Modeling and Matching Design of a Tension ... - Semantic Scholar
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Modeling and Matching Design of a Tension Controller Using Pendulum Dancer in Roll-to-Roll Systems Hyun-Kyoo Kang, Member, IEEE, Chang-Woo Lee, Member, IEEE, Kee-Hyun Shin, Member, IEEE, and Sang-Chul Kim
Abstract—Dancer systems are typical equipment for attenuation of tension disturbances. The two kinds of dancer, active dancer and passive dancer, are distinguished by an external actuator. In the active dancer, the position of the dancer roll is measured and the roll is forced by the external actuator to regulate tension disturbances. However, the passive dancer, composed of a spring, damper and roll has no external actuator. Tension disturbance generates movements of the roll of the passive dancer and the displacements regulate the tension variation. However, the hybrid dancer, which is a mixture of passive and active dancer, is applied for the roll-to-roll systems. It regulates tension disturbances indirectly in the manner of keeping a constant position for the roll by changing the velocity of the driven roller adjacent to the dancer roll. It has different characteristics from those of the passive or active dancer. In this paper, the modeling of the pendulum dancer is derived. The dynamics of the hybrid dancer, which feedbacks the position of the dancer roll, and the PI control of a driven roll are analyzed. The matching logic for tuning gains is developed and experimentally verified. Index Terms—Gain tuning, matching design, pendulum dancer, roll-to-roll, tension control.
N OMENCLATURE lu lu0 ld ld0 l1 l2 θ
Upstream span length of dancer (m). Upstream span length of dancer at steady state (m). Downstream span length of dancer (m). Downstream span length of dancer at steady state (m). Rod length of hinge to cylinder (m). Rod length of hinge to dancer roll (m). Angle of dancer arm.
Manuscript received January 21, 2011; accepted March 8, 2011. Date of publication May 19, 2011; date of current version July 20, 2011. Paper 2011-METC-002, presented at the 2010 Industry Applications Society Annual Meeting, Houston, TX, October 3–7, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Metals Industry Committee of the IEEE Industry Applications Society. This research was supported by the “Seoul R&BD Program (10848) and Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST, K21001001666-10E0100-08810). H.-K. Kang and C.-W. Lee are with the Flexible Display Roll-to-roll Research Center, Konkuk University, Seoul 143-701, Korea (e-mail: hyunkyoo@ gmail.com; [email protected]). K.-H. Shin is with the Department of Mechanical Engineering, Konkuk University, Seoul 143-701, Korea (e-mail: [email protected]). S.-C. Kim is with the School of Computer Science, Kookmin University, Seoul 136-702, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2156376
E rd Jd Jeq bd b vd vd0 Vd vi vi0 Vi ti ti0 Ti P0 A0 Fk εi ρu Au
Young’s modulus (N/m2 ). Radius of dancer idle roll (m). Moment of inertia of dancer idle roll (kgm2 ). Equivalent moment of inertia of dancer (kgm2 ). Rotary bearing friction constant of dancer idle roll. Rotary bearing friction constant of hinge. Tangential velocity of dancer roll (m/s). Tangential velocity of dancer roll at steady state (m/s). Variation of tangential velocity of dancer roll (m/s). Tangential velocity of ith roll (m/s). Tangential velocity of ith roll at steady state (m/s). Variation of tangential velocity of ith roll (m/s). Tension of web in ith span (N). Tension of web in ith span at steady state (N). Variation of tension of web in ith span (N). Pressure of pneumatic cylinder (N/m2 ). Area of piston of pneumatic cylinder (m2 ). Spring force of pneumatic cylinder (N). Strain of web in ith span. Density of unstretched web (kg/m3 ). Cross sectional area of unstretched web (m2 ).
I. I NTRODUCTION
A
WEB is thin and flexible material, in which the width is very less than its length. Film, paper, steel and textile represent examples. In the middle or last step of the production, the web is stored in the form of a wound roll, such as a rolling coil, printing film or paper. Roll-to-roll systems consist of unwinder, driven roller, idle roller and winder for transportation and web processes such as printing, coating, and laminating [1]–[6]. Fig. 1 depicts a direct gravure printing machine. Multi-layered or multi-colored patterns are printed on the web, such as paper or film i.e., OPP, LDPE, or PET. The velocity should be increased to improve production efficiency. In addition, roll-to-roll systems have focused on the manufacture of printed circuits, e.g., RFID tag, signage or solar cell using a roll-to-roll printing machine. It is necessary to research mathematical modeling and control methods of rollto-roll systems to achieve high productivity for printed electronics. Unwinder, infeeder, outfeeder and winder complete the printing machines. Printing and drying processes were applied between the infeeder and outfeeder. It is crucial for high quality printing to maintain constant tension on the web entering the
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KANG et al.: MODELING AND MATCHING DESIGN OF A TENSION CONTROLLER
Fig. 1.
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Schematic of converting machines.
