Transverse registration error model construction method, model, control method and printing machine

Abstract

The invention provides a transverse registration error model construction method, a model, a control method and a printer, and the method comprises the steps: building a coiled material elastic curve relation through a beam theoretical equation according to motion control parameters and material mechanical coupling parameters of a coiled material and a printing roller of a roll-to-roll printer; determining a general solution coefficient of a fourth-order differential equation of an elastic curve of the coiled material according to a given boundary condition of the coiled material between an upstream printing roller and a downstream printing roller to obtain an equation of curvature at the downstream roller; the transverse speed and the transverse acceleration of the coiled material are combined with the curvature equation of the printing roller, and the relation between the printing roller and the transverse displacement of the reel base material is obtained; and combining the relation between the transverse displacement of the printing roller and the transverse displacement of the reel base material with the transverse registration error equation of the printing roller to obtain a final transverse registration error model. According to the registration data output by the transverse registration error model, the upstream disturbance is compensated through the feed-forward controller, the registration precision of roll-to-roll printing is remarkably improved, the production cost is reduced, and the production efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precision printing, in particular to a lateral register error model construction method, model, control method and printing machine. BACKGROUND

[0002] As a high-efficiency, continuous and low-cost manufacturing process, roll-to-roll (R2R) printing technology has wide application prospects in the fields of flexible electronics, thin-film solar cells, organic light-emitting diode (OLED) displays, etc. With the increasing demand for product performance and precision in these fields, R2R printing technology is facing unprecedented challenges and opportunities. Among them, register accuracy is one of the key factors affecting product quality and functionality. Register error not only causes pattern misalignment, short circuit or leakage, etc., but also directly affects the performance and reliability of the equipment. For example, in multi-layer printed flexible electronic devices, a small register error can cause circuit connection failure or signal transmission interruption, thereby affecting the functionality of the entire device. Therefore, improving the register accuracy of R2R printing is not only the need to improve product quality, but also the key to promoting the industrialization development of flexible electronics technology.

[0003] Lateral (CD) register error is an important research direction in R2R printing. CD register error is caused by the lateral movement of the substrate during printing and the lateral position change of the printing roller. Compared with longitudinal (MD) register error, the modeling and control of CD register error are more complex, because it is not only affected by the lateral motion of the substrate, but also closely related to the translational motion of the printing roller. In addition, CD register error is particularly critical in large-area R2R printing, its error is proportional to the width of the substrate, directly affecting the yield and production efficiency of the product. By establishing a mathematical model of CD register error and designing an effective feedforward controller to compensate for upstream disturbances, the register accuracy of R2R printing can be significantly improved, production costs can be reduced, and production efficiency can be improved. This not only helps to improve the technical level of China in the field of flexible electronics manufacturing, but also provides efficient and reliable production solutions for related industries, which has important scientific significance and broad application prospects. At present, there is a lack of research on the mathematical model of CD register error. SUMMARY

[0004] The purpose of the present application is to provide a lateral register error model construction method, model, control method and printing machine, thereby solving the aforementioned problems existing in the prior art.

[0005] In order to achieve the above-mentioned purpose, the technical solutions adopted by the present application are as follows: The present application provides a lateral register error model construction method of a roll-to-roll printing machine, the method comprising: According to the motion control parameters and material mechanical coupling parameters of the roll-to-roll printing machine roll substrate and printing roller, a beam theory equation is used to establish the elastic curve relationship of the roll; According to the given boundary conditions of the roll between the upstream and downstream printing rollers, the coefficients of the general solution of the fourth-order differential equation of the roll elastic curve are determined, and the curvature equation at the downstream roller is obtained; Based on the lateral dynamics of the roll, the lateral velocity and acceleration equations of the roll are combined with the printing roller curvature equation to obtain the relationship between the lateral displacement of the printing roller and the roll substrate and to optimize; The relationship between the optimized lateral displacement of the printing roller and the roll substrate is combined with the lateral register error formula of the printing roller to obtain the final lateral register error model.

