KR101000826B1 - Matching Method Design of a Tension Controller with Pendulum Dancer in Roll-to-Roll Systems - Google Patents

Abstract

A tension control system and method using a pendulum denser of a high speed roll to roll system is disclosed. After modeling the speed of the denser roll and the arm, the transfer function of the system, the frequency of the disturbance disturbance is analyzed, and the gain is selected through the root trajectory diagram in consideration of the operating speed and the dynamic characteristics of the web. Increasing production speed and printing quality can improve price competitiveness and improve production quality.

Roll to Roll, Denser, Arm, Driving Speed, Dynamic Characteristics

Description

Matching Method Design of a Tension Controller with Pendulum Dancer in Roll-to-Roll Systems}

The present invention relates to a tension control system, and in particular, a pendulum of a high-speed roll-to-roll system that can contribute to price competitiveness improvement and production quality improvement by increasing the production speed and printing quality of the system using a tension model before and after the denser roll. A tension control system and a fluoroscopy device using a denser.

A web is a flexible, longitudinally continuous material, such as film, paper, steel, or textile. In many industries, the web is a form of web that can produce intermediate or final products such as rolled coils or film, paper, or printing paper. Saving. 1 is a schematic diagram of a gravure printing press, which is a representative roll-to-roll (R2R) system, and a domestic product has a driving performance of 300 m / min. Increasing process speed (500m / min target) to increase productivity, and recently to produce R2R printing method for RFID tag, signage, flexible display, etc. Printed electronics technology is drawing attention. In order to develop such a printing technology, it is necessary to study the development theory and control theory of each part through basic research of R2R.

The R2R system consists of an unwinder, a winder, an infeeder, an outfeeder, and the like, such as printing and drying between the infeeder and the outfeeder. Process exists. In order to maintain a certain level of print quality, it is essential to keep the tension of the web material uniformly introduced into the printing process. In order to control the tension, the tension is controlled by installing dancer systems in the unwinder and the infeeder section, and the magnitude of the tension error directly affects the printing quality of the web. A study of the dynamics of the web was established by Campbell, Grenfell, and Brandenburg, and Shin proposed real-time distributed tension control in multispan.

There are two types of denser systems, active and passive dacers. The research on the active denser has been proposed by Pagilla, and it has the advantage that it is possible to perform the tension disturbance control and the fine tension control in the wider frequency range than the passive denser. Ramamurthy conducted a comparative study of passive and active capacitors. However, in Hong's additional denser study, active densers have a limit in their ability to compensate for high frequency tension disturbances, because the control performance of active densers is limited by the dynamics of the denser roll actuators. In addition, even when using a high-performance actuator, due to the cost of additional devices and difficulty in implementing the device, compared to a general passive capacitor, an active capacitor has a low applicability as a tension controller.

The passive denser translates the idle roll supported by the spring-damper due to the moment change caused by the tension disturbance of the web, and absorbs the tension disturbance generated in the web by changing the position of the idle roll. . Based on the tension model, Shin proposed the modeling of passive capacitors consisting of springs, dampers and idle rolls, and suggested usable resonance frequencies as design parameters. Shelton analyzed the limitations of using passive densers as tension sensors. Knittel proposed a denser system using H _∞ control. However, the passive denser performs tension control only by changing the span length through the translational movement of the denser roll without an actuator, and has a limitation of the tension control range due to the limitation of the mechanical movement range of the denser roll.

To overcome these shortcomings, the R2R system uses a hybrid of passive and active capacitors. It is a method of controlling the PI (Proportional-Integral) of the driven rollers located before and after the denser roll by feeding back the position of the denser roll while using a passive denser without an additional actuator. This is to stably control the tension by preventing the denser roll out of the physical allowable range due to excessive tension disturbance. The R2R denser system is distinguished from the dynamic characteristics of the existing active or passive denser, and researches on the design of the denser system and the gain setting method of the feedback PI controller are required to improve the productivity by increasing the operation speed. However, no research has been conducted on the mixed denser system using the denser roll position feedback-driven roll speed control method, and the industrial field relies on the skilled engineer of a foreign motor-driver company.