first printing roll. Dancer systems are equipped in the unwinder and infeed sections to attenuate the tension variation. Tension variation directly affects printing errors [7]. Web dynamics have been researched by Campbell [8], Grenfell [9], Brandenburg [10], and Shin [11] to propose real-time distributed tension control methods. The two kinds of dancer systems are active and passive. Pagilla developed an active dancer that is better for precise tension control and attenuation of a wider frequency range of tension disturbance than the case of a passive dancer [12], [13]. Ramamurthy conducted a comparative study of passive and active dancers [14]. It was pointed out that control performance of the active dancer is aggravated under high frequency tension disturbance. It means that the dynamic performance of the active dancer is restricted by the actuator of the dancer roll. Although a high performance actuator could be applied to the dancer, it requires a greater cost and it is difficult to implement the additional actuator and housing and so on. Therefore, the active dancer is rarely applied to roll-to-roll machines. The passive dancer consists of spring, damper and idle roll without an additional actuator. The dancer idle roll, which is positioned by a spring and damper, is moved due to a moment variation caused by tension disturbance. The movement of the dancer idle roll could absorb tension disturbances. Shin developed the mathematical modeling of the passive dancer system including the modeling of web tension. He proposed resonance frequency as a design parameter [11]. Shelton analyzed the limitation of the passive dancer on the measurement of tension as a sensor [16]. Knittel developed the H infinite tension controller for passive dancer systems. However, a hybrid dancer system, which is a mixture of a passive and active dancer, is applied to the roll-to-roll systems to attenuate tension disturbances. The appearance of a hybrid dancer is similar to the passive one. A PI (Proportional-Integral) control loop of velocity of the driven roll is applied to the dancer to regulate position variations of the dancer roll. There is no additional actuator to control the position of the dancer roll directly. The hybrid dancer regulates tension disturbances indirectly in the manner of keeping constant position by changing the velocity of the driven roller adjacent to the dancer roll. Thus, the hybrid dancer
can operate in the allowable swing range physically in spite of huge tension disturbance. Dynamic characteristics of the hybrid dancer differ from the active or passive dancer. Therefore, it is necessary to research the design guidelines and gain tuning method of the PI position feedback dancer control method to increase velocity and productivity. As yet, there is no research on hybrid dancer systems. Thus, the primary objective of this paper is to propose a guideline for dancer hardware and the gain tuning method. Mathematical modeling of the PI position feedback hybrid dancer systems is developed toward this aim. Analysis of poleszeros with varying velocity is conducted using this model. Tension disturbance prediction due to roll eccentricity is conducted. A matching control scheme that considers system characteristics is proposed. II. M ATHEMATICAL M ODEL A. Tension Model of Dancer Systems A control volume could be drawn between two rolls, as shown in Fig. 2. The law of conservation of mass for the control volume can be written as follows: ρu Au v1 (t) ρu Au v2 (t) d − = 1 + ε1 (t) 1 + ε2 (t) dt
l u (t)
ρu Au dx. 1 + ε2 (t)
(1)
0
Substitute lu (t) = lu0 + l2 θ(t) into (1), and rearranging ε˙2 gives ⎡ ⎤ v1 (t) − v2 (t) + v2 (t)ε2 (t) −1 ˙ ⎣ −v1 (t)ε1 (t) − l2 θ(t) ⎦ . (2) ε˙2 (t) = lu0 + l2 θ(t) ˙ +l2 θ(t)ε2 (t) Equation (2) is the nonlinear tension model for upstream of the dancer system. Using the same procedure, the nonlinear tension model of downstream of the dancer system is as in (3) ⎡ ⎤ v2 (t) − v3 (t) + v3 (t)ε3 (t) −1 ˙ ⎣ −v2 (t)ε2 (t) − l2 θ(t) ⎦ . (3) ε˙3 (t) = ld0 + l2 θ(t) ˙ +l2 θ(t)ε3 (t)
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Fig. 4.
Fig. 2. Control volume of dancer systems.
Force on dancer arm.
Equation (6) must be satisfied in the initial steady-state condition with 0 = (t30 − t20 )rd2 − bd v20 .
(9)
Substituting (7)–(9) into (6) gives Jd V˙ d (t) = {T3 (t) − T2 (t)} rd2 − bd Vd (t).
(10)
In (10), tangential velocity is determined by the moment of inertia of the roll, radius of roll, and difference of tension. Fig. 3. Torque on the dancer idle roll.
C. Tangential Velocity of a Dancer Arm
Equation (2) and (3) can be linearized by the Taylor linearization, as follows: 1 AE {−V1 (t) + V2 (t)} + v10 T1 (t) T˙2 (t) = (4) ˙ lu0 −v20 T2 (t) + AEl2 θ(t) 1 AE {−V2 (t) + V3 (t)} + v20 T2 (t) T˙3 (t) = . (5) ˙ ld0 −v30 T3 (t) + AEl2 θ(t) Equations (4) and (5) are the linear tension model of the upstream and downstream span of the dancer system, respectively.
¨ = − l2 {t2 (t) + t3 (t)} Jeq θ(t)
FK
˙ + {P0 A0 − FK (t)} l1 − bθ(t)
0.078 24 + l1 θ(t) + 24. = 0.078 2
(11) (12)
At the steady-state operating condition, (11) should satisfy (13). Substituting (12) and (13) into (11) gives (14). The dancer arm dynamics are affected by the tension difference
B. Tangential Velocity of a Dancer Roll The velocity of the dancer roll is determined by the difference of tension between the upstream and downstream span, as shown in Fig. 3. The torque equation can be written as (6). The tangential velocity is expressed as (7). Let the velocity be as in (8) Jd θ¨d (t) = {t3 (t) − t2 (t)} rd − bd θ˙d (t)
(6)
θ˙d (t)rd = vd (t)
(7)
vd (t) = vd0 + Vd (t).
Fig. 4 depicts the forces on the dancer arm. The torque equation, considering the upstream and downstream span tension, spring force and force of pneumatic cylinder is in (11). The spring force of the pneumatic cylinder is as in (12)
(8)
0 = − l2 (t10 + t20 ) + (P0 A0 − 36)l1
(13)
˙ ¨ = − l2 {T2 (t) + T3 (t)} − 24 l2 θ(t) − bθ(t). (14) Jeq θ(t) 0.078 1 D. Transfer Function of Dancer Systems The Laplace transformations of the tension (4) and (5), tangential velocity of the dancer roll (10) and tangential
KANG et al.: MODELING AND MATCHING DESIGN OF A TENSION CONTROLLER
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Fig. 6. Block diagram of infeed dancer. TABLE I S IMULATION C ONDITIONS
Fig. 5.
PI dancer controller of infeed section.
velocity of the dancer arm (14) are combined then, the inputoutput model of dancer systems is expressed as θ(s) −AE = D(s) V0 (s) A(s) − B(s)
(15)
C(s)
where AEr22 + AEr22 sJ + b2 2
2 −AEr2 24 2 l1 + AEsl2 B(s) = Jeq s2 + sb + (sJ2 + b2 )l2 0.078 2AEr22 C(s) = sld + v20 + v30 + sJ2 + b2
1 24 2 2 l D(s) = − Jeq s + sb + l2 0.078 1
AEr22 × sld + v30 + − AEsl2 . sJ2 + b2 A(s) = slu + v20 +
III. A NALYSIS OF DANCER S YSTEMS AND G UIDELINE FOR G EOMETRICAL D ESIGNS Roll-to-roll systems consist of unwinding, infeeding, printing, outfeeding, and rewinding sections. The tangential velocity of the first printing roll is fixed as the master speed that is the same as the operating velocity. The pressure of the pneumatic cylinder of the dancer system is obtained by (13). The dancer arm angle is measured by a potentiometer and the velocity of the infeeding roll is controlled to regulate the dancer arm position using PI-controller. It regulates the tension disturbance indirectly by balancing the tension and pneumatic pressure. The signal flow and block diagram of the PI position feedback control loop of the infeeding section are depicted as Figs. 5 and 6, respectively. The angle of dancer arm is measured by a potentiometer, filtered by the first order low-pass filter. Then, the velocity of the infeeding roll is controlled.
Fig. 7. Pole-zero map with varying operation velocity (200 ∼ 500 m/min).