[0006] Optionally, the motion control parameters include lateral displacement parameters of the roll substrate and lateral displacement parameters of the printing roller; and the material mechanical coupling parameters include tension and bending stiffness parameters of the roll substrate; According to the motion control parameters and material mechanical coupling parameters of the roll-to-roll printing machine roll substrate and printing roller, a beam theory equation is used to establish the elastic curve relationship of the roll; According to the lateral displacement parameters of the roll substrate, the lateral displacement parameters of the printing roller, the tension and bending stiffness parameters of the roll substrate, a beam theory equation is used to establish a fourth-order equation of the roll elastic curve relationship; The fourth-order equation is solved to obtain the general solution of the fourth-order linear differential equation of the roll elastic curve relationship.

[0007] Optionally, according to the given boundary conditions of the roll between the upstream and downstream printing rollers, the coefficients of the general solution of the fourth-order differential equation of the roll elastic curve are determined, and the curvature equation at the downstream roller is obtained, including: According to the given displacement boundary and corner boundary of the roll between the upstream and downstream printing rollers, the coefficients of the general solution of the fourth-order differential equation of the roll elastic curve are obtained, and the displacement function of the roll elastic curve is determined; The curvature of the roll is obtained from the second derivative of the displacement function, and the curvature equation at the downstream roller is obtained.

[0008] Optionally, based on the lateral dynamics of the roll, the lateral velocity and acceleration equations of the roll are combined with the printing roller curvature equation to obtain the relationship between the lateral displacement of the printing roller and the roll substrate and to optimize, including: Based on the lateral dynamics of the roll, the lateral velocity and acceleration equations of the roll are obtained; The lateral velocity and acceleration equations of the roll are combined with the curvature equation of the downstream printing roller to obtain the relationship between the lateral displacement of the printing roller and the roll substrate; The lateral register error is only controlled by the translational motion of the printing roller, and the terms related to the inclination of the printing roller are removed for optimization to obtain the relationship between the optimized lateral displacement of the roll substrate and the translation of the printing roller.

[0009] Optionally, the relationship between the optimized printing roller and the lateral displacement of the web substrate is combined with the lateral register error formula of the printing roller to obtain a final lateral register error model, including: Laplace transformation is performed on the relationship between the optimized printing roller and the lateral displacement of the web substrate to obtain a frequency domain relationship formula between the lateral displacement of the printing roller and the lateral displacement of the web substrate; All spans between the printing rollers are set to have the same length, and the lateral displacement of the web substrate is expandable, and the lateral register error equation of the printing roller and the relationship formula between the lateral displacement of the printing roller and the lateral displacement of the web substrate are combined to obtain an expanded lateral register error model; According to the idle roller, the lateral register error model is expanded again to obtain a final lateral register error model.

[0010] Optionally, the lateral register error is the difference between the relative positions of the marks of the printing patterns of the upstream printing roller and the marks of the printing patterns of the downstream printing roller.

[0011] Another aspect of the present application provides a lateral register error model constructed by the method of the above lateral register error model, and the lateral register error model includes: A first calculation unit is configured to establish a web elastic curve relationship by using a beam theory equation according to the motion control parameters of the web and the printing rollers of the roll-to-roll printing machine and the material mechanical coupling parameters; A second calculation unit is configured to determine the coefficients of the general solution of the fourth-order differential equation of the web elastic curve according to the given boundary conditions of the web between the upstream and downstream printing rollers to obtain an equation of the curvature at the downstream roller; A third calculation unit is configured to obtain the relationship between the lateral displacement of the printing roller and the web substrate and optimize the relationship by combining the lateral velocity and acceleration equations of the web with the curvature equation of the printing roller based on the lateral dynamics of the web; and a model confirmation unit is configured to combine the relationship between the optimized printing roller and the lateral displacement of the web substrate with the lateral register error formula of the printing roller to obtain a final lateral register error model.

[0012] Another aspect of the present application provides a roll-to-roll printing control method based on the lateral register error model, and the method includes: Real-time detection of the lateral displacement of the upstream n-mth printing roller; The lateral displacement w n-m is input into a feedforward controller in which the lateral register error model is configured; The feedforward controller calculates a feedforward compensation amount U FF based on the lateral register error model; Real-time detecting actual lateral register error of the n th printing unit, calculating difference between the actual lateral register error and target register error; inputting the difference e to the PD controller to calculate feedback control amount U FB ; Adding the feedforward compensation amount U FF and the feedback control amount U FB to obtain comprehensive control amount U. Outputting the comprehensive control amount U to the actuator to drive the n th printing roller to generate corresponding lateral displacement.