In order to solve this problem, the present invention considers the matching of the pole position feedback, the prediction of tension disturbance due to the eccentricity, the tension transfer phenomenon, etc. according to the operating speed of the R2R system performing the PI of the denser position feedback, the driven roller. The objective is to provide gain design techniques for PI controllers.

It is a second object of the present invention to provide a tension control system using a pendulum denser of a high-speed roll-to-roll system that can analyze the maximum tension disturbance considering the filtering effect of the web and the unwinder eccentricity.

It is also a third object of the present invention to provide a tension control system using a pendulum denser of a high speed roll-to-roll system that can select a gain having a minimum dominant pole through a near locus diagram.

A fourth object of the present invention is to provide a tension control method using a pendulum denser of a high-speed roll-to-roll system capable of adjusting a proportional gain according to an angle change of a denser arm and designing a controller within an allowable tension disturbance range.

In order to achieve the above object, a tension control method using a pendulum denser of a high speed roll-to-roll system according to an embodiment of the present invention includes obtaining a transfer function of a denser system, analyzing a frequency of tension disturbance of the denser system, and a denser. Analyzing tension control performance by analyzing the tension disturbance in consideration of the operating speed of the system and the dynamic characteristics of the web, and selecting the gain through the root locus diagram of the denser system.

This transfer function is to obtain the tension modeling of the span before and after the denser roll and the velocity modeling of the denser idle roll. It is characteristic.

Therefore, the transfer function is expressed by the following equation.

는 덴서 암의 힌지중심에 대한 전체 덴서시스템의 등가 관성모멘트를 나 타낸다.Where l _{u and} l _d are the upstream and downstream span lengths of the denser roll, l ₁ is the pneumatic cylinder rod length, l ₂ is the arm length of the denser roll, E is the Young's Modulus, r is the radius of the roll, J is Moment of inertia of the roll, b is the bearing friction coefficient, v is the web speed, V is the web speed change, A is the cross-sectional area,

Represents the equivalent moment of inertia of the entire denser system about the hinge center of the denser arm.

And, the step of analyzing the frequency of the tension disturbance of the denser system is characterized by analyzing the frequency range of the tension disturbance according to the diameter of the unwinder, wherein the frequency range is characterized by the following equation.

The step of analyzing the tension disturbance is characterized by grasping the response characteristics to the change of the operating speed through the pole-zero graph of the denser system, and the step of selecting the gain through the root locus diagram is based on the change of the integral gain. Investigating the dominant pole through the root locus diagram of the step, selecting the proportional gain (K _p ) and the integral gain (T _n ) at the leftmost position in the root locus diagram and the proportion at low speed The gain K _p and the integral gain T _n are adjusted to set the gain.

In addition, it is preferable to further include adjusting the gain through simulation of the response performance of the gain selected as the root locus diagram, and the gain adjustment is 50% of the operating tension of the unwinder (however, it may vary from system to system). Gain adjustment so that the response to the step tension disturbance is within the allowable tension disturbance range of ± 2% (which may vary from system to system), and the angle of the denser arm while increasing the speed at standstill. It is characterized by changing the proportional gain in inverse proportion to the amount of change.

Therefore, according to the present invention, it is possible to analyze the dynamic characteristics of the denser performing the position feedback PI speed control of the idle roll through the pendulum denser mathematical model of the R2R system.

In addition, there is an effect that high speed operation (470 m / min or more) is possible.

In addition, there is an effect that can contribute to the improvement of the price competitiveness and the production quality through the increase in the production speed and the print quality of the system.

The terms or words used in this specification and claims are not to be construed as limiting in their usual or dictionary meanings, and the inventors may properly define the concept of terms in order to best explain their invention in the best way possible. It should be interpreted as meaning and concept corresponding to the technical idea of the present invention.

Hereinafter, descriptions of symbols used in the present invention are as follows.