A. Analysis of Dancer Systems The analysis of the dynamic characteristics of the PI position feedback dancer system was performed by drawing pole-zero maps with varying system parameters, i.e., operating velocity, rod length, span length, and inertia. Table I describes the simulation parameters. As the velocity is increased, oscillation poles are moving left side and dominant poles are fixed in s-plane (Figs. 7 and 8). It means that transient tension disturbances are reduced fast and
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Fig. 8. Pole-zero map with varying velocity (zoom in).
Fig. 10.
Pole-zero map with changed dancer rod (zoom in).
Fig. 11.
Pole-zero map with varying span length.
Fig. 12.
Pole-zero map with varying inertia of Jeq (0.1 ∼ 10).
Fig. 9. Pole-zero map with changed dancer rod.
settling time is not changed in high speed operation. If the PI controller gains are determined for low velocity, it would work sufficiently in high speed. Figs. 9 and 10 depict the poles and zeros with varying rod lengths. The dominant pole moves toward the imaginary axis as the rod lengths is increased. Then, the dancer response capability is decreased. Fig. 11 depicts poles and zeros with varying span length. Poles move toward an imaginary axis as the length of the upstream span is increased. Therefore, the dancer response capability is decreased. In Fig. 12, poles are positioning near the imaginary axis, as the inertia of dancer systems is increased. Then, the dancer response capability is decreased. B. Guidelines for Mechanical Design of Dancer Systems Operating velocity, span length of the upstream and downstream of the dancer roll, and the inertia of the dancer systems are sensitive parameters that affect the performance of the hybrid dancer system. The increased velocity of the web improves the response capability of the hybrid dancer system.
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Fig. 14. Root locus with Tn = 1. Fig. 13. Bode plot of transferred tension (300 ∼ 500 m/min).
The upstream span, in which the span length is shorter than the downstream span, improves the response capability of the dancer system. A lower dancer inertia improves the dancer system response capability. Therefore, the dancer systems have to be designed to have a shorter upstream than downstream span and with less inertia. PI gains tuned in low velocity could work at higher velocity, because dancer poles move to the left of the s-plane in high velocity operation. Then, the PI gains should be determined in the low speed operation. IV. D ESIGN G UIDELINE OF PI T ENSION C ONTROLLER A. Frequency of Tension Disturbance It is necessary to attenuate tension disturbance entering into the printing section for precise register control. Generally, the allowable tension disturbance is ±2% of the operating tension. Therefore, response performance to the maximum tension disturbance is a design criterion of the PI controller. The eccentricity of the unwinding roll is a major cause of disturbance of the tension. As the substrate is unwound, the diameter of the unwinder decreases and the frequency of tension increases. The range of tension disturbance is determined in (16). For example, if the diameter of the unwinder is 1 m to 0.1 m, the maximum frequency is 100 rad/s to 166.7 rad/s in 300 m/min to 500 m/min, respectively ωmax
2v0 = , Du,min
ωmin
2v0 = . Du,max
(16)
Fig. 15. Root locus with Tn = 10.
a tension disturbance 50 N to 2 N is −27.96 dB and the frequencies are 23.13 rad/s, 38.55 rad/s for 300 m/min, 500 m/min, respectively, in Fig. 13. Transferred unwinding tension disturbances above 38.55 rad/s could result in a decrease of less than 2 N. This is in the allowable range in the infeeding section. It is reasonable that the frequency of tension disturbances above ωmax , calculated by (18), do not need to be considered the infeeding section T2 (s) v10 = T1 (s) Ls + v20
top · 0.02 v10
=
.
T1 (s) Ls + v20 s=jωmax
(17) (18)
B. Prediction of Tension Disturbance Tension disturbance is transferred from upstream to downstream, the affect is like the first order low-pass filter. The filter is determined by the span length and initial velocity as in (17). Fig. 13 illustrates the bode plot of (17). For example the allowable disturbance is ±2% of the operating tension, the maximum tension disturbance of the unwinding section is 50 N and the span length is 5.4 m. The magnitude that creates
C. Gain Turing of PI Tension Controller PI controller gains are determined by root locus of dancer system which has control loop as Fig. 5. While I-gain is increased, root locus plots are depicted to calculate a dominant pole in Figs. 14–17. Dominant poles are listed in Table II. P- and I-gains are 0.0402 and 1000, respectively, for the dominant pole positioned in last left side.
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Fig. 16. Root locus with Tn = 100.
Fig. 18. Step response of 50 N unwinder tension disturbance (500 m/min, Kp = 0.0402, Tn = 1000).
Fig. 19.
Three-layer gravure printing machine in FDRC.
Fig. 20.
Operation velocity in experiments (0 ∼ 470 m/min).
Fig. 17. Root locus with Tn = 1000. TABLE II C ONTROLLER G AINS AND P OLES
D. Experimental Gain Tuning Numerical simulation was conducted to validate the performance of the tension regulation of PI dancer controller. In Fig. 18, the response of 50-N step tension disturbance which conducted using PI gains set by root locus plot is depicted. It satisfies the allowable range (±2%) of tension variation. The gains are used for the initial value of the experimental gain tuning. Using the three layer gravure printing system which has dancer system in its feeding section, experimental verification was carried out (Fig. 19). The operation velocity was increased up to 470 m/min as Fig. 20. As the velocity increased from
zero to the operating speed, the P-gain would be changed in inverse proportion to the variation of the dancer arm angle. As the operating speed increases, the system becomes more stable, because oscillation poles moves to the left side of the s-plane as Fig. 8. PI-gains, tuned at low velocity, are reasonable across all operating speeds. The PI-gains determined through the
KANG et al.: MODELING AND MATCHING DESIGN OF A TENSION CONTROLLER
Fig. 21. Unwinder and infeeder tension (200 m/min).
Fig. 24. Unwinder and infeeder tension (470 m/min).
Fig. 22. Unwinder and infeeder tension (300 m/min).
Fig. 23. Unwinder and infeeder tension (400 m/min).
experiment are Kp = 0.08, Tn = 1000. They are suitable for the tension regulation requirement, ±2% of operating tension, as shown in Figs. 21–24. Fig. 25 depicts the procedures for the PI-gain tuning method.
Fig. 25. Matching logic for design of PI dancer controller.
