Journal of Process Control 20 (2010) 643–652

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Journal of Process Control

journal homepage: www.elsevier .com/ locate/ jprocont

A novel cross directional register modeling and feedforward controlin multi-layer roll-to-roll printing

HyunKyoo Kang a,1, ChangWoo Lee b, KeeHyun Shin b,*

a Department of Mechanical Design, Konkuk University, 1 Hwayang-Dong, Gwangjin-Gu, Seoul 143-701, Republic of Koreab Department of Mechanical Engineering, Konkuk University, 1 Hwayang-Dong, Gwangjin-Gu, Seoul 143-701, Republic of Korea

a r t i c l e i n f o

Article history:Received 6 July 2009Received in revised form 22 October 2009Accepted 27 February 2010

Keywords:2-D RegisterMulti-layer registrationFeedforward controlRoll-to-rollGravure printingPrinted electronics

0959-1524/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.jprocont.2010.02.015

* Corresponding author. Tel.: +82 2 450 3072; fax:E-mail addresses: hyunkyoo@gmail.com (H.

(K. Shin).1 Tel.: +82 2 3436 0321; fax: +82 2 447 5886.

a b s t r a c t

For the adaption of roll-to-roll printing method to the printed electronics, it is mandatory to increase theresolution of register control. Therefore, it is desired to derive a mathematical model for register and todevelop a controller to reduce the register error. The cross direction register error was derived consider-ing both the lateral motion of a moving web and the transverse position of a printing roll. And a feedfor-ward control method was proposed to cancel out the disturbance of CD register from upstream span. Theproposed controller could be used to improve the performance of the CD register controller in a large arearoll-to-roll printing machine. The mathematical modeling and proposed control method were validatedby numerical simulations and experimental verifications in various operating conditions using a multi-layer direct gravure printing machine. These results show that the proposed feedforward control schemegreatly improves the control performance of register control in overcoming the upstream disturbances.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The rising demand for the fabrication of flexible electronicsusing roll-to-roll technology exposes the abundant challenges ofconducting low cost and highly productive printing trials forexperiments. Many demonstrations have been conducted usingdiscrete printing methods such as sheet printing, ink-jet printing,spin coating because of their high accessibility and ability to exper-iment with fewer material [1–6]. Other researchers carried out lab-oratory scale continuous printing with gravure, flexography, offset,etc. [7–12], but this is not sufficient to cover the adaption of largearea, continuous roll-to-roll printing for printed electronics. Ifthere are several printing rolls between the unwinder and rewind-er for multi-layer patterning, each printing roll has not only a var-iation of phase but the web also goes along the path with a lateralmovement and variation of strain. Thus the strain and lateral posi-tion of the substrate should be controlled to minimize the registererrors in successive roll-to-roll printing.

Register error of a moving web is defined in two printing rollersas the relative difference of the distance between the previousprinted pattern by the upstream printing roller and the printedpattern in the downstream printing roller. Register error is defined

ll rights reserved.

+82 2 447 5886.Kang), khshin@konkuk.ac.kr

as two-dimensional errors: machine direction (MD) and crossdirection (CD) errors as shown in Fig. 1.

The register error is as critical as surface topography in ensuringthe functionality of a printed circuit without mistakes. It deter-mines the printing quality of final products. In addition, the print-ing quality is more important in printed electronics because shortsor leakages could be generated due to the register error of multi-layered patterns in printed electric devices, such as organic photo-voltaic and flexible displays. Therefore, the register error of a mov-ing web should be precisely controlled for the fabrication ofprinted electronics.

Brandenburg derived a linear mathematical model of the ma-chine direction register error of a moving web in a first-order dif-ferential equation by using an equilibrium equation of masswhich is transported by printing rolls. A non-interacting controlmethod between the tension and cut-off register error was alsoproposed [13,14]. Yoshida proposed a nonlinear MD register con-troller to compensate for a downstream register error caused byupstream tension fluctuation in gravure printing. Komatsu devel-oped a delay-dependent nonlinear control approach by adjustingthe new coordinate and delay-dependent feedback law [15,16].