_u : upstream span length of dancer roll

l _d : downstream span length of dancer roll

l ₁ : rod length of hinge to cylinder

l ₂ : rod length of hinge to dancer roll

E: Young's modulus

r: radius of roll

J: Moment of inertia of roll

b: rotary friction constant of bearing

v: velocity of web

V: change in web velocity from a steady state value

t: tension of web

t _op : operation web tension

T: change in web tension from a steady state value

P: pressure of pneumatic cylinder

K _p : proportional gain

T _n: integral gain

J _eq : equivalent moment of inertia of the entire denser system with respect to the hinge center

θ _d : angle of rotation of the denser arm

Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

2 is a block diagram illustrating a denser system according to an embodiment of the present invention.

Obtain the tension model of the front and rear span of the denser roll.

The denser system of FIG. 2 transfers the web (not shown) in the direction of the arrow by means of the printing roll 112 and the infeed roll 114 to increase the tension of the web by the denser idle roll 110. It is configured to be adjustable, and the denser roll 110 is connected to the pneumatic cylinder 116 via the denser arm 116a and the pneumatic cylinder rod 116b.

Applying the law of conservation of mass in the upstream span of the denser system, we obtain:

) 및 장력과 변형률 관계(T=AEε)를 [수학식1]에 대입하고,

로 정리한 후에 Taylor 정리를 통해 선형화하면, [수학식2]의 덴서롤 상류스팬의 선형 장력 모델을 얻는다.Span length

) And the relationship between the tension and the strain (T = AEε) in [Equation 1],

After linearizing through Taylor's theorem, the linear tension model of the upstream span of the denser roll of Equation 2 is obtained.

In addition, the linear tension model of [Equation 3] is obtained through the same process for the denser idle roll 110 downstream span.

The speed of the denser idle roll 110 is determined by the tension difference of both webs. The torque generated by the tension in the denser idle roll 110 is shown in [Equation 4]. [Equation 5] is the tangential velocity of the roller, and it is assumed that Equation 6 is the relationship between the speed at the equilibrium point and the change amount.

At this time, the tension generated at both ends of the denser idle roll 110 is assumed to be a combination of the tension and the change amount at the equilibrium point, and after substituting [Equation 5], [Equation 6] into [Equation 4] Equation (7), which is a roll speed model, is obtained.

Modeling of Denser Arms

Due to the tension generated in the denser idle roll 110 and the spring force and the pneumatic pressure generated in the pneumatic cylinder 116, the denser arm 116a rotates and the motion equation for this is as shown in [Equation 8]. .

[Equation 8] and equation (10), which is the relationship between the length of the pneumatic cylinder rod (116b) and the spring force, and [10] in the steady-state condition, the equation of the linearized denser arm of [Equation 11] Get the equation of motion

 Transfer Function of Denser System

To obtain the transfer function of the linearized denser system, the tension equations [Equation 2] and [Equation 3] before and after the denser idle roll, [Equation 7] and the equation of rotation model of the denser arm [Equation 7] [11] can be obtained by the following equation (12).

Hereinafter, a controller configuration diagram of the denser system will be described with reference to the drawings.

FIG. 3 is a diagram illustrating a signal flow diagram of a PI density controller in an infeed region used in an R2R machine, and FIG. 4 is a block diagram of an infeed capacitor.

The printing roll tangential speed of the infeed section is fixed as the reference speed of the entire process, that is, the master speed, and the pressure of the pneumatic cylinder 116 is set to satisfy [Equation 10]. At this time, the speed of the infeed roll 114 is controlled by PI-feedback the position of the denser roll so that the denser roll maintains its initial position. This is to control the tension by making the tension of the material and the reaction force caused by the pneumatic cylinder have the same value.

The signal flow diagram of the PI-denser position feedback tension controller in the infeed section used in the R2R machine is shown in FIG. 3, and a block diagram thereof is shown in FIG. 4. 4 shows the position of the denser arm of the denser model 110a with a potentiometer 120, filters the error in the error unit 124 through the filter 122, and then the PI controller 126. It is configured to perform the tension control by the speed change of the infeed roll through.

