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XD

a

ARRAA

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gbdtimcottatntaowmfla

h0

Precision Engineering 45 (2016) 332–341

Contents lists available at ScienceDirect

Precision Engineering

jo ur nal homep age: www.elsev ier .com/ locate /prec is ion

recision design and control of a flexure-based roll-to-rollrinting system

i Zhou, Dien Wang, Ji Wang, Shih-Chi Chen ∗

epartment of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

r t i c l e i n f o

rticle history:eceived 5 May 2015eceived in revised form 1 February 2016ccepted 13 March 2016vailable online 15 March 2016

eywords:

a b s t r a c t

This paper presents the design, characterization, and control of a flexure-based roll-to-roll (R2R) printingsystem that achieves nanometer level precision and repeatability. The R2R system includes an unwind-ing/rewinding module, a web guide mechanism, and a core positioning stage consisting of two monolithiccompliant X–Y stages that control the position/force of the print roller. During the printing process, capac-itance probes, eddy current sensors and load cells are used to monitor the displacements of the flexurestage and contact force in real time. Control strategies, including decoupling, PID, and cascade control,

ompliant mechanismoll-to-roll processecoupling controlicrocontact printing

have been implemented to decouple the cross-axis and cross-stage motion coupling effect and improvethe overall precision and dynamic performance. In actual printing processes, the contact force and rollerposition can be uniformly controlled within ±0.05 N and ±200 nm respectively across a 4 in. wide PET web.To demonstrate the performance, a positive microcontact printing (MCP) process is adapted to the R2Rsystem, printing various fine metal patterns, e.g., optical gratings and electrodes, in a continuous fashion.

. Introduction

In recent years, roll-to-roll (R2R) printing technologies, e.g.,ravure and flexography, have been successfully utilized in a num-er of emerging applications such as organic photovoltaic (OPV)evices and flexible electronics. They present tremendous advan-ages in terms of cost and throughput; however, the technologys limited to a resolution of ∼20 �m [1], which limits the perfor-

ance of electronic devices. The limited print resolution is largelyaused by the mechanical performance of R2R machines, i.e., usef conventional bearings, backlash and assembly errors, etc. Onhe other hand, since R2R processes are inherently a contact prin-ing process, its resolution is not limited by the diffraction of lightnd should therefore reach submicron level. Recently, various con-act printing processes, e.g., microcontact printing (MCP) [2–9] oranoimprint [10–14], have demonstrated 50–100 nm print resolu-ion at laboratory scale. To adapt these methods to R2R processes,

R2R system with matching mechanical precision must be devel-ped; a few prototypes of flexure-based R2R printing systemsere developed with reasonable success [15,16], and the contact

echanism of the MCP process was studied [17–19]. However, a

exure-based R2R platform that meets all required specificationsnd precision for large-area high throughput R2R processing has yet

∗ Corresponding author. Tel.: +852 39434136.E-mail address: scchen@mae.cuhk.edu.hk (S.-C. Chen).

ttp://dx.doi.org/10.1016/j.precisioneng.2016.03.010141-6359/© 2016 Elsevier Inc. All rights reserved.

© 2016 Elsevier Inc. All rights reserved.

to be developed. In this work, we developed a flexure-based R2Rsystem that achieves nanometer level precision and repeatabilityin all critical axes. Multi-axis error correction capability is criticalfor large-area R2R processes as it compensates the “yaw” and “roll”errors between the rollers that cause misalignments, non-uniformpressure distribution, and pattern distortion. We selected MCP overnanoimprint for the R2R application due to its advantage in printingspeed and its more challenging positioning requirements.