All of these results were carried out with the typical assumptionthat a lateral position of a moving web is not changed in the ma-chine direction, so there is no CD register error in multi-layeredprinted patterns. However, actually the lateral position of a movingweb varies along the web path within a certain range, and it makesCD register errors in printed patterns. Therefore, it is necessary to

Fig. 1. Two-dimensional register errors.

644 H. Kang et al. / Journal of Process Control 20 (2010) 643–652

derive a mathematical model of the CD register for more accurateregister control, but there has been no report that deals with thedynamics of the CD register.

In this paper, a mathematical model of the CD register was de-rived by using both the lateral dynamics of a moving web and therelative difference of lateral positions between a printing roll and aweb which goes through the printing section. The CD register wascontrolled by the translation motion of a printing roll, and thetranslation could generate a transient CD register in downstreamprinting sections. A feedforward controller was designed to com-pensate for the deterministic disturbance of the CD register. Themodeling was validated, and the performance of the proposed con-troller was verified by numerical simulations and experiments. Theresults show that the proposed modeling is accurate enough to de-scribe the CD register and the performance of the suggested con-troller is more effective in reducing the deterministic CD registererrors than that of the traditional PID controller.

Fig. 2. Boundary conditions.

2. Mathematical modeling

In this section, the modeling of the lateral motion of a movingweb, which was suggested by Shelton, was summarized and themodeling of CD register was derived by using the lateral motionof a moving web, including translations of printing rolls [17,18].Shelton derived first- and the second-order models of the lateralmotion of a web. The lateral motion could be described more accu-rately by the second-order model than the first-order one. Thus thesecond-order model was summarized and used for the derivationof the CD register error.

2.1. Second-order lateral motion of a moving web

The differential equation of the web elastic curve could be de-rived from beam theory if the tension acts on the web. The beamequation, which is a fourth-order differential equation, is shownin Eq. (1). Eq. (2) is a general solution of Eq. (1), and the boundaryconditions shown in Fig. 2 can be used to determine the coeffi-cients of Eq. (2). The boundary conditions are Eq. (3):

@4y@x4 � K2 @

2y@x2 ¼ 0; K2 ¼ T

EIð1Þ

where EI is the bending stiffness

y ¼ C1 sinhðKxÞ þ C2 coshðKxÞ þ C3xþ C4 ð2Þyð0Þ ¼ y0; hð0Þ ¼ h0; yðLÞ ¼ yL; hðLÞ ¼ hL ð3Þ

Using Eq. (2), the curvature of the downstream roll could be ob-tained as Eq. (4):

@2y@x2

�����x¼L

¼ f1ðKLÞL2 ðy0 � yLÞ þ

f2ðKLÞL

hL þf3ðKLÞ

Lh0 ð4Þ

where

f1ðKLÞ ¼ ðKLÞ2ðcoshðKLÞ�1ÞKL sinhðKLÞ�2 coshðKLÞþ2

f2ðKLÞ ¼ KLðKL coshðKLÞ�sinhðKLÞÞKL sinhðKLÞ�2 coshðKLÞþ2

f3ðKLÞ ¼ KLðsinhðKLÞ�KLÞKL sinhðKLÞ�2 coshðKLÞþ2 :

Fig. 3. Poles of lateral model (KL is 0–10).

H. Kang et al. / Journal of Process Control 20 (2010) 643–652 645

The lateral velocity of a web is as shown in Eq. (5) and the lat-eral acceleration is given by Eq. (6):

dyL

dt¼ V hr �

@yL

@x

� �þ dwL

dtð5Þ

d2yL

dt2 ¼ V2@2y@x2

�����L

þ d2wL

dt2 ð6Þ

where @yL@x is the slope of the web at the downstream roll.

