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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
7MAP lecture, 2003 Hamilton Institute
-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
8MAP lecture, 2003 Hamilton Institute
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
14MAP lecture, 2003 Hamilton Institute
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
17MAP lecture, 2003 Hamilton Institute
Control Issues: Practical 2D Systems
Models and identification
Sensors and sensor signal processing
Control
18MAP lecture, 2003 Hamilton Institute
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
20MAP lecture, 2003 Hamilton Institute
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
23MAP lecture, 2003 Hamilton Institute
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
24MAP lecture, 2003 Hamilton Institute
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
26MAP lecture, 2003 Hamilton Institute
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
29MAP lecture, 2003 Hamilton Institute
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
35MAP lecture, 2003 Hamilton Institute
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
41MAP lecture, 2003 Hamilton Institute
-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
44MAP lecture, 2003 Hamilton Institute
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
45MAP lecture, 2003 Hamilton Institute
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
49MAP lecture, 2003 Hamilton Institute
50MAP lecture, 2003 Hamilton Institute
51MAP lecture, 2003 Hamilton Institute
52MAP lecture, 2003 Hamilton Institute
Typical sprayed steel “flat”
53MAP lecture, 2003 Hamilton Institute
2D Spray Actuation
Painting. Spray coating Metal deposition And many more
For example………..
54MAP lecture, 2003 Hamilton Institute
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’