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V. C ONCLUSION For the regulation of tension disturbances, dancer system is applied in the roll-to-roll system. The two kinds of dancer, active dancer and passive dancer, are distinguished by an external actuator. In the active dancer, the roll position is controlled directly by an external actuator, but the performance is restricted by the limitation of the external actuator. It is more costly and there are difficulties of implementation. Thus, the active dancer is rarely applied to roll-to-roll machines. Moreover, a passive dancer, which regulates tension variations by idle roll, spring and damper, could control small magnitudes of variation due to the limitation of the allowable rotation range of the dancer arm. A hybrid dancer system, a mixture of passive and active dancer, is applied for the roll-to-roll systems to attenuate tension disturbances. The position of the roll is measured by potentiometer. The driven roll is controlled to regulate the position without an external actuator. The characteristics of this dancer differ from those of active and passive dancers. It is necessary to research design guidelines and to determine a tuning method of the PI position feedback dancer control method. However, there was no earlier related research on the hybrid dancer. The following conclusions can be drawn from this paper: 1) a mathematical model of a pendulum dancer has been developed; 2) a dynamics of hybrid dancer systems, which feedback position of the dancer roll and control a driven roller, are analyzed; 3) gains, which have dominant poles, are determined using root locus plots; 4) the matching logic for tuning gains is developed and the logic is experimentally verified at 470 m/min. R EFERENCES [1] K. H. Shin, Tension Control. Atlanta, GA: Tappi Press, 2000. [2] H. Kang, C. Lee, and K. Shin, “A novel cross directional register modeling and feedforward control in multi-layer roll-to-roll printing,” J. Process Control, vol. 20, no. 5, pp. 643–652, Jun. 2010. [3] H. Kang, C. Lee, J. Lee, and K. Shin, “Cross direction register modeling and control in multi-layer gravure printing,” J. Mech. Sci. Technol., vol. 24, no. 1, pp. 391–397, Jan. 2010. [4] H. Kang, C. Lee, and K. Shin, “Novel modeling of correlation between two-dimensional registers in large-area multilayered roll-to-roll printed electronics,” Jpn. J. Appl. Phys., vol. 50, no. 1, pp. 016 701-1–016 701-7, Jan. 2011. [5] C. Lee, H. Kang, H. Kim, H. A. D. Nguyen, and K. Shin, “Quality control with matching technology in roll to roll printed electronics,” J. Mech. Sci. Technol., vol. 24, no. 1, pp. 315–318, Jan. 2010. [6] C. Lee, J. Lee, H. Kang, and K. Shin, “A study on the tension estimator by using register error in a printing section of roll to roll e-printing systems,” J. Mech. Sci. Technol., vol. 23, no. 1, pp. 212–220, Jan. 2009. [7] P. Lin and M. S. Lan, “Effect of PID gains for controller with dancer mechanism on web tension,” in Proc. 2nd Int. Conf. Web Handling, 1991, pp. 66–76. [8] Campbell, Process Dynamics. Hoboken, NJ: Wiley, 1958, pp. 20–21. [9] K. P. Grenfell, “Tension control on paper-making and converting machinery,” in Proc. IEEE 9th Annu. Conf. Elect. Eng. Pulp Paper Ind., 1963, pp. 20–21. [10] G. Brandenburg, “New mathematical models for web tension and register error,” in Proc. 3rd Int. IFAC Conf. Instrum. Autom. Paper, Rubber Plastics Ind., 1977, vol. 1, pp. 411–438. [11] K. H. Shin, “Distributed control of tension in multi-span web transport systems,” Ph.D. dissertation, Oklahoma State Univ., Stillwater, OK, 1991. [12] P. R. Pagilla, L. P. Perera, and R. V. Dwivedula, “The role of active dancers in tension control of webs,” in Proc. 6th Int. Conf. Web Handling, 2001, pp. 227–242.
[13] P. R. Pagilla, “Periodic tension disturbance attenuation in web process lines using active dancers,” J. Dyn. Syst. Meas. Control, vol. 125, no. 3, pp. 361–371, 2003. [14] R. V. Dwivedula, Y. Zhu, and P. R. Pagilla, “Characteristics of active and passive dancers: A comparative study,” Control Eng. Pract., vol. 14, no. 4, pp. 409–423, Apr. 2006. [15] E. Y. Hong, “Aerodynamic dancer and tension transducer in web handling,” Ph.D. dissertation, Oklahoma State Univ., Stillwater, OK, 2005. [16] J. J. Shelton, “Limitations to sensing of web tension by means of roller reaction forces,” in Proc. 5th Int. Conf. Web Handling, 1999. [17] M. Vedrines and D. Knittel, “Modelling and H∞ low order control of web handling systems with a pendulum dancer,” in Proc. 17th World Congr. IFAC, 2008, pp. 1012–1017. [18] B. C. McDow and C. D. Rahn, “Adaptive web-tension control using a dancer arm,” Tappi, vol. 81, no. 10, pp. 197–205, 1998.
Hyun-Kyoo Kang (M’11) received the B.S. degree in mechanical design, and the M.S. and Ph.D. degrees from Konkuk University, Seoul, Korea in 2000, 2003, and 2010, respectively. He is currently a Researcher at the Flexible Display Roll-to-Roll Research Center at Konkuk University. His research interests are in the area of 2-D register modeling and control for printed electronics, dancer and distributed real-time control. He is the holder of several patents related to R2R e-Printing system. Dr. Kang received a Certificate of Recognition from the Metal Industry Committee of Industry Application Society of IEEE in 2010.
Chang-Woo Lee (M’10) received the B.S. degree in mechanical engineering, and the M.S. and Ph.D. degrees from Konkuk University, Seoul, Korea, in 2001, 2003, and 2008, respectively. He is currently a Research Professor in the Flexible Display Roll-to-Roll Research Center, Konkuk University, where he is working on the development of roll-to-roll (R2R) multilayer printing systems for printed electronics. He is the holder of several patents related to the R2R e-printing system. His research interests are in the areas of fault-tolerant control, R2R e-printing line design, noncontacting transportation, and tensionregister control.
Kee-Hyun Shin (M’02) received the B.S. degree from Seoul National University, Seoul, Korea, and the M.S. and Ph.D. degrees in mechanical engineering from Oklahoma State University, Stillwater. Since 1992, he has been a Professor in the Department of Mechanical Engineering, Konkuk University, Seoul, and the Director of the Flexible Display Roll-to-Roll Research Center. He is the author of Tension Control (TAPPI Press, 2000). For more than 18 years, he has covered several research topics in the area of web handling, including tension control, lateral dynamics, and diagnosis of defect rolls/rollers.