Fig. 4. Schematic of three-

Fig. 5. Three-layer gravu

Substituting Eqs. (4) and (5) into Eq. (6), the second-orderdifferential equation could be derived as Eq. (7):

d2yL

dt2 ¼ a1dyL

dtþ a2yL þ a3

dy0

dtþ a4y0 þ a5uL þ a6u0 þ b1

d2wL

dt2

þ b2dwL

dtþ b3

dw0

dtð7Þ

h ¼ @y@x; hr ¼

uc; s ¼ L

V; a1 ¼ �

f2ðKLÞs

; a2 ¼ �f1ðKLÞs2 ;

a3 ¼ �f3ðKLÞ

s; a4 ¼

f1ðKLÞs2 ; a5 ¼

V2

Lcf2ðKLÞ

where a6 ¼ V2

Lc f3ðKLÞ; b1 ¼ 1; b2 ¼ f2ðKLÞs ; b3 ¼ f3ðKLÞ

s , L = span length,V = velocity, c = half width of roll and u = arc of rotation.

In the printing section, the CD register error should be con-trolled by only translational motions of printing rollers so thatthe lateral motion of Eq. (7) yields as in Eq. (8). The transferfunction, the response of yL to the input of y0, wu and w0 couldbe derived as Eq. (9):

d2yL

dt2 ¼ a1dyL

dtþ a2yL þ a3

dy0

dtþ a4y0 þ b1

d2wL

dt2 þ b2dwL

dtþ b3

dw0

dtð8Þ

YLðsÞ ¼ AðsÞY0ðsÞ þ BðsÞWLðsÞ þ CðsÞW0ðsÞ ð9Þ

where AðsÞ ¼ a3sþa4s2�a1s�a2

; BðsÞ ¼ b1s2þb2ss2�a1s�a2

and CðsÞ ¼ b3ss2�a1s�a2

.

For the stability analysis of the lateral model equation (9), poles

of the model are determined as a1 þ a21 þ 4a2

� �1=2h i

=2 and

layer printing system.

re printing machine.

Fig. 6. CD register errors and lateral position of the web at each printing roll causedby the translation of the second printing roll (30 m/min, 100 N).

Fig. 7. CD register error and lateral position of the web at each printing rolls causedby translation of the second printing roll (40 m/min, 100 N).

646 H. Kang et al. / Journal of Process Control 20 (2010) 643–652

a1 � a21 þ 4a2

� �1=2h i

=2. In Fig. 3, poles of lateral model were de-picted with varying KL (0–10). In roll-to-roll system, the ‘KL’ is lessthan 1, because of large amount of Young’s modulus (E) of sub-strate. In the experiment, the parameter ‘KL’ is 0.66. Therefore,the range of KL, 0–10, is reasonable and it can be proved the lateralmodel is stable in various KL.

2.2. Cross directional register error modeling

The schematic view of the three-layer printing system is shownin Fig. 4. When the second printing roll prints a pattern on the web,the CD register error is produced by the relative difference of thelateral positions of both the successive printing roll and the movingweb. The CD register may occur due to the relative distances ofprinting rolls even with a straight moving web. Furthermore, thereare no translations of printing rolls, and the CD register error is alsoinduced by the variation of lateral positions of the moving web.Accordingly it is significant to control the lateral position of boththe web and the printing roll, compared to the lateral position ofthe upstream-pattern that has traveled in the instance of currentprinting of a pattern for CD registration.

The CD register is composed of two patterns that imply the his-tory of printing as a period of time constant (L/V). This means thatthe upstream-pattern (roll No. 1 in Fig. 4) made ahead of the ‘‘timeconstant‘‘ and the pattern currently being printed downstream(roll No. 2 in Fig. 4) complete the definition of the CD register asshown in Eq. (10):

ry;nðtÞ ¼ ½ynðtÞ �wnðtÞ� � ½yn�1ðt � sÞ �wn�1ðt � sÞ� ð10Þ

where ry,i is the ith CD register, yi is the lateral position of the ithweb and wi is the lateral position of the ith roll.

