Recent%20Developments%20in%20Spatially%20Distributed%20Control%20Systems%20on%20the%20Paper%20Machine

1
Recent Developments in Spatially Distributed
Control Systems on the Paper Machine

• Greg Stewart and James Fan
• Honeywell, North Vancouver
• Presented by Guy Dumont
• University of British Columbia

2
Outline

• Industrial Paper Machine Operation
• Selected recent developments
• Automatic Tuning for Multiple Array Spatially
  Distributed Processes
• Closed-Loop Identification of CD Controller
  Alignment

3
Industrial Paper Machine Operation
4
The Paper Machine
5
Headbox and Table

• Pulp stock is extruded on to a wire screen up to
  11 metres wide and may travel faster than 100kph.

Initially, the pulp stock is composed of about
99.5 water and 0.5 fibres.
6
Press Section

• Newly-formed paper sheet is pressed and further
  de-watered.

7
Dryer Section
finished reel

• The pressed sheet is then dried to moisture
  specifications

The paper machine picturedis 200 metres long and
the paper sheet travels over 400 metres.
8
Dry End
scanner

• The finished paper sheet is wound up on the reel.

The moisture content at the dry end is about 5.
It began as pulp stock composed of about 99.5
water.
9
Control Objectives

• Properties of interest
• weight
• moisture content
• caliper (thickness of sheet)
• coating misc.
• Regulation problem to maintain paper properties
  as close to targets as possible.
• Variance is a measure of the product quality.

10
Paper Machine Process
11
Cross-Directional Profile Control

• control objective flat profiles in the
  cross-direction (CD)
• a distributed array of actuators is used to
  access the cross-direction

CD
MD
12
Scanning Sensor

• Paper properties are measured by a sensor
  traversing the full sheet width.

13
Cross-Directional Control
14
Profile Control Loop
15
Supercalendering process

• Supercalendering is often an off-machine process
  used in the production of high quality printing
  papers
• The supercalendering objectives are to enhance
  paper surface properties such as gloss, caliper
  and smoothness
• Typical end products are magazine paper, high end
  newsprint and label paper

16
Supercalenders

• Gloss, caliper and smoothness are all affected
  by
• The lineal nip load
• The sheet temperature
• The sheet moisture content
• With the induction heating actuators we can
  change the sheet temperature and the local
  nipload
• With the steam showers we can change the sheet
  temperature and the sheet moisture content

17
Automatic Tuning for Multiple Array Spatially
Distributed Processes
18
Automated Tuning Overview

• Control problem
• Multi-array cross-directional process models
• Industrial model predictive controller
  configuration
• Objectives of automated tuning
• Two-dimensional frequency domain
• Tuning procedure
• Industrial software and examples
• Conclusions

19
Multiple-array CD process models

• Multiple-array process model

20
Industrial MPC Configuration
Automated MV Tuning
Efficient and robust tuning
21
Objective function of CD MPC
Measurement weight
Prediction horizon
Control horizon
Aggressiveness penalty

• The objective function
• is minimized subject to actuator constraints
• for optimal control solution

Picketing penalty
Energy penalty
22
Objectives of automated tuning

• The tuning problem is to set the parameters of
  the MPC
• Prediction and control horizons (Hp, Hc)
• Optimization weights (Q1, Q2, Q3, Q4)
• To provide good closed-loop performance with
  respect to model uncertainty (balance between
  performance and robustness)
• Software tool requirements
• Computationally efficient implementation required
  for use in the field
• Easy to use by the expected users

23
Automated Tuning Overview

• Control problem
• Multi-array cross-directional process models
• Industrial model predictive controller
  configuration
• Objectives of automated tuning
• Two-dimensional frequency domain
• Tuning procedure
• Industrial software and examples
• Conclusions

24
Circulant matrices and rectangular circulant
matrices
25
Two-dimensional frequency

• Based on the novel rectangular circulant
  matrices (RCMs) theory for CD processes,

26
Single-array plant model in the 2-D frequency
domain
27
Multiple-array plant model in the 2-D frequency
domain

• The model can be considered as rectangular
  circulant matrix blocks and its 2-D frequency
  representation is

28
Closed-loop transfer function matrices

• Derive the closed-loop transfer functions of
  the system with unconstrained MPC.

• Performance defined by sensitivity function

• Robust Stability depended on control
  sensitivity function

29
Sensitivity function for single array systems
30
Control sensitivity function for single array
systems
31
Robust Stability (RS) Condition


K(z)
G(z)

• For additive unstructured uncertainty
• where is the representation of Tud(z) in the
  two -dimensional frequency domain.