Typical R2R systems consist of a rewinding module, unwindingmodule, tension controller, web guide module and other functionalmodules, e.g., deposition, inking, printing, thermal processing,etching, cleaning, and packaging. The rewinding module drivesthe continuous web/substrate passing through each functionalmodules while the unwinding module holds the web/substrate tobalance the tension; the tension controller enables the web to movein a steady state with constant tension; the web guide modulealigns the lateral position of the web on the roller. To adapt MCP, ourR2R system must meet the following requirements: (1) ∼100 nmrepeatability, (2) submicron level position control in all criticalaxes, (3) better than 0.1 N printing force control, and (4) 10 ± 0.1 Nweb tension control. These stringent requirements are necessarybecause in MCP an elastomer stamp with fine features are used totransfer the nanoscale patterns; since the features on the stamp

must have a ∼1:1 (height to feature size) aspect ratio, the relativeposition between the print roller and the web becomes criticallyimportant; over pressing the stamp will cause failure of patterntransfer. For high quality prints, web tension is usually controlled

dx.doi.org/10.1016/j.precisioneng.2016.03.010http://www.sciencedirect.com/science/journal/01416359http://www.elsevier.com/locate/precisionhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.precisioneng.2016.03.010&domain=pdfmailto:scchen@mae.cuhk.edu.hkdx.doi.org/10.1016/j.precisioneng.2016.03.010

X. Zhou et al. / Precision Engine

Table 1Functional requirements of the R2R system.

Print resolution 300 nm, i.e., multi-axis roller motion controlwith 100 s nm precision

Printing force 0–25 ± 0.1 N

wTltt

2

sumpcK(fitcfe

Fc

Printing speed 0–50 ft/minWeb tension 0–50 ± 0.10 N

ithin 10–25% of its strength to prevent web sagging/wrinkling.he tension value is calculated based on PET substrates. To realizearge-area and high throughput, a 4 in PET web was selected andhe target print speed is 2 ft/min. The functional requirements ofhe R2R system are summarized in Table 1.

. Design of the R2R system

Fig. 1 presents the prototype of our R2R printing system [20]. Theystem consists of the following submodules: (1) rewinding mod-le, (2) printing module, (3) tension control module, (4) web guideodule, and (5) unwinding module, where precise MCP printing is

erformed at the critical printing module. The rewinding moduleonsists of custom-built rollers driven by a servo motor (AKM12E,ollmorgen). The printing module consists of an impression roller

red), affixed to a coarse Z-stage, and a print roller, guided by aour-axis compliant positioner. During the printing process, thempression roller is first lowered to the vicinity (

3 ngineering 45 (2016) 332–341

soeaVoadKtsoiri

3

smttcdptttbapiYLbe±ut

E

k

k

K

bFpXpstbFgctrr

Fig. 3. Kinematic and dynamic model of the print roller assembly, where the springsat the two ends of the print roller represent the X–Y stages. In the model, kyi and cyiare the stiffness and damping coefficients of each X–Y stage (i = 1, 2); K� and C� are

34 X. Zhou et al. / Precision E

hown in Fig. 2(b). The compliant stage is designed to have a rangef 2 mm in both X and Y directions. Both stages are driven by lin-ar stepper motors (M230.10S, PI) in the X direction, and voice coilctuators (VCA) (NCC03-15-050-2X, H2W) in the Y direction. TheCA is selected due to its high bandwidth (450 Hz) and high forceutput; when paired with proper amplifiers (MP-111, APEX), itchieves a resolution of 0.2 �m with a stroke of 6.4 mm. Motionetection is performed by the eddy current sensors (EX-416V,eyence) and capacitance probes (C30/CPL290, Lion Precision) in

he X and Y directions respectively. During printing processes, twotepper motor actuators adjust the yaw angle (�y) and the positionf the print roller to ensure it is aligned with the impression rollern the X–Z plane. Simultaneously, the VCAs actively adjust the printoller position to ensure the parallelism with the impression rollern the Y–Z plane [20].

. Modeling

In this section, we first model the stiffness of the compliant X–Ytage in different directions based on beam theory. A parametricodel for the four-axis positioner, i.e., print roller assembly, is

hen established to provide a deterministic relationship betweenhe print roller position and the actuator inputs. These modelsan guide the flexure design processes and predict the static andynamic behavior of the R2R system. In the model, we assume therint roller is rigid as its stiffness is ∼100 times higher than that ofhe X–Y stage. Each X–Y stage, shown in Fig. 2(b), consists of mul-iple slender beams connected in series or in parallel to decouplehe in-plane parasitic motions. The stiffness of the X–Y stage cane found by solving the beam equation, Eq. (1), with proper bound-ry conditions. The resulting stiffness in the Y and X directions isresented in Eqs. (2) and (3) respectively; the torsional stiffness

n the �Z direction is presented in Eq. (4). In Eqs. (1)–(4), E is theoung’s modulus, Iy and Ix are the moments of inertia and Ly andx are the lengths of the vertical (y) and horizontal (x) constituenteams in the X–Y stages respectively. Note that linear beam mod-ls are used in the analyses as the stroke of the X–Y stage, i.e.,1 mm, is designed to be much smaller than the lengths of individ-al beams, i.e., 65 mm. (For practical applications, each X–Y stageypically moves within 100 s �m.)