The lateral position of a moving web is calculated by Eq. (9), andthe lateral position of a printing roll is the input value of a transla-tional motion. Eq. (10) could be Laplace-transformed as in Eq. (11):

Ry;nðsÞ ¼ ½YnðsÞ �WnðsÞ� � ½Yn�1ðsÞ �Wn�1ðsÞ�e�ss ð11Þ

Under the assumption that all spans, which are structured be-tween printing rolls have same length, Eq. (9) of the lateral positionof the web would be expanded as in Eq. (12):

Yn�1ðsÞ ¼ AðsÞYn�2ðsÞ þ BðsÞWn�1ðsÞ þ CðsÞWn�2ðsÞYnðsÞ ¼ AðsÞYn�1ðsÞ þ BðsÞWnðsÞ þ CðsÞWn�1ðsÞ

ð12Þ

Substituting Eq. (12) into (11) and rearranging the resulting equa-tion yields Eq. (13):

Fig. 8. Block diagram of CD register controller. (a) Conventional CD register controller using feedback. (b) Proposed CD register error controller using feedforward andfeedback loop.

Fig. 9. Simulation model.

Table 1Simulation parameters.

Simulation parameters Values

Operating tension 100 NOperating velocity 30, 40 m/minLength of span (between idle rolls) 1 mLength of span (between printing rolls) 8 mP gain of CD register feedback controller 0.01D gain of CD register feedback controller 0.15Thickness of web 12 lmWidth of web 1 mYoung’s modulus 3.6 GPaMoment of inertia (I) 1 � 10�6 m4

Number of span between printing rolls 8Warm gear ratio 4.7746 � 10�4 m/rad

H. Kang et al. / Journal of Process Control 20 (2010) 643–652 647

Ry;nðsÞ ¼ AðsÞ½Yn�1ðsÞ � Yn�2ðsÞe�ss� þ BðsÞ½WnðsÞ�Wn�1ðsÞe�ss� þ CðsÞ½Wn�1ðsÞ �Wn�2ðsÞe�ss�� ½WnðsÞ �Wn�1ðsÞe�ss� ð13Þ

In addition, the roll-to-roll printing machine consists of manyidle rolls in the middle of the printing sections for the preventionof wrinkling of a moving web or the construction of desired spanlength and wrap angle for dryers, prevention of slippage, and soon, as Fig. 5. Therefore, Eq. (10) of the CD register should be ex-panded in order to include idle rolls as in Eq. (14). SubstitutingEq. (12) of the lateral position of the web into Eq. (14) and its La-place-transformation yields Eq. (15):

ry;nðtÞ ¼ ½ynðtÞ �wnðtÞ� � ½yn�mðt � smÞ �wn�mðt � smÞ� ð14Þ

648 H. Kang et al. / Journal of Process Control 20 (2010) 643–652

Ry;nðsÞ ¼ AðsÞm�1½AðsÞBðsÞ þ CðsÞ�wn�mðsÞ þ BðsÞwnðsÞ �wnðsÞþwn�mðsÞe�sms � BðsÞwn�mðsÞe�sms ð15Þ

where m is the number of spans between a pair of printing rollsstructured by idle rolls and s is the complex number.

Step responses of the lateral position and the CD register causedby a translational motion of the second printing roll are depicted inFigs. 6 and 7 at different operating conditions. The translation gen-erates a transient variation of the lateral position of y1, and the lat-eral variation transferred to the downstream as y2 after time delay(L/V), as shown in Figs. 6(b) and 7(b). On the other side, the trans-lation motion induces steady-state CD register disturbances at thesecond printing roll (Ry1), and they are transferred to the down-stream printing roll (Ry2). The transferred CD register has the samemagnitude and reverse direction compared with the upstream CDregister in Figs. 6(a) and 7(a). Therefore, in order to increase theresolution of the registration, the transferred CD register of thedownstream should be compensated. In Figs. 6 and 7, there weredifference in the settling time of Ry2 between the estimated andexperimental results because each actual span length of printingsections structured by idle rolls are different from estimated ones

Fig. 10. Performance of the feedforward including PID controller (computersimulation: T = 100 N, V = 30 m/min). (a) CD register error. (b) Lateral position.

which were assumed to be the same. The difference is also due tomechanical loss such as belting and inertia effect.