[0013] Another aspect of the present application provides a printing machine, which is one of roll-to-roll printing machines, comprising: an unwinding section, a winding section, an inlet section, an outlet section, a multi-color printing unit, a register error detection system, a tension control system, the roll-to-roll printing machine further comprising: a lateral register error control system, the lateral register error control system comprising: a feedforward controller, a side motor, a motor driver and an optical sensor for measuring register error, the motor driver receiving control instructions to drive the side motor to act, the side motor being used to drive corresponding printing roller to move laterally; the feedforward controller comprising: a lateral register error model constructed as above, the model generating control instructions by calculating predicted results and real-time errors, the feedforward controller outputting the control instructions to the motor driver.

[0014] Another aspect of the present application provides a computer program product, comprising a computer program, characterized in that the computer program is executed by a processor to realize the method steps as described above.

[0015] The present application has the following beneficial effects: According to the motion control parameters and material mechanical coupling parameters of the roll-to-roll printing machine, the present application adopts beam theory equation to establish the elastic curve relationship of the roll material; according to the given boundary conditions of the roll material between the upstream and downstream printing rollers, the equation of the curvature at the downstream roller is determined; combined with the lateral velocity and lateral acceleration equations of the roll material, the relationship between the lateral displacement of the printing roller and the roll substrate is obtained; combined with the lateral register error equation, the lateral register error model is finally constructed; according to the register data output by the lateral register error model, the upstream disturbance is compensated through the feedforward controller, which can significantly improve the register accuracy of the roll-to-roll printing, reduce the production cost and improve the production efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a flowchart of the construction method of the lateral register error model of the roll-to-roll printing machine proposed by the present application; Figure 2 is a schematic diagram of the boundary condition structure of the beam fourth-order differential equation in the construction process of the lateral register error model of the roll-to-roll printing machine proposed by the present application; Figure 3This is a schematic diagram of the feedforward-PD control method for roll-to-roll printing press based on a lateral registration error model proposed in this application. Figure 4 This is a schematic diagram of the transverse and longitudinal registration error structure in a roll-to-roll printing press. Figure 5 This is a schematic diagram of a roll-to-roll printing press. Figure 6 yes Figure 5 A schematic diagram of the roll-to-roll three-layer printing system of a roll-to-roll printing press; Figure 7 yes Figure 6 Schematic diagram of the lateral displacement of the substrate of the second and third unit rolls; Figure 8 yes Figure 6 A schematic diagram of the lateral alignment error of the second and third units after adopting the feedforward control of this application; Figure 9 This is a schematic diagram of the lateral registration error model structure of the construction method of the lateral registration error model adopted in this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0018] This application focuses on the modeling and feedforward control technology of lateral registration error in roll-to-roll printing. By deeply studying the lateral dynamic characteristics of the moving substrate and the relative lateral positional difference between the printing roller and the substrate, a precise mathematical model for CD registration error is derived. This model can effectively describe the dynamic characteristics of CD registration error caused by the lateral movement of the substrate and the translational movement of the printing roller during the printing process. Based on this model, a feedforward control method and controller are further designed specifically to compensate for deterministic CD registration error interference generated in the upstream printing process.

[0019] The roll-to-roll printing system used in this application mainly consists of modules such as an unwinding section, a rewinding section, a feeding section, an unwinding section, a multi-color printing unit, a registration error detection system, a tension control system, and a lateral registration error control system. The tension controller and drive motor control the roll material to travel at a constant speed and tension, ensuring the substrate to be printed passes precisely through each printing unit. The lateral registration error control system consists of a feedforward controller, a side-mounted motor, a motor driver, and an optical sensor for measuring registration error, providing a complete lateral registration error control system.

[0020] like Figure 1As shown, this application proposes a method for constructing a lateral registration error model for a roll-to-roll printing press, the method comprising: Step S100: Based on the motion control parameters and material mechanical coupling parameters of the roll substrate and printing roller of the roll-to-roll printing machine, the elastic curve relationship of the roll material is established using beam theory equations.

