Advanced Multivariable Fiber Orientation Control and Twist ... ppt.pdfFO Btm 0.66 0.30 54% 2.33 1.85...

Advanced Multivariable Fiber Orientation Control and Twist

OptimizationDanlei Chu, Ph.D., P.Eng.Cristian Gheorghe, P.Eng.Cristian Gheorghe, P.Eng.Johan Backstrom, P.Eng.

PaperCon 2011 Page 2412

Outline

• Introduction to Fiber Orientation (FO)t oduct o to be O e tat o ( O)

- FO angle, curl and twist

• Process Model• Process Model

- Band pass characteristics in the spatial frequency domain

• Controller Design

- Actuator edge padding (AEP) and gain retune

• Mill trial results

• Conclusions

PaperCon 2011 413

Introduction: Fiber Orientation

• Fiber orientation

- Fiber orientation (FO) refers to the dominant alignment

direction for fibers in a paper web. It can be expressed by a

fiber orientation angle and a fiber ratio.

α: Fiber Orientation Angleg

Fiber Ratio:

)( AxisShort )( Axis Long

sl

A cut and dry test


Introduction: Practical Issues

• Several paper quality properties are highly related to fiber orientation of whichorientation, of which

- The web strength, and- The dimensional stability are the most importantThe dimensional stability are the most important

(The ability of paper samples to retain their shape when subjected to varying degrees of temperature, moisture, stress, etc)

• Poor FO can ca se m ltiple practical iss es incl ding• Poor FO can cause multiple practical issues, including

- Paper jam in sheet-fed device,

- Mis-register in color printing,

- Twist in multilayer board, and

- Weakened corrugated containerboard.


Introduction: Curl & Twist

• Curl and twist are two measurements to indicate the deflection of a paper sheet

Rapid drying

of a paper sheet

xykykxkyxd xyyx 22),(non-uniform FO properties

• x: CD coordinate

non uniform FO properties

• y: MD coordinate• kx : CD curl coefficient• ky : MD curl coefficienty• kxy: Twist coefficient (diagonal curl coefficient)• d: deflection index


Introduction: Curl & Twist1

150600

0.5

d(x,

y)

1

0

50

100

0

20

40

Cross DirectionMachine Direction

500

0.5

1

d(x,

y)

MD Curl

10

2040

6080

100120

010

2030

4050

Cross DirectionMachine Direction

CD Curl

-0.5

0

0.5

d(x,

y)

btmtop

MDCDbtmtopfTwist

),,,,(

010

2030

4050

0

50

100

150-1

C Di tiMachine Direction

Twist

p Cross DirectionMachine Direction


Process Model: Spatial Frequency Characteristics

• Compares CDFO Processes to Standard CD Processes

0

0.5

1Spatial Impulse Response

eigt

h (g

sm)

0

1Spatial Impulse Response

(deg

)

-800 -600 -400 -200 0 200 400 600 800-0.5

0

CD Coordinate (mm)

Dry

We

Gain Spectrum

)

-800 -600 -400 -200 0 200 400 600 800-1

CD coordinate (mm)

FO

Gain Spectrum

0

0.1

0.2

Dry

Wei

gth

(gsm

)0

0.1

0.2

FO (d

eg)

Standard CD Processes:• Headbox Slice Lip Dry Weight

CD Fiber Orientation Processes• Headbox Slice Lip Fiber Orientation Angle

0 1 2 3 4 5 6 7

x 10-3

0

Spatial Frequency (1/mm)0 1 2 3 4 5 6 7

x 10-3

0

Spatial Frequency (1/mm)

• Low pass characteristics in spatial frequency• band pass characteristics in spatial frequency


Process Model: Spatial Model

• Slice Lip FO Angle Model

Th I l RTh I l R

• Process Gain

Defines the peak value of th ti l i l

0.1X: 68.45Y: 0.09996

The Impulse Response

0.1*20% = 0.02 deg

0.1X: 68.45Y: 0.09996

The Impulse Response

0.1*20% = 0.02 deg

the spatial impulse responses of a CDFO process

(gain = 0.1 deg/mil)0

0.05

Deg

)

X: 502.5Y: 0.01949

X: -502.50

0.05

Deg

)

X: 502.5Y: 0.01949

X: -502.5 (g g )

• Response Width

Defines the location where -0.05

0

FO (D

X: 502.5Y: -0.01949

-0.05

0

FO (D

X: 502.5Y: -0.01949

the impulse response drops to 20% of its peak value(width = 1000 mm)

-1000 -800 -600 -400 -200 0 200 400 600 800 1000

-0.1 Response Width = 1000 mm

-1000 -800 -600 -400 -200 0 200 400 600 800 1000

-0.1 Response Width = 1000 mm

CD Coordinates (mm)CD Coordinates (mm)


Process Model: Identification

• Model Test Results on a Three-layer Board Machine

0

0.5

Deg

Top FO Angle

Pl

0.5

1

eg

Bottom FO Angle

PlantModel

0 50 100 150 200 250 300 350 400-1

-0.5

CD Bins

D

1000Top Slice Bumps

PlantModel

0 50 100 150 200 250 300 350 400-0.5

0

CD Bins

De

Bottom Slice Bumps

1000

0

1000

mic

ron

0

1000

mic

ron

Model identification results on the top headbox• Process Gain = ‐0.0025 deg/micron

Model identification results on the bottom headbox• Process Gain = 0.002 deg/micron