Frequency Analysis of Tension Disturbance

For high quality printing, the web material entering the printing process must maintain a uniform tension, and the allowable tension disturbance is set within ± 2% of the operating tension (which can be changed according to printing requirements). To this end, the design performance of the controller is based on the response performance to the maximum tension disturbance. The unwinder's eccentricity is a representative cause of tension disturbance. The unwinding of the material causes diameter reduction and tension frequency increase. The frequency range of the tension disturbance according to the diameter is shown in [Equation 13]. When the unwinder diameter change is 1 ~ 0.1m, the maximum frequencies for the operating speeds 300 and 500 (m / min) are 100 and 166.7 (rad / s), respectively.

Analysis of influence of driving speed

The pole-zero graph for the R2R denser system including the PI controller is used to identify the response characteristics to the operating speed change. The parameters used in the simulation are shown in [Table 1].

5 and 6 show the pole change with respect to the change in operating speed (200 ~ 500m / min). As the driving speed increases, the dominant pole is fixed, and the oscillation pole moves to the left to reduce the vibration effect, which improves the control performance with increasing speed. However, the control gain should be designed to satisfy the system response performance at low operating speed because acceleration and deceleration such as start and end of the system have to go through.

Controller design

Prediction of Tension Disturbance Considering Web Dynamics

The tension disturbance of the unwinder is transmitted to the infeed section, where the tension transmission has the effect of a low pass filter. When there is no speed change in the tension model of Shin, the filtering effect of the transmitted tension is shown in [Equation 14], through which the board diagram of FIG. 7 is plotted to select the frequency range of the tension disturbance.

If the allowable tension disturbance is ± 2% of the driving tension, the maximum tension disturbance of the unwinder is 50N, and the span length is 5.4m, the magnitude when the tension disturbance 50N of the unwinder decreases to 2N in the infeed section is- The frequency is 27.96 dB and the frequencies are 23.13 and 38.55 rad / s at 300 and 500 m / min, respectively (see Fig. 7). This means that in case of 500m / min operation, when 50N tension disturbance occurs in the unwinder and is transmitted to the infeed section, the disturbance over frequency 38.55rad / s exists within the allowable tension disturbance range (± 2% of driving tension). it means. As a result, tension disturbances exist within a frequency (ω _max ) satisfying Equation (15).

Gain selection through near locus diagram

PI control gain of the denser is determined through the root locus diagram of the denser system including the PI controller of FIGS. 8 to 11. Investigate the dominant pole through each root locus of change of integral gain to select proportional gain (K _p ) and integral gain (T _n ) at the leftmost position.

The root locus diagram for the integral gain change (1 to 1000) under the conditions of [Table 1] is shown in FIGS. 8 to 11, and the respective dominant poles are shown in [Table 2]. When the proportional gain 0.0402 and the integral gain 1000 are the smallest dominant poles, the corresponding gain is selected.

K _p 0.012 0.00111 0.04 0.0402 T _n One 10 100 1000 Dominant pole -0.169 -0.169 -0.875 ± 16i -0.896

Tension Control Performance Analysis and Experimental Adjustment

The response performance of the gain selected as the root locus diagram is verified through simulation. 50N step tension of unwinder (maximum size of expected tension disturbance. In this example, 50N, which is 50% for 100N operating tension, is assumed to be tension disturbance and can be changed depending on system conditions). After confirming the presence in (± 2%) in Figure 12, the gain is adjusted through the experiment. Change the proportional gain to increase the speed at rest and inversely proportional to the angle change of the denser arm. As the operating speed increases, the oscillation pole moves to the left and stabilizes (see FIG. 6), so that a gain suitable for the overall operating speed can be set by adjusting the gain at a low speed. In the experiment using the converting machine of FIG. 13, a proportional gain of 0.08 and an integral gain of 1000 were obtained, and it can be seen from FIGS. 14 to 18 that the tension control performance for this satisfies the tension disturbance requirement (± 2%). The flowchart for the controller design is shown in FIG. 19.

Hereinafter, a controller design method according to an embodiment of the present invention will be described with reference to the drawings.