[0021] Step S100 of this application establishes the most fundamental mathematical relationship that the elastic curve of the roll material should satisfy based on the beam theory equation, namely the differential equation of the elastic curve of the roll material, to describe the lateral elastic deformation of the roll material. The motion control parameters include: the lateral displacement parameters of the roll substrate and the lateral displacement parameters of the printing roller; the material mechanical coupling parameters include: the tension and bending stiffness parameters of the roll substrate. The method of this application is applicable to roll-to-roll printing machines, especially R2R gravure roller printing machines, wherein the roll substrate includes, but is not limited to, continuous flexible materials such as paper, plastic film, and metal foil. The roll substrate is referred to as roll material. In this embodiment, this application uses an R2R gravure roller printing machine as an example to describe the process of constructing a lateral registration error model.

[0022] The elasticity curve of the roll material is expressed as follows:

[0023] in, y This refers to the lateral displacement of the roll substrate. x Let T be the lateral displacement of the printing roller, T be the tension of the roll substrate, and EI be the bending stiffness of the roll substrate. K These represent material mechanical coupling parameters, used to quantify the relative influence of tension and bending stiffness on the transverse dynamics of the coil. The fourth-order equations can simultaneously describe how the bending stiffness EI and tension T of the coil jointly determine the transverse equilibrium state under given boundary conditions.

[0024] The fourth-order beam equation describes the lateral deformation of the rolled material. To simplify subsequent formulas, the general form of this fourth-order linear curve differential equation is: Y ( x ): Y ( x) = C 1sinh( Kx )+ C 2cosh( Kx )+ C 3 x + C 4 in, C 1. C 2. C 3. C 4 represents undetermined coefficients that need to be determined through boundary conditions.

[0025] Step S200: Based on the given boundary conditions of the roll material between the upstream and downstream printing rollers, determine the coefficients of the general solution of the fourth-order differential equation of the roll material elasticity curve, and obtain the equation for the curvature at the downstream roller.

[0026] In step S200 of this application, given the boundary conditions, the beam equation is a fourth-order differential equation, and four boundary conditions are needed to determine the coefficients of the general form solution of the fourth-order differential equation.

[0027] like Figure 2 As shown, based on the given boundary conditions of the roll material between the upstream and downstream printing rollers, specifically: y ( 0 )= y 0, θ ( 0 )= θ 0, y ( L )= y L , θ ( L )= θ L The displacement boundaries include: y ( 0 )= y 0 indicates the lateral displacement of the roll material at the starting end (such as at the upstream printing roller). y ( L )= y L This indicates the lateral displacement of the roll material at the terminating end (below the downstream printing roller); the corner boundary includes: θ ( 0 )= θ 0 indicates the lateral deflection angle of the roll material at the starting end, i.e. θ = dy / dx, θ ( L )= θ L This indicates the lateral deflection angle of the roll material at the end. These conditions reflect the geometric constraints of the roll material at the printing rollers, such as the clamping or guiding effect of the rollers on the roll material. y 0, y L It can be determined by the lateral position of the printing roller or the initial offset of the substrate. θ 0, θ L Depending on the tilt angle of the printing rollers or the tension distribution of the roll material, uneven tension can cause edge warping. Boundary conditions are considered during the offline modeling stage. y 0, θ 0, y L , θ LGiven parameters, the lateral displacement of the output roll material is determined. y L The mathematical relationship between the input and the four boundary conditions. In the online control stage, the lateral displacement and lateral registration error of the roll material are measured in real time by sensors. The boundary conditions (or the model parameters derived from them) need to be detected or estimated in real time by sensors, and the model is dynamically updated to achieve feedforward control.

[0028] Substituting the boundary conditions into the general form of the fourth-order linear curve differential equation, we can establish the following about... C 1~ C The system of linear equations of equation 4 yields four related to... C 1~ C 4. The relevant relationships are used to solve for the coefficients and determine the specific shape of the elastic curve of the roll material, i.e., the displacement function. y ( x ).