Sang-Chul Kim received the B.S. and M.S. degrees in electrical engineering from Kyungpook National University and Computer Science from Changwon National University, Changwon, Korea, in 1994 and 1998, respectively, and the Ph.D. degree in electrical and computer engineering from Oklahoma State University, Stillwater, in 2005. During 1994–1999, he worked in Samsung SDS as a System Engineer. He is currently an Associate Professor in the School of Computer Science at Kookmin University, Seoul, Korea. His research areas of interests are wireless communications and real-time operating systems.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 4, JULY/AUGUST 2011
Modeling and Matching Design of a Tension Controller Using Pendulum Dancer in Roll-to-Roll Systems Hyun-Kyoo Kang, Member, IEEE, Chang-Woo Lee, Member, IEEE, Kee-Hyun Shin, Member, IEEE, and Sang-Chul Kim
Abstract—Dancer systems are typical equipment for attenuation of tension disturbances. The two kinds of dancer, active dancer and passive dancer, are distinguished by an external actuator. In the active dancer, the position of the dancer roll is measured and the roll is forced by the external actuator to regulate tension disturbances. However, the passive dancer, composed of a spring, damper and roll has no external actuator. Tension disturbance generates movements of the roll of the passive dancer and the displacements regulate the tension variation. However, the hybrid dancer, which is a mixture of passive and active dancer, is applied for the roll-to-roll systems. It regulates tension disturbances indirectly in the manner of keeping a constant position for the roll by changing the velocity of the driven roller adjacent to the dancer roll. It has different characteristics from those of the passive or active dancer. In this paper, the modeling of the pendulum dancer is derived. The dynamics of the hybrid dancer, which feedbacks the position of the dancer roll, and the PI control of a driven roll are analyzed. The matching logic for tuning gains is developed and experimentally verified. Index Terms—Gain tuning, matching design, pendulum dancer, roll-to-roll, tension control.
N OMENCLATURE lu lu0 ld ld0 l1 l2 θ
Upstream span length of dancer (m). Upstream span length of dancer at steady state (m). Downstream span length of dancer (m). Downstream span length of dancer at steady state (m). Rod length of hinge to cylinder (m). Rod length of hinge to dancer roll (m). Angle of dancer arm.
Manuscript received January 21, 2011; accepted March 8, 2011. Date of publication May 19, 2011; date of current version July 20, 2011. Paper 2011-METC-002, presented at the 2010 Industry Applications Society Annual Meeting, Houston, TX, October 3–7, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Metals Industry Committee of the IEEE Industry Applications Society. This research was supported by the “Seoul R&BD Program (10848) and Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST, K21001001666-10E0100-08810). H.-K. Kang and C.-W. Lee are with the Flexible Display Roll-to-roll Research Center, Konkuk University, Seoul 143-701, Korea (e-mail: hyunkyoo@ gmail.com; [email protected]). K.-H. Shin is with the Department of Mechanical Engineering, Konkuk University, Seoul 143-701, Korea (e-mail: [email protected]). S.-C. Kim is with the School of Computer Science, Kookmin University, Seoul 136-702, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2156376
E rd Jd Jeq bd b vd vd0 Vd vi vi0 Vi ti ti0 Ti P0 A0 Fk εi ρu Au
Young’s modulus (N/m2 ). Radius of dancer idle roll (m). Moment of inertia of dancer idle roll (kgm2 ). Equivalent moment of inertia of dancer (kgm2 ). Rotary bearing friction constant of dancer idle roll. Rotary bearing friction constant of hinge. Tangential velocity of dancer roll (m/s). Tangential velocity of dancer roll at steady state (m/s). Variation of tangential velocity of dancer roll (m/s). Tangential velocity of ith roll (m/s). Tangential velocity of ith roll at steady state (m/s). Variation of tangential velocity of ith roll (m/s). Tension of web in ith span (N). Tension of web in ith span at steady state (N). Variation of tension of web in ith span (N). Pressure of pneumatic cylinder (N/m2 ). Area of piston of pneumatic cylinder (m2 ). Spring force of pneumatic cylinder (N). Strain of web in ith span. Density of unstretched web (kg/m3 ). Cross sectional area of unstretched web (m2 ).
I. I NTRODUCTION
A
WEB is thin and flexible material, in which the width is very less than its length. Film, paper, steel and textile represent examples. In the middle or last step of the production, the web is stored in the form of a wound roll, such as a rolling coil, printing film or paper. Roll-to-roll systems consist of unwinder, driven roller, idle roller and winder for transportation and web processes such as printing, coating, and laminating [1]–[6]. Fig. 1 depicts a direct gravure printing machine. Multi-layered or multi-colored patterns are printed on the web, such as paper or film i.e., OPP, LDPE, or PET. The velocity should be increased to improve production efficiency. In addition, roll-to-roll systems have focused on the manufacture of printed circuits, e.g., RFID tag, signage or solar cell using a roll-to-roll printing machine. It is necessary to research mathematical modeling and control methods of rollto-roll systems to achieve high productivity for printed electronics. Unwinder, infeeder, outfeeder and winder complete the printing machines. Printing and drying processes were applied between the infeeder and outfeeder. It is crucial for high quality printing to maintain constant tension on the web entering the
0093-9994/$26.00 © 2011 IEEE
KANG et al.: MODELING AND MATCHING DESIGN OF A TENSION CONTROLLER
Fig. 1.
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Schematic of converting machines.