19 is a flowchart illustrating a controller design step, in which tension disturbance is analyzed using a frequency band and a magnitude that may be generated (S200). At this time, the frequency range of the tension disturbance according to the diameter is obtained as shown in [Equation 13].

The maximum disturbance frequency considering the primary filtering of the web is set (S201).

In this case, when the unwinder diameter change is 1 ~ 0.1m, the maximum frequencies for the operating speeds 300 and 500 (m / min) are 100 and 166.7 (rad / s), respectively. That is, the tension disturbance is present within the frequency (ω _max ) satisfying [Equation 15].

Then, the transfer function of the entire system including the PI controller is derived (S202).

After that, a root locus diagram according to the integral gain is drawn and a minimum dominant pole proportional gain is selected (S203).

PI control gain of the denser is determined through the root locus diagram of the denser system including the PI controller of FIGS. 8 to 11. Investigate the dominant pole through each root locus of change of integral gain to select proportional gain (K _p ) and integral gain (T _n ) at the leftmost position.

The root locus diagram for the integral gain change (1 to 1000) under the conditions of [Table 1] is shown in FIGS. 8 to 11, and the respective dominant poles are shown in [Table 2]. When the proportional gain 0.0402 and the integral gain 1000 are the smallest dominant poles, the corresponding gain is selected.

In step S204, it is determined through simulation that the ± 2% disturbance control performance is satisfied. If it is satisfied, step S205 is performed. If not, step S203 is repeated.

Specifically, the response performance of the gain selected as the root locus diagram is verified through simulation. After confirming that the response to the 50N step tension disturbance of the unwinder is within the allowable tension disturbance range (± 2%), the gain is adjusted through experiments. Change the proportional gain to increase the speed at rest and inversely proportional to the angle change of the denser arm. As the operating speed increases, the oscillation pole moves to the left and stabilizes (see FIG. 6), so that a gain suitable for the overall operating speed can be set by adjusting the gain at low speed.

In step S205, the gain is adjusted through an acceleration (stop-operation speed) experiment, and it is determined whether there is vibration of the denser arm (S206).

If it is determined in step S206 that vibration of the denser arm is present, the proportional gain is reduced (S208), and the gain setting is completed (S209).

On the other hand, if it is determined in step S206 that the vibration of the denser arm does not exist, the proportional gain is increased (S207) to complete the gain setting (S209).

As described above, the present invention proposes a controller design method of the denser system for performing PI denser roll position feedback speed control based on a mathematical model of the denser of the R2R system.

The research on the existing denser is divided into active and passive denser. The active denser controls the position of the denser roll directly through the external actuator, but the dynamic characteristics of the actuator limits the dynamic characteristics of the entire denser system. have. In addition, the passive denser absorbing the tension disturbance through the idle roll supported by the spring damper has a disadvantage that only a narrow range of tension control is possible due to the limitation of the mechanical movement range of the denser roll. As a result, the R2R system feeds back the idle roll position change of the denser system composed of the passive denser to control the speed PI of the driven roller located upstream or downstream.

Since the denser system is distinguished from the dynamic characteristics of the existing active or passive denser, it is necessary to study the design of the denser system and the gain setting method of the PI controller to improve the productivity by increasing the operating speed, but the denser roll position feedback-speed control method Has not been studied for mixed denser systems. The results of the present invention are as follows.

(1) Through the Pendulum Denser mathematical model of the R2R system, the dynamic characteristics of the denser performing position feedback PI velocity control of the idle roll were analyzed.

(2) We analyzed the maximum tension disturbance considering the filtering effect of the web and the unwinder eccentricity.

(3) The gain with the minimum dominant pole was selected from the root locus diagram.

(4) Adjust the proportional gain according to the angle change of the denser arm, design the controller within the allowable tension disturbance range, and experimentally verify that high speed operation (470m / min) is possible.

Although the present invention has been described in detail only with respect to the described embodiments, it will be apparent to those skilled in the art that various changes and modifications can be made within the technical scope of the present invention, and such modifications and modifications belong to the appended claims.