I Y ′′ = M + FL (1)

y = 24EIxL3x

(2)

x =48EIy

L3y(3)

�z =E

Lx8Ix

+ Ly16Iy(4)

Next, we consider the four-axis compliant positioner formedy the two X–Y stages, joined by the print roller as shown inig. 2(a). The goal here is to identify the relationship between theosition/orientation of the printer roller and the inputs of the two–Y stages. It is worth to note that cross-stage motion coupling isresent due to the print roller. To capture the coupling effect andimplify the model, we first construct the model only consideringhe Y-axis; the schematic of the model is shown in Fig. 3. This is validecause X and Y axes are decoupled through the flexure design. Inig. 3, each spring represents individual X–Y stages; fi are the forcesenerated by each VCA; kyi and cyi are the stiffness and damping

oefficients of each X–Y stage (i = 1, 2). Due to the constraints ofhe air bushings, a torque (�0) is generated when the print rollerotates about the X-axis (for �x), i.e., when the X–Y stages generateelative motions in the Y direction; K� and C� are the corresponding

the torsional stiffness and damping coefficients of the print roller assembly in the�x direction; m and I are the equivalent mass and moment of inertia, respectively,of the print roller and air bushings; l is the length of the print roller.

torsional stiffness and damping coefficients of the four-axis posi-tioner in the �x direction. K� can be estimated by Eq. (5), where Jt isthe polar moment of inertia of the horizontal slender beams in theX–Y stage, and � is the Poisson ratio. Note that as Eq. (5) does notinclude the stiffness of the air bushing assembly and print roller,the calculated K� will be larger than its actual value. A more preciseK� was obtained experimentally as discussed in Section 4.

K�∼ 4EJt(1 + �)Lx (5)

With torsional stiffness, K� , and damping coefficients, C� , wedevelop the kinematic and dynamic models for the print rollerassembly. The static model is derived in Eqs. (6)–(8), and thedynamic model is presented in Eq. (11) to (14). In the model, yand �x represent the center location/orientation of the print roller;m and I are the equivalent mass and moment of inertia of the shaftand air bushings respectively; l is the length of the print roller; fand ��x represent the force and torque applied to the center of theprint roller; f0 and �0 are coupling force and torque induced by therigid print roller, where their relationships are described by Eq. (6).Applying the coupling force f0 to individual X–Y stage, the relation-ship between the stage displacements, i.e., y1 and y2, and actuatorinputs, i.e., f1 and f2, can be derived in Eq. (7). Next, we solve fory1 and y2 in Eq. (7) to obtain Eq. (8). As the print roller is rigid, thecenter of the print roller and its two ends are related by Eq. (9).Combining Eqs. (8) and (9), we have established the deterministicrelationship between the print roller position and actuator inputsfor static cases.

�0 = K��x = K�y1 − y2

l= f0l (6)

{f1 − f0 = ky1 y1f2 + f0 = ky2 y2

⇒[

f1

f2

]=

⎡⎢⎣

K�l2

+ ky1 −K�l2

−K�l2

K�l2

+ ky2

⎤⎥⎦

[y1

y2

](7)

[y1

y2

]=

⎡⎢⎣

ky2l2 + K�ky1ky2l2 + K�ky1 + K�ky2

K�ky1ky2l2 + K�ky1 + K�ky2

K�ky1ky2l2 + K�ky1 + K�ky2

ky1l2 + K�ky1ky2l2 + K�ky1 + K�ky2

⎤⎥⎦[ f1

f2

]