[0029] The curvature κ of the roll material x The displacement function satisfies the fourth-order linear curve differential equation. y The second derivative determines: κ( x )= d 2 y / dx 2 From this, the downstream roller curvature κ can be obtained. L The equation for is: κ(L)=

[0030] in, , , , L This represents the span length between any two adjacent printing rollers. During the modeling phase, the boundary conditions are known. The boundary conditions are only given during the modeling phase and are used to derive the relationship between the lateral displacement of the printing rollers and the lateral displacement of the roll material. The obtained relationship is used for subsequent modeling of lateral registration error.

[0031] During the control phase, the lateral registration error of each printing roller needs to be calculated separately, but follows the same error model.

[0032] Step S300: Based on the transverse dynamics of the roll material, the transverse velocity and transverse acceleration equations of the roll material are combined with the curvature equation of the printing roller to obtain and optimize the relationship between the transverse displacement of the printing roller and the roll substrate.

[0033] Based on the transverse dynamics of the roll material, namely the Euler-Bernoulli beam model, i.e., the aforementioned fourth-order partial differential equations. The equations for the transverse velocity and transverse acceleration of the roll material are incorporated into the equation for the curvature of the printing roller to establish the relationship between the translation of the printing roller and the transverse displacement of the roll substrate.

[0034] The equations for the transverse velocity and transverse acceleration of the roll material are as follows:

[0035] in, θ r Indicates the tilt angle of the printing roller, w L This represents the lateral displacement of the printing roller. This is only used here to obtain y. L and w L The mathematical relationship is as follows. The subsequent lateral registration error model is detected in real time. The lateral displacement of the substrate is represented by the lateral displacement of the printing roller.

[0036] By combining the equations for the lateral velocity and lateral acceleration of the roll material with the expression for the curvature of the printing roller in step S200, the relationship between the lateral displacement of the printing roller and the roll substrate can be obtained. The specific expression is as follows:

[0037] in, , L The span length between two adjacent printing rollers. V For the speed of the roll substrate, V It also refers to the speed at which the roll travels in the machine direction; c is the half-width of the roll. u Let τ be the rotational radius of the printing roller, and τ represent the time delay of disturbance propagation. θ This indicates the angle of the elastic curve of the roll material at a certain point; u 0, u L These represent the rotational radians at the upstream and downstream ends of the printing roller, respectively. w 0, w L These represent the lateral displacements upstream and downstream of the printing roller, respectively.

[0038] Since the lateral registration error should be controlled solely by the translational movement of the printing roller, the optimal relationship between the lateral displacement of the roll substrate and the translational movement of the printing roller is obtained as follows:

[0039] Lateral registration error should be controlled solely by the translational movement of the printing roller; tilting the roller is not permitted to control lateral registration. a 5 u L and a 6 u 0 is all and uTherefore, items related to (printing roller tilt) are removed during model optimization. a 5 u L and a 6 u 0.

[0040] Step S400: Combine the optimized relationship between the lateral displacement of the printing roller and the roll substrate with the lateral registration error formula of the printing roller to obtain the final lateral registration error model.

[0041] Step S400 of this application is based on the definition of lateral registration error to obtain the model expression of the final lateral registration error.

[0042] By applying a Laplace transform to the optimal relationship between the lateral displacement of the roll substrate and the translation of the printing roller in step S300, the frequency domain relationship between the lateral displacement of the printing roller and the lateral displacement of the roll substrate is obtained as follows: YL ( s )= A ( s ) Y0 ( s )+ B ( s ) WL ( s )+ C ( s ) W 0( s ) The equation describes the relationship between the lateral displacement W of the printing roller and the lateral displacement Y of the roll substrate, that is, the lateral displacement of the substrate can be represented by the lateral displacement of the printing roller. Y 0( s ), W 0( s The numbers () represent the lateral displacements of the upstream roll substrate and the upstream printing roller after the Laplace transformation, respectively. Y L ( s ), W L ( s ) represent the lateral displacements of the downstream roll substrate and the downstream printing roller after the Laplace transformation, respectively. . A ( s ), B ( s )and C ( s ) is a transfer function that includes system dynamics (such as parameters like velocity V and span L).