1 is a schematic view of a gravure printing press, which is a roll-to-roll (R2R) system;

2 is a block diagram illustrating a denser system according to an embodiment of the present invention;

3 is a signal flow diagram illustrating a PI denser controller in an infeed region used in an R2R machine;

4 is a block diagram of an infeeder;

5 to 6 is a view showing a pole change with respect to the change in operating speed (200 ~ 500m / min),

7 is a schematic diagram of a board diagram for selecting a frequency range of tension disturbance;

8 to 11 are diagrams showing the root locus diagram for the integral gain change (1 to 1000),

12 is a diagram showing a response performance of a gain selected as a root locus diagram;

13 shows a converting machine used for an experiment,

14 to 18 show tension disturbance requirements;

And,

19 is a flowchart illustrating a controller design.

<Description of the symbols for the main parts of the drawings>

110: denser roll 110a: denser model

112: printing roll 114: infeed roll

116: pneumatic cylinder 116a: denser arm

116b: pneumatic cylinder rod 120: potentiometer

122: filter 124: error unit

126: PI controller

Claims (9)

(a) obtaining a transfer function of the denser system; (b) analyzing the frequency of tension disturbance of the denser system; (c) analyzing the tension disturbance in consideration of the operating speed of the denser system and the dynamic characteristics of the web; And (d) selecting gain through a root locus diagram of the denser system; Tension control method using a pendulum denser of the high-speed roll-to-roll system to analyze the tension control performance by configuring to include. The method of claim 1, Step (a) is Obtaining tension modeling of the span before and after the denser roll; Obtaining velocity modeling of the denser idle roll; And Obtaining velocity modeling of the denser arm; And Obtaining a transfer function using the tension modeling, idle roll speed modeling, and arm modeling; Tension control method using a pendulum denser of the high-speed roll-to-roll system for analyzing the tension control performance, characterized in that comprises a. The method of claim 1, The transfer function in step (a) is a tension control method using a pendulum denser of a high-speed roll-to-roll system for analyzing the tension control performance, characterized in that expressed by the following equation.

Where l _{u and} l _d are the up and down span length of the denser roll, l ₁ is the pneumatic cylinder rod length, l ₂ is the arm length of the denser roll, E is the Young's modulus, r is the roll radius, J is the moment of inertia of the roll, b Is the bearing friction coefficient, v is the web speed, V is the web speed change, A is the cross-sectional area,

Represents the equivalent moment of inertia about the hinge center of the denser arm. The method of claim 3, wherein Step (b) is And a frequency range of tension disturbance according to a diameter, wherein the frequency range is a tension control method using a pendulum denser of a high-speed roll-to-roll system for analyzing a tension control performance expressed by the following equation.

The method of claim 4, wherein Step (c) is Tension control method using a pendulum denser of the high-speed roll-to-roll system for analyzing the tension control performance, characterized in that the response characteristics to the change in the operating speed through the pole-zero graph for the denser system. The method of claim 5, Step (d) Investigating a dominant pole through each root locus plot for changes in integral gain; Selecting a proportional gain (K _p ) and an integral gain (T _n ) when the dominant pole is located at the leftmost point in the root locus diagram; And Setting a gain by adjusting the proportional gain (K _p ) and the integral gain (T _n ) at a low speed; Tension control method using a pendulum denser of a high-speed roll-to-roll system for analyzing the tension control performance, characterized in that consisting of. The method of claim 6, Step (d) (e) adjusting the gain through simulation of the response performance of the gain selected as the root locus diagram; tension control using a pendulum denser of a high-speed roll-to-roll system for analyzing tension control performance Way. The method of claim 7, wherein Step (e) is Tension control method using a pendulum denser of a high-speed roll-to-roll system analyzing tension control performance, in which gain is adjusted so that the response to the unwinder's 50N step tension disturbance is within the allowable tension disturbance range (± 2%). . The method of claim 8, The gain adjustment 10. A tension control method using a pendulum denser of a high-speed roll-to-roll system for analyzing tension control performance, characterized in that the proportional gain is changed in inverse proportion to the change in the angle of the denser arm while increasing the speed in the stationary state.

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