(8)⎡ ⎤

[y

�x

]= ⎢⎣

12

12

1l

−1l

⎥⎦[

y1

y2

]= Ty

[y1

y2

](9)

ngine

aVaat0ratdarafcEm[

[︸

4−

2

)s2

I

l2

)s)

+ c

m

4−)

+ c

X. Zhou et al. / Precision E

The force and torque applied to the center of the print rollerre described in Eq. (10), where the forces generated by the twoCAs, i.e., f1 and f2, are controlled by their driving voltages, i.e., v1nd v2, respectively. Specifically, the VCAs are connected to powermplifiers that generate the driving currents linearly proportionalo the command voltages; the amplifier and VCA constants are.43 A/V and 15.6 N/A respectively; a1 and a2 are coefficients thatelate the input voltages to the output forces of the VCA, i.e.,1 = a2 = 0.43 × 15.6 = 6.7. Using Eqs. (7), (9) and (10) in combina-ion with the Newton’s second law, we can derive the second orderynamic model of the print roller assembly in Eq. (11), where ynd �x represent the center location and orientation of the printoller respectively. As the print roller assembly is symmetric, we set1 = a2 = a, ky1 = ky2 = k, and cy1 = cy2 = c. Accordingly, Eq. (11) can beurther simplified and arranged as Eq. (12), where the variables areonverted from (y, �x) to individual stage displacements (y1, y2) viaq. (9) for the ease of studying and characterizing the cross-stagingotion coupling effect.

f

��x

]=

[1 1l

2− l

2

] [f1

f2

]=

[1 1l

2− l

2

] [a1 0

0 a2

][v1

v2

]

=

⎡⎣ a1 a2

a1l

2−a2l

2

⎤⎦[ v1

v2

]= Fq

[v1

v2

](10)

m 0

0 I

] ︷︷ ︸

Mq

[ÿ

�̈x

]+

⎡⎢⎣ (cy1 + cy2 )

l(cy1 − cy2 )2

l(cy1 − cy2 )2

l2(cy1 + cy2 )4

+ C�

⎤⎥⎦

︸ ︷︷ ︸Cq

[ẏ

�̇x

]

+

⎡⎢⎢⎣

(ky1 + ky2 )l(ky1 − ky2 )

2

l(ky1 − ky2)2

[l2(ky1 + ky2 )

4+ K�

]⎤⎥⎥⎦

︸ ︷︷ ︸Kq

[y

�x

]

⎡⎢⎣

1a

[(m

4+ I

l2

)s2 +

(c + C�

l2

)s + k + K�

l2

]1a

[(m

1a

[(m

4− I

l2

)s2 − C�

l2s − K�

l2

]1a

[(m

4+ I

l

G11 = G22 =a[(

m

4+

mI

l2s4 +

[2(

m

4+ I

l2

)c + mC�

l2

]s3 +

[2k

(m

4+ I

l2

G12 = G21 =a[−

(mI

l2s4 +

[2(

m

4+ I

l2

)c + mC�

l2

]s3 +

[2k

(m

4+ I

l2

=

⎡⎣ a1 a2

a1l

2−a2l

2

⎤⎦

︸ ︷︷ ︸Fq

[v1

v2

](11)

ering 45 (2016) 332–341 335

My

[ÿ1

ÿ2

]+ Cy

[ẏ1

ẏ2

]+ Ky

[y1

y2

]=

[v1

v2

]

My = F−1q MqTy =

⎡⎢⎣

1a

(m

4+ I

l2

)1a

(m

4− I

l2

)1a

(m

4− I

l2

)1a

(m

4+ I

l2

)⎤⎥⎦

Cy = F−1q CqTy =

⎡⎢⎣

1a

(c + C�

l2

)− C�

al2

− C�al2

1a

(c + C�

l2

)⎤⎥⎦

Ky = F−1q KqTy =

⎡⎢⎣

1a

(k + K�

l2

)− K�

al2

− K�al2

1a

(k + K�

l2

)⎤⎥⎦

(12)

Taking Laplace transform of Eq. (12), the stage outputs can beexpressed in the frequency domain, i.e., y1(s) and y2(s), as a functionof VCA inputs, i.e., v1(s) and v2(s), as shown in Eq. (13). SolvingEq. (13) for y1 and y2, we can obtain Eq. (14), where the transferfunction matrix (Gs) relates stage displacements to VCA inputs. InGs, it is worthwhile to note that the cross-stage motion couplingeffect is described by the off-diagonal elements, i.e., G12 and G21,while the diagonal elements, G11 and G22, are the transfer functionsof the X–Y stage 1 and 2 respectively.