32
Automated Tuning Overview

• Control problem
• Multi-array cross-directional process models
• Industrial model predictive controller
  configuration
• Objectives of automated tuning
• Two-dimensional frequency domain
• Tuning procedure
• Industrial software and examples
• Conclusions

33
Impact of MPC weights on Sensitivity Function1

• Interesting result
• MPC weight Q2 on ?u does not impact the spatial
  bandwidth
• MPC weight Q4 does not impact the dynamical
  bandwidth
• Encourages a separable approach to the tuning
  problem

4.5
4
cycles/metre
3.5
Q4
3
n
2.5
2
1.5
i2
p
w
spatial frequency
t
(
n
,e
)lt0.7071
yd
1
Q2
0.5
-3
x 10
1
2
3
4
5
6
dynamical frequency
w
cycles/second
1 Two-dimensional frequency analysis for
unconstrained model predictive control of
cross-directional processes, Automatica, vol 40,
no. 11, p. 1891-1903, 2004.
34
Tuning procedure
Input plant info and knob positions
Scaling
Model preparation
Horizon calculation
Spatial tuning
Dynamical tuning
Results display
Output tuning parameters
35
Automated Tuning Overview

• Control problem
• Multi-array cross-directional process models
• Industrial model predictive controller
  configuration
• Objectives of automated tuning
• Two-dimensional frequency domain
• Tuning procedure
• Industrial software and examples
• Conclusions

36
Spatial tuning knobs in the tool
37
Tune the controller using spatial gain functions
38
Dynamical tuning knobs in the tool
39
Example 1 linerboard paper machine (1)

• Four CD actuator arrays
• u1 Secondary slice lip
• u2 Primary slice lip
• u3 Steambox
• u4 Rewet shower
• Two controlled sheet properties
• y1 Dry weight
• y2 Moisture
• Overall model G(z) is a 984-by-220 transfer
  matrix.

Performance comparison between traditional
decentralized control and auto-tuned MPC.
40
Example 1 linerboard paper machine (2)
41
Example 2 Supercalendars (1)

• Four CD actuator arrays
• u1 top steambox
• u2 top induction heating
• u3 bottom steambox
• u4 bottom induction
• heating
• Three controlled sheet properties
• y1 caliper
• y2 top gloss
• y3 bottom gloss
• Overall model G(z) is a 2880-by-190 transfer
  matrix.

Performance comparison between traditional
decentralized control, manually tuned MPC, and
auto-tuned MPC.
42
Example 2 Supercalendars(2)
43
Example 2 Performance Comparison
Before control (2sigma) Traditional control (2sigma) Manual Tuning (2sigma) Automated Tuning (2sigma)
Caliper 0.0882 0.0758 (-14.06) 0.0565 (-35.94) 0.0408 (-53.74)
Topside Gloss 2.8711 4.0326 (40.45) 2.8137 (-2) 1.5450 (-46.19)
Wireside Gloss 3.5333 2.7613 (-21.85) 2.6060 (-26.24) 2.3109 (-34.60)
44
Conclusions

• A technique was presented for solving an
  industrial controller tuning problem
  multi-array cross-directional model predictive
  control.
• To be tractable the technique leverages
  spatially-invariant properties of the system.
• Implemented in an industrial software tool.
• Controller performance was demonstrated for two
  different processes.

45
Closed-Loop Identification of CD Controller
Alignment
46
Motivation

• Uncertainty in alignment grows over time and can
  lead to degraded product and closed-loop unstable
  cross-directional control.
• Typically due to sheet wander and/or shrinkage.

Measured Bump response
Actuator profile
CD position space
47
Motivation

• In many practical papermaking applications the
  alignment is sufficiently modeled by a simple
  function.
• We assume it to be linear throughout this
  presentation.(Although the proposed technique is
  not restricted to linear alignment.)

xj f(j)
48

• Current and
• Proposed Solutions

49
Solutions for Identification of Alignment

• Current Industrial Solutions
• Open-Loop Bumptest
• Closed-Loop Probing
• Proposed Solution
• Closed-loop bumptest

50
Feedback diagram

• The standard closed-loop control diagram.
• r target (bias target)
• u actuator setpoint profile
• y scanner measurement profile

du
dy


y
r
u



G
K
-
51
Open-Loop Bumptest

• Procedure
• Open-loop insert perturbation at du
• Then record the response in y, to extract model G.

du
dy


y
r
u



G
K
-

• Whenever possible, closed-loop techniques are
  preferred in a quality-conscious industry.

52
Closed-Loop Probing

• Procedure
• Keep controller in closed-loop
• Insert probing perturbation du on top of the
  actuator profile
• Then record the response in y, to extract model
  G.

du
dy


y
r
u



G
K
-

• Technique relies on transient response of y. In
  practice a noisy process and scanning sensor make
  dynamics difficult to extract reliably.