first printing roll. Dancer systems are equipped in the unwinder and infeed sections to attenuate the tension variation. Tension variation directly affects printing errors [7]. Web dynamics have been researched by Campbell [8], Grenfell [9], Brandenburg [10], and Shin [11] to propose real-time distributed tension control methods. The two kinds of dancer systems are active and passive. Pagilla developed an active dancer that is better for precise tension control and attenuation of a wider frequency range of tension disturbance than the case of a passive dancer [12], [13]. Ramamurthy conducted a comparative study of passive and active dancers [14]. It was pointed out that control performance of the active dancer is aggravated under high frequency tension disturbance. It means that the dynamic performance of the active dancer is restricted by the actuator of the dancer roll. Although a high performance actuator could be applied to the dancer, it requires a greater cost and it is difficult to implement the additional actuator and housing and so on. Therefore, the active dancer is rarely applied to roll-to-roll machines. The passive dancer consists of spring, damper and idle roll without an additional actuator. The dancer idle roll, which is positioned by a spring and damper, is moved due to a moment variation caused by tension disturbance. The movement of the dancer idle roll could absorb tension disturbances. Shin developed the mathematical modeling of the passive dancer system including the modeling of web tension. He proposed resonance frequency as a design parameter [11]. Shelton analyzed the limitation of the passive dancer on the measurement of tension as a sensor [16]. Knittel developed the H infinite tension controller for passive dancer systems. However, a hybrid dancer system, which is a mixture of a passive and active dancer, is applied to the roll-to-roll systems to attenuate tension disturbances. The appearance of a hybrid dancer is similar to the passive one. A PI (Proportional-Integral) control loop of velocity of the driven roll is applied to the dancer to regulate position variations of the dancer roll. There is no additional actuator to control the position of the dancer roll directly. The hybrid dancer regulates tension disturbances indirectly in the manner of keeping constant position by changing the velocity of the driven roller adjacent to the dancer roll. Thus, the hybrid dancer
can operate in the allowable swing range physically in spite of huge tension disturbance. Dynamic characteristics of the hybrid dancer differ from the active or passive dancer. Therefore, it is necessary to research the design guidelines and gain tuning method of the PI position feedback dancer control method to increase velocity and productivity. As yet, there is no research on hybrid dancer systems. Thus, the primary objective of this paper is to propose a guideline for dancer hardware and the gain tuning method. Mathematical modeling of the PI position feedback hybrid dancer systems is developed toward this aim. Analysis of poleszeros with varying velocity is conducted using this model. Tension disturbance prediction due to roll eccentricity is conducted. A matching control scheme that considers system characteristics is proposed. II. M ATHEMATICAL M ODEL A. Tension Model of Dancer Systems A control volume could be drawn between two rolls, as shown in Fig. 2. The law of conservation of mass for the control volume can be written as follows: ρu Au v1 (t) ρu Au v2 (t) d − = 1 + ε1 (t) 1 + ε2 (t) dt
l u (t)
ρu Au dx. 1 + ε2 (t)
(1)
0
Substitute lu (t) = lu0 + l2 θ(t) into (1), and rearranging ε˙2 gives ⎡ ⎤ v1 (t) − v2 (t) + v2 (t)ε2 (t) −1 ˙ ⎣ −v1 (t)ε1 (t) − l2 θ(t) ⎦ . (2) ε˙2 (t) = lu0 + l2 θ(t) ˙ +l2 θ(t)ε2 (t) Equation (2) is the nonlinear tension model for upstream of the dancer system. Using the same procedure, the nonlinear tension model of downstream of the dancer system is as in (3) ⎡ ⎤ v2 (t) − v3 (t) + v3 (t)ε3 (t) −1 ˙ ⎣ −v2 (t)ε2 (t) − l2 θ(t) ⎦ . (3) ε˙3 (t) = ld0 + l2 θ(t) ˙ +l2 θ(t)ε3 (t)
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Fig. 4.
Fig. 2. Control volume of dancer systems.
Force on dancer arm.
Equation (6) must be satisfied in the initial steady-state condition with 0 = (t30 − t20 )rd2 − bd v20 .
(9)
Substituting (7)–(9) into (6) gives Jd V˙ d (t) = {T3 (t) − T2 (t)} rd2 − bd Vd (t).
(10)
In (10), tangential velocity is determined by the moment of inertia of the roll, radius of roll, and difference of tension. Fig. 3. Torque on the dancer idle roll.
C. Tangential Velocity of a Dancer Arm
Equation (2) and (3) can be linearized by the Taylor linearization, as follows: 1 AE {−V1 (t) + V2 (t)} + v10 T1 (t) T˙2 (t) = (4) ˙ lu0 −v20 T2 (t) + AEl2 θ(t) 1 AE {−V2 (t) + V3 (t)} + v20 T2 (t) T˙3 (t) = . (5) ˙ ld0 −v30 T3 (t) + AEl2 θ(t) Equations (4) and (5) are the linear tension model of the upstream and downstream span of the dancer system, respectively.
¨ = − l2 {t2 (t) + t3 (t)} Jeq θ(t)
FK
˙ + {P0 A0 − FK (t)} l1 − bθ(t)
0.078 24 + l1 θ(t) + 24. = 0.078 2
(11) (12)
At the steady-state operating condition, (11) should satisfy (13). Substituting (12) and (13) into (11) gives (14). The dancer arm dynamics are affected by the tension difference
B. Tangential Velocity of a Dancer Roll The velocity of the dancer roll is determined by the difference of tension between the upstream and downstream span, as shown in Fig. 3. The torque equation can be written as (6). The tangential velocity is expressed as (7). Let the velocity be as in (8) Jd θ¨d (t) = {t3 (t) − t2 (t)} rd − bd θ˙d (t)
(6)
θ˙d (t)rd = vd (t)
(7)
vd (t) = vd0 + Vd (t).
Fig. 4 depicts the forces on the dancer arm. The torque equation, considering the upstream and downstream span tension, spring force and force of pneumatic cylinder is in (11). The spring force of the pneumatic cylinder is as in (12)
(8)
0 = − l2 (t10 + t20 ) + (P0 A0 − 36)l1
(13)
˙ ¨ = − l2 {T2 (t) + T3 (t)} − 24 l2 θ(t) − bθ(t). (14) Jeq θ(t) 0.078 1 D. Transfer Function of Dancer Systems The Laplace transformations of the tension (4) and (5), tangential velocity of the dancer roll (10) and tangential
KANG et al.: MODELING AND MATCHING DESIGN OF A TENSION CONTROLLER
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Fig. 6. Block diagram of infeed dancer. TABLE I S IMULATION C ONDITIONS
Fig. 5.
PI dancer controller of infeed section.
velocity of the dancer arm (14) are combined then, the inputoutput model of dancer systems is expressed as θ(s) −AE = D(s) V0 (s) A(s) − B(s)
(15)
C(s)
where AEr22 + AEr22 sJ + b2 2
2 −AEr2 24 2 l1 + AEsl2 B(s) = Jeq s2 + sb + (sJ2 + b2 )l2 0.078 2AEr22 C(s) = sld + v20 + v30 + sJ2 + b2
1 24 2 2 l D(s) = − Jeq s + sb + l2 0.078 1
AEr22 × sld + v30 + − AEsl2 . sJ2 + b2 A(s) = slu + v20 +
III. A NALYSIS OF DANCER S YSTEMS AND G UIDELINE FOR G EOMETRICAL D ESIGNS Roll-to-roll systems consist of unwinding, infeeding, printing, outfeeding, and rewinding sections. The tangential velocity of the first printing roll is fixed as the master speed that is the same as the operating velocity. The pressure of the pneumatic cylinder of the dancer system is obtained by (13). The dancer arm angle is measured by a potentiometer and the velocity of the infeeding roll is controlled to regulate the dancer arm position using PI-controller. It regulates the tension disturbance indirectly by balancing the tension and pneumatic pressure. The signal flow and block diagram of the PI position feedback control loop of the infeeding section are depicted as Figs. 5 and 6, respectively. The angle of dancer arm is measured by a potentiometer, filtered by the first order low-pass filter. Then, the velocity of the infeeding roll is controlled.
Fig. 7. Pole-zero map with varying operation velocity (200 ∼ 500 m/min).