I

l2

)s2 − C�

l2s − K�

l2

]+

(c + C�

l2

)s + k + K�

l2

]⎤⎥⎦

[y1(s)

y2(s)

]=

[v1(s)

v2(s)

](13)

[y1(s)

y2(s)

]=

[G11 G12

G21 G22

][v1(s)

v2(s)

]= GS

[v1(s)

v2(s)

](14)

2 +(

c + C�l2

)s + k + K�

l2

](

c + 2C�l2

)+ m K�

l2

]s2 +

[2c

(k + K�

l2

)+ 2kC�

l2

]s + k

(k + 2K�

l2

)I

l2

)s2 + C�

l2s + K�

l2

](

c + 2C�l2

)+ m K�

l2

]s2 +

[2c

(k + K�

l2

)+ 2kC�

l2

]s + k

(k + 2K�

l2

)

4. Mechanical characterization

In this section, we characterize the (1) mechanical properties ofthe monolithic X–Y stage including stiffness, natural frequency, anddamping coefficient, (2) the cross-axis motion coupling, and (3) thecross-stage motion coupling. The X–Y stages are made of Aluminum7075 to achieve good flexure property and fabricated via wire-EDM to minimize manufacturing errors. The stiffness, ky, for eachstage is measured to be 22.6 N/mm and 21.6 N/mm respectively;the simulated stiffness is 24.1 N/mm, where the difference is mainlyattributed to manufacturing errors. To measure the torsional stiff-ness K� , two forces, i.e., f1 and f2, of equal magnitude and oppositedirections are applied to the X–Y stages. From the displacementmeasurement, i.e., y1 and y2, K� is calculated to be 1.73 Nm/mrad viaEq. (8). Impulse response and step response tests were performed

to find the natural frequency and damping coefficient of the of theflexure stage. After the impulse/step, the displacement data werecollected via capacitance probes (C30/CPL290, Lion Precision); fastFourier transform (FFT) was performed to obtain the frequencyspectra of the flexure stages; the results show natural frequencies

336 X. Zhou et al. / Precision Engineering 45 (2016) 332–341

Table 2Parameters and constants used in the print roller assembly model.

Parameters Value Unit

Stiffness of the 1st X–Y stage in Y-axis ky1 22.6 N/mmStiffness of the 2nd X–Y stage in Y-axis ky2 21.6 N/mmDamping coefficient of the 1st X–Y stage in Y-axis cy1 28.7 kg/sDamping coefficient of the 2nd X–Y stage in Y-axis cy2 21.9 kg/sVoltage to force coefficient of the VCA a 6.7 N/VLength of the print roller l 486 mmEquivalent mass of print roller assembly m 2.4 kg

2

oBflltrp

4

mttccssawpmsaey

x

x

y

y

Moment of inertia of the equivalent mass l Torsional stiffness K�Torsional damping coefficient C�

f the two compliant stages are 31.6 Hz and 31.4 Hz respectively.y measuring the settling time, the damping coefficients of theexures stages are calculated to be 28.7 and 21.9 respectively. Fol-

owing the same procedure, the torsional damping coefficient ofhe print roller assembly is measured to be 1.1. Table 2 summa-izes important parameters and constants used in the model of therint roller assembly.