3. Proposed CD register controller

3.1. Block diagram of CD register controller

In this section, experiments on the CD register control of a mov-ing web using a feedforward controller are described. For the exper-iment, the step input of the translation motion is generated by thesecond printing roll as a disturbance. The third printing roll is usedto control the CD register error in this experiment. The block dia-gram of a conventional CD register controller using feedback con-trol is illustrated in Fig. 8(a). The CD register control system iscomposed of a side-lay motor, motor driver and optical sensorsfor measuring register error. The CD register error could be regu-lated by the translation motion of the printing rolls compared withthe relative transverse position of a pair of printed patterns.

The mathematical model of side-lay motor is described in Eq.(16):

GmðsÞ ¼hðsÞUðsÞ ¼

km

s2 þ amsþ kmð16Þ

Fig. 11. Performance of the feedforward including PID controller (computersimulation: T = 100 N, V = 40 m/min). (a) CD register error. (b) Lateral position.

Fig. 12. Experimental setup.

Fig. 13. Three-layer gravure printing machine.

H. Kang et al. / Journal of Process Control 20 (2010) 643–652 649

where U(s) is the motor input, am, km are motor constants and h isthe angular position of motor.

The rotation of the side-lay motor is converted into the transla-tion motion of the printing roll using the worm gear as in Eq. (17):

KðsÞ ¼ wðsÞhðsÞ ¼ kw ð17Þ

where kw is constant of worm gear ratio.The lateral dynamics of a web caused by translation motion is

determined by a transfer function as in Eq. (18) and the effect oftranslation motion of upstream printing roll which was transferredseveral idle rolls is expressed as in Eq. (19):

BðsÞ ¼ b1s2 þ b2ss2 � a1s� a2

ð18Þ

DðsÞ ¼ AðsÞðm�1ÞfAðsÞBðsÞ þ CðsÞg ð19Þ

where m is the number of spans between a pair of printing rollsstructured by idle rolls and s is the complex number.

A block diagram of the proposed feedforward controller isshown in Fig. 8(b). A translation motion of the printing roll couldreduce the CD register error in current roll but it also causes aCD disturbance for the CD register error to the following printingroll. As a result of that the proposed controller is aimed to compen-sate for the CD register error generated by translation of the up-stream printing roll. Substituting Eqs. (9) and (12) into Eq. (18)and the Laplace-transforming CD register error yields Eq. (20):

The control input to eliminate the effect of the upstream distur-bance of wn–m is calculated as Eq. (21) and the control input of theCD register error is shown in Eq. (22):

Ry;nðsÞ ¼ HusðsÞwn—mðsÞ þ HdsðsÞwnðsÞ ð20Þ

UFFðsÞ ¼HusðsÞHdsðsÞ

wn�mðsÞ ð21Þ

UðsÞ ¼ UFBðsÞ þ UFFðsÞ ð22Þ

where HusðsÞ ¼ DðsÞ þ ½1þ BðsÞ�e�sms; HdsðsÞ ¼ BðsÞ � 1 andUFB ¼ control input of PID controller.

3.2. Simulation results

Numerical simulations to verify the performance of the pro-posed feedforward CD register controller were carried out usingSIMULINK (The Mathworks Inc., Natick, MA). The three-layer print-ing system is designed as shown in Fig. 9. The system includes twokinds of measuring sensors: EPS (edge position sensor) for the lat-eral position of the web and OS (optical sensor) for the register er-ror of the printed pattern.

All of the tensions except the printing section are controlledwith a PI controller and loadcell. In the printing sections, the print-ing rolls are controlled to preserve the same phase of the printingpatterns for MD register control. The printing rolls also have side-lay motors and worm gears to regulate the CD register by transla-tion. The simulation conditions are described in Table 1.

Fig. 14. Loadcell (left), optical sensor (middle) and infrared sensor (right).

Fig. 15. Performance of the feedforward including the PID controller. (a) CD registererror at 100 N, 30 m/min. (b) CD register error at 100 N, 40 m/min. Fig. 16. Lateral position of the web (experiment: T = 100 N, V = 30 m/min). (a)

Lateral position of the PD control. (b) Lateral position of the feedforward includingthe PD control.

