Elastic Web Processing Lines : Optimal Master Roller Position

Elastic Web Processing Lines : Optimal Master Roller Position

Jonathan FRECHARD Dominique KNITTEL

Web Handling Research Group, University of Strasbourg, France

and

LGeCo, INSA Strasbourg, France

[email protected]

1 AIMCAL Europe Web Handling Conference 2012

Introduction & motivation

Roll-to-Roll systems

• Modelling

• Control strategy

Influence of the master roller position

• Reference tracking performances

• Disturbance rejection

• Parametric robustness

Influence of the speed loop bandwidth

Conclusion

Outline


Roll-to-Roll experimental plant at University of Strasbourg

• Goal of this plant:

o To move the web at the expected speed

o To maintain the web tensions in a small range

Roll-to-Roll systems

Introduction


Roll-to-Roll systems usually contain a large number of

actuators

• The tension control requires an adequate position of the master

roller

• The master roller imposes the web speed of the processing line

• The other actuators ensure web tension control

Problem statement :

• Where is the optimal master roller position, in order to respect

the system requirements ?

• What is the influence of the master roller position on the web

tensions in the processing line ?

Problem formulation

Introduction


A dedicated system model has been developed for this study

• 7 driven rollers, 6 idle rollers having load cells

• Inputs : ui Control signal of the driven roller

Tin Web tension at system entrance

Vout Web speed at system exit

Tout Web tension at system exit

• Outputs : Ti Web tensions

Ωi Driven roller rotational speed

Modelling

Roll-to-roll systems


Web speed of the kth roller (assuming no slippage) :

Web strain between two consecutive rollers:

Linearization of the tension equation around a working point

T0 v0:

Modelling of Roll-to-Roll systems



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Speed control (Cv : IP controller : does not introduce a zero

in the closed-loop transfer function)

Tension control (Ct : PI controller)

Control strategy



Control strategy



decentralized control strategy with the master driven roller in second position

INFLUENCE OF THE MASTER ROLLER POSITION

11

• Web tensions close to the

master roller have better

performances

• Performances decrease for

web tensions far from the

master roller

Reference tracking performances

Influence of master roller position

12

Simulation with a web tension reference variation (step) :

Bode diagram of the three configurations :

• Solid lines : direct transfer function Trefi -> Ti

• Dashed lines : coupling transfer function Trefi -> Tj

Reference tracking performances


13

Disturbance signal composed of four sinus

• Fundamental : eccentricity

• Harmonics : non-circularity

• This disturbance signal is then added on several tensions in

order to test the disturbance rejection property of the three

configurations

Disturbance rejection



Disturbance on Tin

• Configuration with the master roller in second position is the

worst case

• The two other configurations give better results




Disturbance on TS5

• Web tensions close to the master roller have better

performances




Web elasticity variations :

• Configuration with the

master roller in sixth position

is not robust to web elasticity

variations

• Configuration with the

master roller in second

position is the most robust to

elasticity variations

• The observed results are

confirmed by the system

transfer function

Parametric robustness



Master roller in 2nd position 4th position 6th position

H∞ norm for E0 90 92 197

H∞ norm for E0 / 2 115 200 2812

H∞ norm increase(%) 28% 117% 1327%

Summary



Summary



Summary of the comparison between the 3 configurations

Master roller in Mean of reference

tracking error

Disturbance rejection Robustness regarding

E Variations

Second Position +++ + +++

Fourth Position ++ +++ ++

Sixth Position + +++ +

A lower bandwidth of

the speed loop filter

the tension reference

variation

Time domain simulation



Bode diagram of the closed loop system

• With lower crossover frequency of speed loop the maximum

singular value is lower

Frequency domain comparison



Master roller position depends on the plant requirements :

• Web tensions close to the master roller have better

performances

• The master roller should be chosen in the area where the web

tensions have to follow the reference with an higher precision

• To guarantee a better robustness to web elasticity variations,

the master roller should be located close to the unwinder

Application

• This study has also been validated on the nonlinear model of

an industrial roll-to-roll system

Conclusion


Elastic Web Processing Lines : Optimal Master Roller Position

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