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. 2HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 4HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain The Paper Machine

5. 5HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Headbox and Table sheet travel 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. 6HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Press Section suction presses Newly-formed paper sheet is pressed and further de-watered.

7. 7HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Dryer Section finished reel The pressed sheet is then dried to moisture specifications The paper machine pictured is 200 metres long and the paper sheet travels over 400 metres.

8. 8HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 9HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 10HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Paper Machine Process Measurement gauges MD CD weightmoisturecaliper

11. 11HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 12HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Scanning Sensor Paper properties are measured by a sensor traversing the full sheet width.

13. 13HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Cross-Directional Control Measured profile response, y(t) Actuator setpoint array, u(t) CD MD Sensor measurements

14. 14HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Profile Control Loop LAN connection INPUT SIGNAL, u(t) OUTPUT SIGNAL, y(t) CONTROLLER, K(z) PROCESS, G(z) TARGET, r(t)

15. 15HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 16HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Supercalenders Off Machine Supercalender 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. 18HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 19HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Multiple-array CD process models Multiple-array process model:

20. 20HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Trial and error, Closed-loop simulations CD-MPC weights and closed-loop prediction LAN ( local area network ) LAN Direct connection LAN connected when needed Sensor measurementsActuator setpoints CD Processes CD-MPC Controller Real time QP solver Model identification Industrial MPC Configuration Efficient and robust tuning Automated MV Tuning

21. 21HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Objective function of CD MPC The objective function is minimized subject to actuator constraints for optimal control solution Aggressiveness penalty Energy penalty Picketing penalty Measurement weightPrediction horizonControl horizon

22. 22HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Objectives of automated tuning The tuning problem is to set the parameters of the MPC: - Prediction and control horizons (H p, H c ) - Optimization weights (Q 1, Q 2, Q 3, Q 4 ) 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. 23HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 24HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Circulant matrices and rectangular circulant matrices A 10-by-5 rectangular circulant matrices A 5-by-5 circulant matrices

25. 25HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Two-dimensional frequency Based on the novel rectangular circulant matrices (RCMs) theory for CD processes,

26. 26HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Single-array plant model in the 2-D frequency domain

27. 27HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 28HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Closed-loop transfer function matrices Performance defined by sensitivity function KrKr K(z) Y sp U(z) Y(z) G(z) + D(z) _ + + Robust Stability depended on control sensitivity function Derive the closed-loop transfer functions of the system with unconstrained MPC.

29. 29HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Sensitivity function for single array systems Two-dimensional frequency bandwidth contour

30. 30HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Control sensitivity function for single array systems

31. 31HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain For additive unstructured uncertainty where is the representation of T ud (z) in the two -dimensional frequency domain. Robust Stability (RS) Condition K(z)G(z) + + (z)

32. 32HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 33HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Impact of MPC weights on Sensitivity Function 1 Interesting result: - MPC weight Q 2 on  u does not impact the spatial bandwidth - MPC weight Q 4 does not impact the dynamical bandwidth Encourages a separable approach to the tuning problem: 1 “Two-dimensional frequency analysis for unconstrained model predictive control of cross-directional processes”, Automatica, vol 40, no. 11, p. 1891-1903, 2004. 123456 x 10 0.5 1 1.5 2 2.5 3 3.5 4 4.5 |t yd (,e i2  )<0.7071 dynamical frequency  [cycles/second] spatial frequency [cycles/metre] -3 Q4Q4 Q2Q2

34. 34HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Tuning procedure ScalingModel preparation Input plant info and knob positions Horizon calculation Spatial tuningDynamical tuning Results displayOutput tuning parameters

35. 35HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 36HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Spatial tuning knobs in the tool

37. 37HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Tune the controller using spatial gain functions

38. 38HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Dynamical tuning knobs in the tool

39. 39HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Example 1: linerboard paper machine (1) Four CD actuator arrays: u 1 = Secondary slice lip; u 2 = Primary slice lip; u 3 = Steambox; u 4 = Rewet shower; Two controlled sheet properties: y 1 = Dry weight; y 2 = Moisture; Overall model G(z) is a 984-by-220 transfer matrix. Performance comparison between traditional decentralized control and auto-tuned MPC.

40. 40HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Example 1: linerboard paper machine (2)

41. 41HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Example 2: Supercalendars (1) Four CD actuator arrays: u 1 = top steambox; u 2 = top induction heating; u 3 = bottom steambox; u 4 = bottom induction heating; Three controlled sheet properties: y 1 = caliper; y 2 = top gloss; y 3 = 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. 42HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Example 2: Supercalendars(2)

43. 43HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Example 2: Performance Comparison Before control (2sigma) Traditional control (2sigma) Manual Tuning (2sigma) Automated Tuning (2sigma) Caliper0.08820.0758 (-14.06%) 0.0565 (-35.94%) 0.0408 (-53.74%) Topside Gloss 2.87114.0326 (+40.45%) 2.8137 (-2%) 1.5450 (-46.19%) Wireside Gloss 3.53332.7613 (-21.85%) 2.6060 (-26.24%) 2.3109 (-34.60%)

44. 44HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 46HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Motivation Actuator profile Measured Bump response CD position [space] 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.

47. 47HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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.) x j = f(j)

48. 48HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Current and Proposed Solutions

49. 49HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Solutions for Identification of Alignment Current Industrial Solutions: - Open-Loop Bumptest - Closed-Loop Probing Proposed Solution: - Closed-loop bumptest

50. 50HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Feedback diagram The standard closed-loop control diagram. - r = target (bias target) - u = actuator setpoint profile - y = scanner measurement profile G u y dydy + + + + dudu K - + r

51. 51HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Open-Loop Bumptest Procedure - Open-loop insert perturbation at d u - Then record the response in y, to extract model G. G u y dydy + + + + dudu K - + r Whenever possible, closed-loop techniques are preferred in a quality-conscious industry.

52. 52HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Closed-Loop Probing Procedure - Keep controller in closed-loop - Insert probing perturbation d u on top of the actuator profile - Then record the response in y, to extract model G. G u y dydy + + + + dudu K - + r Technique relies on transient response of y. In practice a noisy process and scanning sensor make dynamics difficult to extract reliably.

53. 53HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Proposed Solution: Closed-Loop Bumptest Procedure - Leave loop in closed-loop control - Insert perturbation on target d r as shown - Record the response in the actuator profile u. G uy dydy + + K + r drdr + + The control loop is exploited to extract alignment information. No need of addressing (exciting and modeling) dynamics to extract alignment information.

54. 54HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Overview of Background Theory

55. 55HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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 actuator 1 1 S.R. Duncan, "The Cross-Directional Control of Web Forming Processes", PhD thesis, University of London, 1989.

56. 56HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 57HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 58HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 59HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Example

60. 60HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 20mm60mm

61. 61HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Regular steady-state closed-loop operation CD controller tuned ‘as usual’ with integral action at low spatial frequencies.

62. 62HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Closed-loop response of profiles Bumps inserted into the bias target profile while CD control is in closed-loop.

63. 63HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Response relative to baseline profiles

64. 64HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain Profile partitioning DFT gain phase

65. 65HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 66HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 29.5mm 50.9mm x j = f(j)

67. 67HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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. 68HONEYWELL - CONFIDENTIAL CDC-ECC'05 Seville, Spain 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”, CDC’03, 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.