53
Proposed Solution Closed-Loop Bumptest

• Procedure
• Leave loop in closed-loop control
• Insert perturbation on target dr as shown
• Record the response in the actuator profile u.

dy
dr


u
y
r



G
K

• The control loop is exploited to extract
  alignment information. No need of addressing
  (exciting and modeling) dynamics to extract
  alignment information.

54

• Overview of Background Theory

55
Spatially Invariant Systems

• The theory of spatially invariant systems allows
  the convolution to be converted to multiplication
  in the frequency domain
• Allows the spatial frequency response of the
  entire array to be written as the Fourier
  transform of the response to a single actuator1

1S.R. Duncan, "The Cross-Directional Control of
Web Forming Processes", PhD thesis, University of
London, 1989.
56
Appearance of Alignment in Frequency Domain
Spatial domain
Spatial Frequency domain

• A shift in x will appear as a linear term in the
  phase of its Fourier transform.

57
Closed-loop spatial frequency response

• At steady-state (temporal frequency ?0) the
  closed-loop input and output can be written in
  spatial frequency

• For those spatial frequencies where the control
  has integral action we find the steady-state
  expressions

58
Practical Consequence

• Combining these results we see that the change in
  alignment is contained in the phase of the
  actuator array

Practical consequence We can identify changes
in the alignment of the CD process by inserting
perturbations into the setpoint to the CD
controller.

• Advantages
• Straightforward execution
• CD control can remain in closed-loop no need to
  work against the control action
• Size of disruption in paper is more predictable
  than with actuator bumps

59

• Example

60
Simulation Setup

• We introduce a combined sheet wander and
  shrinkage into the simulation by artificially
  moving the low side and high side sheet edges by
  20mm and 60mm respectively.

20mm
60mm
61
Regular steady-state closed-loop operation

• CD controller tuned as usual with integral
  action at low spatial frequencies.

62
Closed-loop response of profiles

• Bumps inserted into the bias target profile while
  CD control is in closed-loop.

63
Response relative to baseline profiles
64
Profile partitioning
DFT
DFT
gain
gain
phase
phase
65
Frequency domain analysis of actuator profile

• Low side phase has a slope of 29.5mm at zero
  frequency.

High side phase has a slope of 50.9mm at zero
frequency.
66
Derivation of global alignment

• Here we make an assumption of linear alignment
  shift and thus need only two points to define a
  straight line.
• Confirm that the ends of the straight line
  correspond to the 20mm and 60mm alignment change.

xj f(j)
50.9mm
29.5mm
67
Conclusions

• The proposed closed-loop bumptest uses a
  perturbation in the setpoint profile and
  identifies the response of the actuator array.
• Technique is sensitive to changes in alignment of
  the paper sheet a practically important model
  uncertainty.
• Technique can be implemented with minor changes
  to existing installed base of CD control systems.
• Initial experiments have begun on industrial
  paper machines.
• While not necessary to date, more complex
  shrinkage models would simply require more than
  two bumps for identification.

68
References

• CDC-ECC 2005 - TuB09, Process Control II
• J. Fan and G.A. Dumont, Structured uncertainty
  in paper machine cross-directional control, to
  appear in TuB09, Process Control II , Seville,
  Spain, 2005.
• Borrelli, Keviczky, Stewart, Decentralized
  Constrained Optimal Control Approach to
  Distributed Paper Machine Control TuB09, Process
  Control II , Seville, Spain, 2005
• Other
• J. Fan and G.E. Stewart, Automatic tuning of
  large-scale multivariable model predictive
  controllers for spatially-distributed
  processes, US Patent (No.11/260,809) filed
  2005.
• J. Fan, G.E. Stewart, G.A. Dumont, J. Backström,
  and P. He, Approximate steady-state performance
  prediction of large-scale constrained model
  predictive control systems, IEEE Transactions on
  Control Systems Technology, vol 13, no. 6, p.
  884-895, 2005.
• J. Fan, G.E. Stewart, and G.A. Dumont,
  Two-dimensional frequency analysis for
  unconstrained model predictive control of
  cross-directional processes, Automatica, vol 40,
  no. 11, p. 1891-1903, 2004.
• J. Fan, Model Predictive Control for Multiple
  Cross-Directional Processes Analysis, Tuning,
  and Implementation, PhD thesis, The University
  of British Columbia, Vancouver, Canada, 2003.
• J. Fan and G.E. Stewart, Fundamental spatial
  performance limitation analysis of multiple array
  paper machine cross-directional processes, ACC
  2005, p. 3643-3649 Portland, Oregon, 2005.
• J. Fan, G.E. Stewart, and G.A. Dumont,
  Two-dimensional frequency response analysis and
  insights for weight selection of
  cross-directional model predictive control,
  CDC03, p. 3717-3723, Hawaii, USA, 2003.
• G.E. Stewart, Reverse Bumptest for Closed-Loop
  Identification of CD Controller Alignment, US
  Patent filed Aug. 22, 2005.