-1
0
Past Data
QP support f or M =4 and N=3
Future Data
Current measurement
direction of scan
This structure for
2-D control
j=0
j=1
j=2
j=3
i = -4 -3
-2
-1
0
1
2
3
4
Past Data
SHP support for M=4 and N=3
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Identification
 2-D identification: 2D-ARMAX estimation

2-D adaptive memory methods

non causal model estimation methods

edge effects
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Identification
Future Data
non causal model
estimation methods
 uses row-recursive
methods for FIR 2-D
filter implementation
to generate prediction
errors and simulate

Current data
Past Data
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Identification
2-D adaptive
memory methods
 2-D forgetting factors
give selected weights
to information from
all directions

(m ,n )
j
(m -i,n -j)
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i
i
15
(m +i,n -j)
Hamilton Institute
Identification


Structure estimation
Future Data
Example shows a
method for QP support
size estimation
Current m easurement
layer 1
layer 2
layer 3
layer 4
layer 5
increasing
model
order
layer 6
Past Data
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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
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Scanning gauge data collection
But what is happening
to the product
here?
And here
And here
Data collected
on this path
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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
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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.
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Sampling theory reminder
One dimension


Two dimensions
time/space domain
time domain
t
0
T
2T 3T 4T 5T 6T 7T
0
T
2T
3T
4T
5T
2-D frequency domain
frequency domain
f1
Data spectrum
1/T
f2
f
-2/T
-1/T
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1/T
Data spectrum
2/T
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-1/T
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Spectra of scanning
gauges
Frequency Domain
f1
Time Domain
left scan
The scans are NOT in the
CD,
 Alternate scans are in
opposite directions

f2
f1
2T

right scan
f2
RESULT: the two sets of
spectra are distorted and
in different ways
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Scan averaging interpretation
In a basic
scanner
the results of
adjacent scans
are averaged
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Result of basic gauge signal processing
Data spectrum
left scan
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Right scan
spectrum 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

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Generalised Sampling

a
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.
T
a
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a
5T
3T
a
a
a
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Hamilton Institute
a
Signal processing interpretation
2T
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
Actual MD data
Reconstruction of
MD using
conventional
signal processing
Results using
conventional methods
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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.
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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.
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Multi-gauge scanning array
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Practical 2D Systems: Scanning Sensor Array
Research System
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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
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Control Issues: Practical 2D Systems
 Models
and identification
 Sensors
 Control
MAP lecture, 2003
and sensor signal processing
(Courtesy of Honeywell)
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Hamilton Institute
CD Profile Control Loop
CD Controller

CD Process
The pursuit of better paper quality has placed new
demands on Cross Directional (CD) control systems
– smaller zone sizes
– faster response
– lower CD spreads
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Tuning: just right!!!
smooth paper!
active, but
not picketing
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CD actu ator a rray
sensors
m aterial w eb
Cross d irection,
(CD)
gau ge p ath
Machine d irection, (MD)
Delivery
m echanism
sensor signal
processing
scann ing
gau ge
actuation
1
0.8
controllers
B estimates
0.6
estimators
0.4
0.2
0
-0.2
0
5
10
15
20
25
actuator position
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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)
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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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Part being Sprayed
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
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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
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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
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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
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Typical sprayed steel “flat”
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2D Spray Actuation
 Painting.
 Spray
coating
 Metal deposition
 And many more
For example………..
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And 2D Sensing again:
Sub-sea profiling
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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’
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