.1. Cross-axis motion coupling

In this section, we experimentally investigate the cross-axisotion coupling on the X–Y stages [22]. As flexures are repeatable

o nanometer scale, the parasitic errors can be largely eliminatedhrough closed-loop control. In the first experiment, stage 1 wasommanded to move in the Y direction (y1) for ±200 �m, and theoupling X motions on both stage 1 (x1) and stage 2 (x2) were mea-ured. The results are presented in Fig. 4. In the next experiment,tage 1 was commanded to move in the X direction (x1) for ±90 �m,nd the coupling Y motions on both stage 1 (y1) and stage 2 (y2)ere measured. These results prove that each monolithic com-liant stage has excellent motion decoupling capability and thatotions from different direction cause parasitic motions on the

cale of 100 – 200 nm. More importantly, these parasitic motionsre relatively linear and can be eliminated by proper control strat-gy. Linear relationships between y1 and x1/x2 as well as x1 and1/y2 can be described by Eqs. (15)–(18) respectively:

1 = 4.12 × 10−3 + 3.29 × 10−3 · y1 (15)

2 = 4.15 × 10−4 + 9.52 × 10−4 · y1 (16)

1 = −5.32 × 10−4 − 4.06 × 10−4 · x1 (17)

2 = 8.70 × 10−5 + 1.53 × 10−3 · x1 (18)

Fig. 4. Cross-axis motion coupling behavior in Y direction.

0.079 kg m1.73 Nm/mrad1.1 kg m/(s·mrad1/2)

4.2. Cross-stage motion coupling

In this section, we experimentally investigate the cross-stagemotion coupling and compare the results with the transfer func-tion matrix (Gs), derived in Eq. (14). All elements in Gs, includingG11, G22, G12 and G21, were measured experimentally. To obtainGs, step response tests were performed on each X–Y stage in theprint roller assembly. The linear coefficients a1 and a2 are assumedto be constant as the VCA driver is operated in the current modewith a bandwidth of 1 kHz. Fig. 5(a) presents the measured G11 andG22 together with the analytic model, where we find the exper-imental data match the model well from low frequency region to∼100 Hz. Fig. 5(b) presents the measured G12 and G21 together withthe analytic model, where strong cross-stage motion coupling withpeak frequencies at 21 Hz and 38 Hz is both predicted by the modeland experimentally observed. The measured data well-match theanalytic model from low frequency region to ∼100 Hz; the dis-tortions occur in the high frequency region are caused by systemuncertainties, e.g., electronic noises, nonlinearities of the actuatorsand drivers. As the high-resolution printing only occurs in the lowfrequency region, the distortion in high frequency region can beneglected.

It is important to note that during the roll-to-roll printing pro-cess, overshoot or ringing of the print roller must be entirelyeliminated, as over pressing the elastomer stamp can cause failureof pattern transfer [3]. In the meantime, the settling time shouldbe minimized. This can be achieved by the decoupling and cascadecontrol, presented in the next section.

5. Control strategy

In this section, we present decoupling control and cascade con-trol implemented on the printing module to achieve nanometerlevel positioning precision and uniform printing force. As variousforces/speeds may be required when printing patterns of differentresolution, the flexure positioner should be able to generate arbi-trary printing force from 0 to 15 ± 0.05 N with minimized settlingtime and no overshoot. The four-axis positioner controls the yawangle (�y) and roll angle (�x) of the print roller. Through exper-imental observation, the print quality is highly sensitive to theinstantaneous roll angle fluctuation and less sensitive to the yawangle and the X position of the print roller once aligned, and thusthe control in the X and Y directions can be decoupled. Here, wereport the control strategy in the critical Y direction, i.e., control ofroll angle (�x) and Y position of the print roller; this method can beimplemented in the X-axis and run independently.

From Sections 3 and 4, we learn the motions of the two X–Ystages are coupled, and thus the control issue cannot be addressed

by a single controller. Decoupling control, a variation of the feedfor-ward control, is used to eliminate measurable external disturbances[23,24]. As discussed in Section 4.1, since the coupling behav-ior is repeatable and can be seen as the measurable external

X. Zhou et al. / Precision Engine

Fat

dbpt

Fc

ig. 5. (a) Measured G11 and G22 plotted with analytic model; and (b) measured G12nd G21 plotted with analytic model; the voltage to force conversion coefficient ofhe VCA is 6.7 N/V.

isturbances, we design decouplers to compensate the couplingehavior. As shown in Fig. 6, D21(s) and D12(s) represent the decou-lers. The decouplers are designed as the ratio of the gains of theransfer functions by setting s = 0, as shown in Eqs. (19) and (20):

ig. 6. Block diagram of the decoupling cascade control for the R2R system. MP: master ontrollers; r1, r2: position set points sent to the slave loops; p1, p2: force readings from t

ering 45 (2016) 332–341 337

D21(s) =G21(s)G22(s)

∣∣∣s=0

(19)

D12(s) =G12(s)G11(s)

∣∣∣s=0

(20)

where G11, G22, G12, and G21 are defined in Eq. (14). The accuracyof the decouplers relies on the accuracy of the compliant stage andanalytic model presented in Section 3.

