Title: Recent%20Developments%20in%20Spatially%20Distributed%20Control%20Systems%20on%20the%20Paper%20Machine
1Recent 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
2Outline
- Industrial Paper Machine Operation
- Selected recent developments
- Automatic Tuning for Multiple Array Spatially
Distributed Processes - Closed-Loop Identification of CD Controller
Alignment
3Industrial Paper Machine Operation
4The Paper Machine
5Headbox 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.
6Press Section
- Newly-formed paper sheet is pressed and further
de-watered.
7Dryer 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.
8Dry 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.
9Control 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.
10Paper Machine Process
11Cross-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
12Scanning Sensor
- Paper properties are measured by a sensor
traversing the full sheet width.
13Cross-Directional Control
14Profile Control Loop
15Supercalendering 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
16Supercalenders
- 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
17Automatic Tuning for Multiple Array Spatially
Distributed Processes
18Automated 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
19Multiple-array CD process models
- Multiple-array process model
20Industrial MPC Configuration
Automated MV Tuning
Efficient and robust tuning
21Objective 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
22Objectives 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
23Automated 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
24Circulant matrices and rectangular circulant
matrices
25Two-dimensional frequency
- Based on the novel rectangular circulant
matrices (RCMs) theory for CD processes,
26Single-array plant model in the 2-D frequency
domain
27Multiple-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
28Closed-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
29Sensitivity function for single array systems
30Control sensitivity function for single array
systems
31Robust Stability (RS) Condition
K(z)
G(z)
- For additive unstructured uncertainty
-
- where is the representation of Tud(z) in the
two -dimensional frequency domain.
32Automated 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
33Impact 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.
34Tuning procedure
Input plant info and knob positions
Scaling
Model preparation
Horizon calculation
Spatial tuning
Dynamical tuning
Results display
Output tuning parameters
35Automated 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
36Spatial tuning knobs in the tool
37Tune the controller using spatial gain functions
38Dynamical tuning knobs in the tool
39Example 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.
40Example 1 linerboard paper machine (2)
41Example 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.
42Example 2 Supercalendars(2)
43Example 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)
44Conclusions
- 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.
45Closed-Loop Identification of CD Controller
Alignment
46Motivation
- 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
47Motivation
- 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
49Solutions for Identification of Alignment
- Current Industrial Solutions
- Open-Loop Bumptest
- Closed-Loop Probing
- Proposed Solution
- Closed-loop bumptest
50Feedback 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
-
51Open-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.
52Closed-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.
53Proposed 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
55Spatially 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.
56Appearance 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.
57Closed-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
58Practical 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 60Simulation 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
61Regular steady-state closed-loop operation
- CD controller tuned as usual with integral
action at low spatial frequencies.
62Closed-loop response of profiles
- Bumps inserted into the bias target profile while
CD control is in closed-loop.
63Response relative to baseline profiles
64Profile partitioning
DFT
DFT
gain
gain
phase
phase
65Frequency 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.
66Derivation 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
67Conclusions
- 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.
68References
- 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.