A. Analysis of Dancer Systems The analysis of the dynamic characteristics of the PI position feedback dancer system was performed by drawing pole-zero maps with varying system parameters, i.e., operating velocity, rod length, span length, and inertia. Table I describes the simulation parameters. As the velocity is increased, oscillation poles are moving left side and dominant poles are fixed in s-plane (Figs. 7 and 8). It means that transient tension disturbances are reduced fast and
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Fig. 8. Pole-zero map with varying velocity (zoom in).
Fig. 10.
Pole-zero map with changed dancer rod (zoom in).
Fig. 11.
Pole-zero map with varying span length.
Fig. 12.
Pole-zero map with varying inertia of Jeq (0.1 ∼ 10).
Fig. 9. Pole-zero map with changed dancer rod.
settling time is not changed in high speed operation. If the PI controller gains are determined for low velocity, it would work sufficiently in high speed. Figs. 9 and 10 depict the poles and zeros with varying rod lengths. The dominant pole moves toward the imaginary axis as the rod lengths is increased. Then, the dancer response capability is decreased. Fig. 11 depicts poles and zeros with varying span length. Poles move toward an imaginary axis as the length of the upstream span is increased. Therefore, the dancer response capability is decreased. In Fig. 12, poles are positioning near the imaginary axis, as the inertia of dancer systems is increased. Then, the dancer response capability is decreased. B. Guidelines for Mechanical Design of Dancer Systems Operating velocity, span length of the upstream and downstream of the dancer roll, and the inertia of the dancer systems are sensitive parameters that affect the performance of the hybrid dancer system. The increased velocity of the web improves the response capability of the hybrid dancer system.
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Fig. 14. Root locus with Tn = 1. Fig. 13. Bode plot of transferred tension (300 ∼ 500 m/min).
The upstream span, in which the span length is shorter than the downstream span, improves the response capability of the dancer system. A lower dancer inertia improves the dancer system response capability. Therefore, the dancer systems have to be designed to have a shorter upstream than downstream span and with less inertia. PI gains tuned in low velocity could work at higher velocity, because dancer poles move to the left of the s-plane in high velocity operation. Then, the PI gains should be determined in the low speed operation. IV. D ESIGN G UIDELINE OF PI T ENSION C ONTROLLER A. Frequency of Tension Disturbance It is necessary to attenuate tension disturbance entering into the printing section for precise register control. Generally, the allowable tension disturbance is ±2% of the operating tension. Therefore, response performance to the maximum tension disturbance is a design criterion of the PI controller. The eccentricity of the unwinding roll is a major cause of disturbance of the tension. As the substrate is unwound, the diameter of the unwinder decreases and the frequency of tension increases. The range of tension disturbance is determined in (16). For example, if the diameter of the unwinder is 1 m to 0.1 m, the maximum frequency is 100 rad/s to 166.7 rad/s in 300 m/min to 500 m/min, respectively ωmax
2v0 = , Du,min
ωmin
2v0 = . Du,max
(16)
Fig. 15. Root locus with Tn = 10.
a tension disturbance 50 N to 2 N is −27.96 dB and the frequencies are 23.13 rad/s, 38.55 rad/s for 300 m/min, 500 m/min, respectively, in Fig. 13. Transferred unwinding tension disturbances above 38.55 rad/s could result in a decrease of less than 2 N. This is in the allowable range in the infeeding section. It is reasonable that the frequency of tension disturbances above ωmax , calculated by (18), do not need to be considered the infeeding section T2 (s) v10 = T1 (s) Ls + v20
top · 0.02 v10
=
.
T1 (s) Ls + v20 s=jωmax
(17) (18)
B. Prediction of Tension Disturbance Tension disturbance is transferred from upstream to downstream, the affect is like the first order low-pass filter. The filter is determined by the span length and initial velocity as in (17). Fig. 13 illustrates the bode plot of (17). For example the allowable disturbance is ±2% of the operating tension, the maximum tension disturbance of the unwinding section is 50 N and the span length is 5.4 m. The magnitude that creates
C. Gain Turing of PI Tension Controller PI controller gains are determined by root locus of dancer system which has control loop as Fig. 5. While I-gain is increased, root locus plots are depicted to calculate a dominant pole in Figs. 14–17. Dominant poles are listed in Table II. P- and I-gains are 0.0402 and 1000, respectively, for the dominant pole positioned in last left side.
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Fig. 16. Root locus with Tn = 100.
Fig. 18. Step response of 50 N unwinder tension disturbance (500 m/min, Kp = 0.0402, Tn = 1000).
Fig. 19.
Three-layer gravure printing machine in FDRC.
Fig. 20.
Operation velocity in experiments (0 ∼ 470 m/min).
Fig. 17. Root locus with Tn = 1000. TABLE II C ONTROLLER G AINS AND P OLES
D. Experimental Gain Tuning Numerical simulation was conducted to validate the performance of the tension regulation of PI dancer controller. In Fig. 18, the response of 50-N step tension disturbance which conducted using PI gains set by root locus plot is depicted. It satisfies the allowable range (±2%) of tension variation. The gains are used for the initial value of the experimental gain tuning. Using the three layer gravure printing system which has dancer system in its feeding section, experimental verification was carried out (Fig. 19). The operation velocity was increased up to 470 m/min as Fig. 20. As the velocity increased from
zero to the operating speed, the P-gain would be changed in inverse proportion to the variation of the dancer arm angle. As the operating speed increases, the system becomes more stable, because oscillation poles moves to the left side of the s-plane as Fig. 8. PI-gains, tuned at low velocity, are reasonable across all operating speeds. The PI-gains determined through the
KANG et al.: MODELING AND MATCHING DESIGN OF A TENSION CONTROLLER
Fig. 21. Unwinder and infeeder tension (200 m/min).
Fig. 24. Unwinder and infeeder tension (470 m/min).
Fig. 22. Unwinder and infeeder tension (300 m/min).
Fig. 23. Unwinder and infeeder tension (400 m/min).
experiment are Kp = 0.08, Tn = 1000. They are suitable for the tension regulation requirement, ±2% of operating tension, as shown in Figs. 21–24. Fig. 25 depicts the procedures for the PI-gain tuning method.
Fig. 25. Matching logic for design of PI dancer controller.