Next, we combine decoupling and cascade control to furtherminimize the response time against disturbances and improvecontrol quality. The block diagram is shown in Fig. 6, where theforce/position loops are the master/slave loops respectively. Themaster loop monitors the contact forces constantly via the mastercontroller (MC) and sends computed set points to the slave loops.The reference positions of the slave loops are measured in advancefrom the load cells integrated at the two ends of the impressionroller; contact forces, i.e., sum of force readings from the load cellssubtracted by the web tension in the Y direction, are defined tobe uniform when the two load cells receive equal readings. Whenthe set points from the master loop are received, controllers inslave loops respond immediately and drive both X–Y stages simul-taneously to keep the contact force uniform. The output of thePID controllers, i.e., C11 and C22, in slave loops will go throughthe decouplers to eliminate the coupling behaviors. The two PIDcontrollers, i.e., C11 and C22, were experimentally characterized.The phase margin and gain margin of C11/C22 with plant (G11/G22)are 82.8◦/53.6◦ and 14.8 dB/6.7 dB respectively, which indicate thesystem is stable.

6. R2R printing experiments

6.1. Motion decoupling experiment with PID and cascade control

In this section, we examine the effectiveness of the decouplingcascade control by comparing it with a closed-loop PID controller[20]. For the PID scheme, each X–Y stage is controlled by an inde-pendent PID controller, where the target positioning (or printingforce) signals are calculated based on Eqs. (7) and (8) and sent tothe VCAs. In the motion-decoupling printing experiment, while theprint roller was in contact with the impression roller, one X–Y stagewas commanded to move 10 �m in the Y direction, hold the posi-tion for 3 s, and return to the initial position; and the aim was tokeep the position of the second X–Y stage constant. The results

with PID controller and decoupling cascade control are presentedin Fig. 7(a) and (b) respectively. From the blow-up windows, onecan conclude that the decoupling cascade control entirely removesthe motion coupling effect across the two X–Y stages; while the

process; MC: master (PID) controller; D21(s), D12(s): decouplers; C11(s), C22(s): PIDhe load cells.

338 X. Zhou et al. / Precision Engineering 45 (2016) 332–341

a) PID

Pwttw

qlttprt

F(

Fig. 7. Motion decoupling experiment with (

ID controller reduces the coupling motion to within 0.5 �m. It isorth to note that a ∼3.5 �m coupled motion will be introduced if

he experiment is performed without the controller. Note also thathis experiment was performed when the rollers were stationaryith appropriate web tension (10 N) applied.

To better understand the results, we next characterized the fre-uency response of the master (force) and slave (displacement)

oops with and without the decoupling control, i.e., decoupling con-rol versus PID control. Fig. 8(a) presents the frequency response of

he master (force) loop; Fig. 8(b) and (c) present the slave (dis-lacement) loop performance with PID and the decoupling controlespectively. Comparing Fig. 8(b) and (c), one can clearly observehat the coupling motions, i.e., r1 to y2 and r2 to y1, have been

ig. 8. (a) Frequency response of the master (force) loop; (b) frequency response of the sdisplacement) loop with decoupling control; y1, y2: stage positions; r1, r2: position set p

control and (b) decoupling cascade control.

effectively suppressed in the low frequency region, where the mag-nitudes are decreased by more than 20 dB. It is worthwhile to notethat the responses of r1 to y1 and r2 to y2, remain largely unchanged.These results reconfirm the experimental observation in the timedomain as presented in Fig. 7.

6.2. Contact force and positioning experiment with cascadecontrol

We devised two experiments to verify the contact force and rollangle control capability, where the roll angle is defined as the differ-ence of the position readings from the capacitance probes, shownin Fig. 2(a), divided by the length of the print roller. In the first

lave (displacement) loop with PID control; and (c) frequency response of the slaveoints sent to the slave loops.