650 H. Kang et al. / Journal of Process Control 20 (2010) 643–652

Figs. 10 and 11 show the performance of the conventional andthe proposed controller at different operating velocities. The dis-turbance of the translation of the second printing roll starts at

5 s, and the third printing roll controls the CD register with PDand feedforward controller. The operating tension is 100 N. Theline speed is 30 and 40 m/min in Figs. 10 and 11, respectively.

Fig. 17. Lateral position of the web (experiment: T = 100 N, V = 40 m/min). (a)Lateral position of the PD control. (b) Lateral position of the feedforward includingthe PD control.

H. Kang et al. / Journal of Process Control 20 (2010) 643–652 651

As shown in Figs. 10 and 11, the proposed controller reducedthe CD register error to less than 70% of the overshoot of the sys-tem response where the feedback control was used. The residueof CD register errors are caused by the feedforward controller notincluding the side-lay motor dynamics. The proposed controlmethod could be used to reject the CD register caused by transitionof a printing roll between adjacent spans.

3.3. Experimental results

The experimental studies were carried out in order to verify theperformance of the proposed feedforward CD register controllerusing the three-layer gravure printing machine. The experimentalsetup is shown in Fig. 12, and experimental conditions are sameas those of Table 1.

Fig. 13 shows the system configuration for the experiment. Thesystem includes unwinding, rewinding, infeeding, outfeeding,three printing rollers, a commercial register controller (ArTec.Co.), and a main controller (Bosch Rexroth, PPC). In each span, ten-sions were measured by the loadcell (Dover, Model C2DFL) with an

amplifier (Dover, TI17), as shown in Fig. 14(left). The registermarks were measured by an optical sensor and amplifier (ArTec.Co.), as shown in Fig. 14(middle). The lateral positions of the mov-ing web were measured by infrared sensor (FIFE, SE-23) with anamplifier, as shown in Fig. 14(right). Data acquisition software,LabView 8.2 (National Instruments), was used for collecting andsaving the signal of loadcell, infrared sensor and optical sensorswith DAQ board (National Instruments, SCC-68) and an A/D con-verter (National Instruments, PXI-6251).

The experimental results are shown in Figs. 15–17, and theoperating conditions are 100 N of tension and 30 and 40 m/minof velocity. The proposed controller reduced the transient CD reg-ister error 0.2 mm lower than the PD controller in simulation, asshown in Figs. 10(a) and 11(a). The CD register error was decreased0.5–0.3 mm lower than by the PD controller in experimental resultas shown in Fig. 15. The difference in performance is due to themodeling error, mechanical loss and cross direction slip betweenthe web and the nip roller in printing.

In Figs. 16 and 17, the second lateral position of web (y2) of thefeedforward including the PD control is changed more than that ofthe PD control. However, the larger displacement lateral (y2) of thefeedforward control increases the performance of the CD register.

It is concluded that even though the proposed controller cannotreject the CD register error perfectly, the proposed control methodreduces the transient CD register error more than 50% in settlingtime and 40% in overshoot compared with the PD control only.

4. Conclusion

A novel mathematical model for the CD register error was de-rived by using the lateral position of a moving web, translation mo-tion of printing rolls and time constant (L/V). The register erroroccurred because of the relative difference between adjacentprinted patterns on the web. Therefore, the lateral position of aweb should be considered to control the CD register error. A feed-forward controller was designed to reject the deterministic distur-bance in a previous span caused by the translational motion of theprinting roll. The performance of the proposed controller was dem-onstrated to be very effective by the numerical simulations andexperimental studies.

Generally printing rolls should be translated to control the CDregister; therefore, the proposed feedforward controller is veryuseful for improving the performance of the CD registration.

Acknowledgements

This research was supported by the Seoul R&BD Program(10848) and the Korea Foundation for International Cooperationof Science & Technology (KICOS) through a grant provided by theKorean Ministry of Education, Science & Technology (MEST) inK20701040600-09A0404-05410.

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