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V. C ONCLUSION For the regulation of tension disturbances, dancer system is applied in the roll-to-roll system. The two kinds of dancer, active dancer and passive dancer, are distinguished by an external actuator. In the active dancer, the roll position is controlled directly by an external actuator, but the performance is restricted by the limitation of the external actuator. It is more costly and there are difficulties of implementation. Thus, the active dancer is rarely applied to roll-to-roll machines. Moreover, a passive dancer, which regulates tension variations by idle roll, spring and damper, could control small magnitudes of variation due to the limitation of the allowable rotation range of the dancer arm. A hybrid dancer system, a mixture of passive and active dancer, is applied for the roll-to-roll systems to attenuate tension disturbances. The position of the roll is measured by potentiometer. The driven roll is controlled to regulate the position without an external actuator. The characteristics of this dancer differ from those of active and passive dancers. It is necessary to research design guidelines and to determine a tuning method of the PI position feedback dancer control method. However, there was no earlier related research on the hybrid dancer. The following conclusions can be drawn from this paper: 1) a mathematical model of a pendulum dancer has been developed; 2) a dynamics of hybrid dancer systems, which feedback position of the dancer roll and control a driven roller, are analyzed; 3) gains, which have dominant poles, are determined using root locus plots; 4) the matching logic for tuning gains is developed and the logic is experimentally verified at 470 m/min. R EFERENCES [1] K. H. Shin, Tension Control. Atlanta, GA: Tappi Press, 2000. [2] H. Kang, C. Lee, and K. Shin, “A novel cross directional register modeling and feedforward control in multi-layer roll-to-roll printing,” J. Process Control, vol. 20, no. 5, pp. 643–652, Jun. 2010. [3] H. Kang, C. Lee, J. Lee, and K. Shin, “Cross direction register modeling and control in multi-layer gravure printing,” J. Mech. Sci. Technol., vol. 24, no. 1, pp. 391–397, Jan. 2010. [4] H. Kang, C. Lee, and K. Shin, “Novel modeling of correlation between two-dimensional registers in large-area multilayered roll-to-roll printed electronics,” Jpn. J. Appl. Phys., vol. 50, no. 1, pp. 016 701-1–016 701-7, Jan. 2011. [5] C. Lee, H. Kang, H. Kim, H. A. D. Nguyen, and K. Shin, “Quality control with matching technology in roll to roll printed electronics,” J. Mech. Sci. Technol., vol. 24, no. 1, pp. 315–318, Jan. 2010. [6] C. Lee, J. Lee, H. Kang, and K. Shin, “A study on the tension estimator by using register error in a printing section of roll to roll e-printing systems,” J. Mech. Sci. Technol., vol. 23, no. 1, pp. 212–220, Jan. 2009. [7] P. Lin and M. S. Lan, “Effect of PID gains for controller with dancer mechanism on web tension,” in Proc. 2nd Int. Conf. Web Handling, 1991, pp. 66–76. [8] Campbell, Process Dynamics. Hoboken, NJ: Wiley, 1958, pp. 20–21. [9] K. P. Grenfell, “Tension control on paper-making and converting machinery,” in Proc. IEEE 9th Annu. Conf. Elect. Eng. Pulp Paper Ind., 1963, pp. 20–21. [10] G. Brandenburg, “New mathematical models for web tension and register error,” in Proc. 3rd Int. IFAC Conf. Instrum. Autom. Paper, Rubber Plastics Ind., 1977, vol. 1, pp. 411–438. [11] K. H. Shin, “Distributed control of tension in multi-span web transport systems,” Ph.D. dissertation, Oklahoma State Univ., Stillwater, OK, 1991. [12] P. R. Pagilla, L. P. Perera, and R. V. Dwivedula, “The role of active dancers in tension control of webs,” in Proc. 6th Int. Conf. Web Handling, 2001, pp. 227–242.
[13] P. R. Pagilla, “Periodic tension disturbance attenuation in web process lines using active dancers,” J. Dyn. Syst. Meas. Control, vol. 125, no. 3, pp. 361–371, 2003. [14] R. V. Dwivedula, Y. Zhu, and P. R. Pagilla, “Characteristics of active and passive dancers: A comparative study,” Control Eng. Pract., vol. 14, no. 4, pp. 409–423, Apr. 2006. [15] E. Y. Hong, “Aerodynamic dancer and tension transducer in web handling,” Ph.D. dissertation, Oklahoma State Univ., Stillwater, OK, 2005. [16] J. J. Shelton, “Limitations to sensing of web tension by means of roller reaction forces,” in Proc. 5th Int. Conf. Web Handling, 1999. [17] M. Vedrines and D. Knittel, “Modelling and H∞ low order control of web handling systems with a pendulum dancer,” in Proc. 17th World Congr. IFAC, 2008, pp. 1012–1017. [18] B. C. McDow and C. D. Rahn, “Adaptive web-tension control using a dancer arm,” Tappi, vol. 81, no. 10, pp. 197–205, 1998.
Hyun-Kyoo Kang (M’11) received the B.S. degree in mechanical design, and the M.S. and Ph.D. degrees from Konkuk University, Seoul, Korea in 2000, 2003, and 2010, respectively. He is currently a Researcher at the Flexible Display Roll-to-Roll Research Center at Konkuk University. His research interests are in the area of 2-D register modeling and control for printed electronics, dancer and distributed real-time control. He is the holder of several patents related to R2R e-Printing system. Dr. Kang received a Certificate of Recognition from the Metal Industry Committee of Industry Application Society of IEEE in 2010.
Chang-Woo Lee (M’10) received the B.S. degree in mechanical engineering, and the M.S. and Ph.D. degrees from Konkuk University, Seoul, Korea, in 2001, 2003, and 2008, respectively. He is currently a Research Professor in the Flexible Display Roll-to-Roll Research Center, Konkuk University, where he is working on the development of roll-to-roll (R2R) multilayer printing systems for printed electronics. He is the holder of several patents related to the R2R e-printing system. His research interests are in the areas of fault-tolerant control, R2R e-printing line design, noncontacting transportation, and tensionregister control.
Kee-Hyun Shin (M’02) received the B.S. degree from Seoul National University, Seoul, Korea, and the M.S. and Ph.D. degrees in mechanical engineering from Oklahoma State University, Stillwater. Since 1992, he has been a Professor in the Department of Mechanical Engineering, Konkuk University, Seoul, and the Director of the Flexible Display Roll-to-Roll Research Center. He is the author of Tension Control (TAPPI Press, 2000). For more than 18 years, he has covered several research topics in the area of web handling, including tension control, lateral dynamics, and diagnosis of defect rolls/rollers.
Sang-Chul Kim received the B.S. and M.S. degrees in electrical engineering from Kyungpook National University and Computer Science from Changwon National University, Changwon, Korea, in 1994 and 1998, respectively, and the Ph.D. degree in electrical and computer engineering from Oklahoma State University, Stillwater, in 2005. During 1994–1999, he worked in Samsung SDS as a System Engineer. He is currently an Associate Professor in the School of Computer Science at Kookmin University, Seoul, Korea. His research areas of interests are wireless communications and real-time operating systems.