X. Zhou et al. / Precision Engineering 45 (2016) 332–341 339

ps, an

easwsciSmwrFbtc

Fv

Fig. 9. (a) Closed-loop contact force plot of 0.5 N force ste

xperiment, the print roller was commanded to move downnd up in 0.5 N force steps, while the position difference waset to be zero, i.e., parallel to the impression roller, and theeb was stationary with appropriate tension. The results are

hown in Fig. 9(a), where throughout the experiment contact forcean be controlled within ±0.01 N without any overshoot, whichs 10 times better than the requirement (±0.1 N) discussed inection 1. In the second experiment, the print roller was com-anded to rotate about the X-axis while the web was stationaryith appropriate tension; since the value of �x is small, we

eport the results in terms of position difference, as shown in

ig. 9(b). From the results, we find the position difference cane controlled within ±200 nm. In other words, angular resolu-ion about X-axis of ∼0.085 arcsecond is achieved with the cascadeontrol.

ig. 10. (a) Contact force plot with decoupling cascade control versus no control; (b) posiiew of contact force plot (a); and (d) blow-up view of position difference plot (b).

d (b) closed-loop position difference plot of 10 �m steps.

6.3. Contact force and position control during R2R printingprocess

To verify the contact force and position control will satisfy thedesign requirements, i.e., ±0.05 N, in actual printing processes, werecorded the contact force and position difference of the printroller for one revolution (360◦). During the experiment, the webwas driven by the rewinding module with closed-loop tensioncontrol at a web speed of 1 mm/s; we then performed the MCPprinting without any control and with decoupling cascade control.Fig. 10 shows the printing force data with a target printing force

of 7.0 N. The results with decoupling cascade control, blue line inFig. 10(a) and (b), show consistent precision throughout the experi-ments (±0.05 N), while results without control, black line Fig. 10(a)and (b), show significant deviation due to roller eccentricity that

tion difference plot with decoupling cascade control versus no control; (c) blow-up

340 X. Zhou et al. / Precision Engineering 45 (2016) 332–341

F tment( m.

cscpnFSrcs

7

7

npctpwaw

7

rab

ig. 11. (a) PDMS stamp tightly bonded to a glass cylinder by oxygen plasma treagold lines) with the line widths of 300 nm and 600 nm respectively, scale bar = 6 �

annot be avoided at submicron level. The results also suggest thatubmicron patterning via MCP can be achieved with our decouplingascade control. The two spikes in Fig. 10(c) are due to the incom-lete wrap of the PDMS stamp around the print roller; this is alsootable in the open-loop result between 15 and 75 degree shown inig. 10(a). The details of the stamp preparation are described in theection 7. The position difference under open loop condition couldeach 50 �m, while it can be controlled within ±0.35 �m under cas-ade control. More experiments indicate slowing down the printingpeed can further improve the force and angular control accuracy.

. Device fabrication

.1. Stamp and substrate preparation

To adapt the MCP process for R2R operation, we replaced theormal substrate with a 4 in. wide metal-coated PET roll. For stampreparation, PDMS stamps are first fabricated by standard MCP pro-edures [3], following which the stamp is bonded to a glass cylinderhat is then tightly mounted to an air-expandable, motor-drivenrint roller shaft. Fig. 10(a) shows an image of the glass cylinderith a bonded PDMS stamp. We have also developed new inking

nd etching recipes for both gold and silver that are compatibleith the fast R2R process (etch time

ngine

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X. Zhou et al. / Precision E

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Precision design and control of a flexure-based roll-to-roll printing system1 Introduction2 Design of the R2R system2.1 Four-axis compliant positioner

3 Modeling4 Mechanical characterization4.1 Cross-axis motion coupling4.2 Cross-stage motion coupling

5 Control strategy6 R2R printing experiments6.1 Motion decoupling experiment with PID and cascade control6.2 Contact force and positioning experiment with cascade control6.3 Contact force and position control during R2R printing process

7 Device fabrication7.1 Stamp and substrate preparation7.2 Device fabrication

8 ConclusionAcknowledgementsReferences