0 5 10 15 20 25 30 35 40-1000

Actuator Zones0 5 10 15 20 25 30 35 40

-1000

Actuator Zones

• Response Width = 2000 mm • Response Width = 2000 mm


Controller Design

• The Schematic of a CDFO Control System Capture Nonlinearity

Capture Severe Edge Effect


Control: Actuator Edge Padding

• Actuator Edge Padding Captures Severe Edge Effects

-5

0

5

Set

poin

t

Flat padding

physicalvirtual

uGzhy •1 2 3 4 5 6 7 8 9 10

-5

Actuator zones

10

t

Linear padding

augauguGzhy•

uuu

u

lpad

d

•

1 2 3 4 5 6 7 8 9 10-10

0

Actuator zones

Set

poin

t uuuuhpad

aug mod

•

-5

0

5

Set

poin

t

Reflection padding

uGzhy aug mod)( •

G’1 2 3 4 5 6 7 8 9 10Actuator zones

G’


MPC: Gain Retune

• Gain Retune Captures the nonlinearity of Fiber Orientation ProcessProcess

kqq

lamo

eqq

gg

2)(

0

1

• q: the difference between the Jet Speed and the Wire Speed;

• q0: The crossover point where the paper machine is operated in neither “rush” nor “drag”

• glam: Laminar Gain (Model Parameter)

• k: Jet Turbulence (Model Parameter)


Control: MPC

• The Fiber Orientation CD-MPC Controller

||)(||||(||min 2

1

2

)( 21kUYikY Q

H

iQspkU

p

)()(||)(|| 42

1)(

3kUQkUUkU T

Qtgt

i

Subject toSubject to,

)1()( kCUbkUA

)()()( kUzhGkY

Actuator Physical Limits

Fiber Orientation P M d l)()()( kUzhGkY Process Model

Besides FO angles and twist profiles, other CD measurement, (dry weight, g p , , ( y g ,moisture, caliper) can be optionally added to the above MPC controller.


Mill Test Results

• Mill Configuration - A multi-ply carton board machine in Finland.p y- Control Scenario

ControllerType

Actuators Measurements(420 CD Bins)Type (420 CD Bins)

Top Headbox Slice Lip(42 zones)

Top Fiber Orientation Angle

MPC ( ) g

Bottom Fiber Orientation AngleBottom Headbox Slice Lipp

(42 zones)Twist Proxy

(Top – Bottom Angle)


Mill Trial Results - Profiles

4

6

8

e (d

eg)

The profiles of top FO angle

2

4

e (d

eg)

The profiles of bottom FO angle

2

4

6

e (d

eg)

The profiles of twist

0 2000 4000 6000-2

0

2

FO A

ngle

0 2000 4000 6000

-4

-2

0

FO A

ngle

0 2000 4000 6000

-4

-2

0

FO A

ngle

0 2000 4000 6000

CD Position (mm)0 2000 4000 6000

CD Position (mm)0 2000 4000 6000

CD Position (mm)

500

1000

The setpoints of top slice lip

rons

)

500

1000The setpoints of bottom slice lip

rons

)

1000

-500

0

Set

poin

t (M

icr

1000

-500

0

Set

poin

t (M

icr

Before MPCAfter MPC

Fiber Orientation Angles and Twist Proxy Profiles• All controllable disturbances are effectively removed by the MPC controller

0 10 20 30 40-1000

Actuator Zones

0 10 20 30 40

-1000

Actuator Zones

• All controllable disturbances are effectively removed by the MPC controller.


Mill Trial Results – Power Spectrum

1The Power Spectrum of FO Angle Top

0 25The Power Spectrum of FO Angle Btm

0 8The Power Spectrum of Twist

0 6

0.8

1

r (de

g)

0 15

0.2

0.25

r (de

g)

0.5

0.6

0.7

0.8

r (de

g)

Before MPCAfter MPC

0.2

0.4

0.6

Abs

olut

e po

wer

2Xa-3db Xc

0.05

0.1

0.15

Abs

olut

e po

wer

2Xa-3db Xc

0.2

0.3

0.4

Abs

olut

e po

wer

2Xa

inf 694 347 2310

Spatial wavelength (mm)

inf 694 347 231

0


inf 694 347 231

0

0.1


Fiber Orientation Angles and Twist Proxy Profiles• All controllable disturbances are effectively removed by the MPC controller.


Mill Test Results – Average & 2-Sigma

• Comparisons Before and After the Fiber Orientation Control

Statistics Average Two-Sigma

Before After Improve Before After ImproveMeas. Before After Improvement

Before After Improvement

FO Top 2.72 1.26 54% 2.26 1.54 32%

FO Btm 0.66 0.30 54% 2.33 1.85 20%

Twist 1.65 0.96 42% 2.50 2.20 12%

Both the averages and the 2-sigma spreads (two times of the standard derivation) ofBoth the averages and the 2 sigma spreads (two times of the standard derivation) of FO angle profiles and twist profiles are improved significantly.


Mill Test Results – Lab Measurements

• Comparisons Before and After the Fiber Orientation Control

Here, the twist average values are measured in the lab.


Conclusions

• The CDFO spatial model has only two parameters. The model is very

intuitive and easy to identify.

• Actuator edge padding algorithm captures the severe edge effects of the

fiber orientation process.

• Gain retune algorithm captures the nonlinearity of the fiber orientation

process with respect to Jet/Wire ratio and wire speed.

• Automatic controller retune algorithms make the CDFO controller adaptive

to the processes variation

• The resulting MPC controller is able to significantly reduce the variance of

twist and CD fiber orientation angle profiles.


Advanced Multivariable Fiber Orientation Control and Twist ... ppt.pdfFO Btm 0.66 0.30 54% 2.33 1.85...

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