[0043] Lateral registration error is defined as the difference in relative position between the markings on the upstream printing roller and the downstream printing roller, where the markings are registration marks used for optical sensor identification. Figure 4 As shown, the bottom substrate represents the roll material, the middle narrow plate represents the pattern printed by the upstream printing roller (because it is a roller structure, it will be printed multiple times on the roll material), and the top wide plate represents the superimposed pattern printed by the downstream printing roller. r y , r x These represent the registration errors in the lateral and machine directions between the markings on the upstream and downstream printing rollers, respectively; the error expressions are:

[0044] in, r y,n ( t ) is the first n Lateral registration error of each printing roller y n (t) and w n (t) are respectively the th n The unit roll substrate (roll material) and the printing roller in t Lateral displacement at any given moment. y n-1 ( t - τ ), w n-1 ( t - τ ) respectively represent the first n Individual rolls and printing rollers t - τ The lateral displacement at any given moment. This application only considers... r y That is, the lateral registration error. r x This refers to the registration error in the machine direction (longitudinal), which is not considered in this application. It is generally calculated starting from the second printing roller. The registration error differs for each printing unit and needs to be calculated separately.

[0045] Assuming all spans between printing rollers have the same length, and the lateral displacement of the roll substrate (roll material) can be expanded, a lateral registration error model can be obtained:

[0046] in, Y n-1 ( s ), Y n-2 ( s ) represent the lateral displacements of the (n-1)th and (n-2)th rolls, respectively;e -τs Time delay representation after Laplace transform; W n ( s ) indicates the first n Lateral displacement of each printing roller; R y,n ( s The optimal relationship between the lateral displacement of the roll material and the translation of the printing roller is obtained by Laplace transformation. Y L ( s The result is obtained by combining the equations for the lateral registration error and the equation for the transverse registration error.

[0047] Furthermore, roll-to-roll printing presses have numerous idle rollers in the middle of the printing section to prevent wrinkling of the moving paper web or to provide the necessary span and wrap angle for the drying mechanism, preventing slippage, etc. Therefore, the lateral registration error model should be extended to include the idle rollers in the equation, resulting in the following expression for the lateral registration error model: Ry,n ( s )= A ( s ) m -1[ A ( s ) B ( s )+ C ( s )] Wn-m ( s )+ B ( s ) Wn ( s )- Wn ( s )+ Wn-m ( s ) e -τms- B ( s ) Wn-m ( s )) e -τms in, m This refers to the span between adjacent printing rollers, specifically the total span from the current nth printing roller to its nearest upstream printing roller used for registration control. . W n-m ( s ) represents the lateral displacement of the upstream nth printing roller, that is, the lateral displacement of the upstream printing roller that is m spans away from the current nth printing roller; Wn ( s ) represents the lateral displacement of the nth printing roller. The total time delay τ represents the time required for a disturbance to propagate from the upstream nth printing roller to the current nth printing roller. m Laplace transform, s This represents the basic Laplace transform, transforming from the time domain t to the complex domain s. The registration error of each printing roller needs to be calculated independently. The input to the registration error model is the lateral displacement of the printing roller, and the output is the registration error. The registration error is eliminated by adjusting the lateral displacement of the printing roller, making the target registration error zero. The final lateral registration error model is a general model structure, derived offline, but the model parameters need to be updated online to ensure control accuracy. In other words, the final lateral registration error model is a general transfer function structure that describes the universal law of how upstream disturbances affect downstream errors. The parameters in the model (such as the coefficients in A(s), B(s), and C(s), and the time delay τ) are... m The span (m) varies with different printing unit positions, different substrate types (tension T, bending stiffness EI), and different machine speeds (V). Therefore, in practical applications, it is necessary to instantiate a separate model for each printing unit that needs to be controlled (starting from the second one) and configure or identify a set of correct parameters for it online.

[0048] By utilizing the lateral dynamics of the moving paper roll and the relative lateral positional difference between the printing roller and the paper roll passing through the printing section, a mathematical model of lateral error is established, revealing the error generation and propagation mechanism. This fills the gap in existing technologies regarding the lack of a mathematical model for CD registration error.

[0049] like Figure 9 As shown, this application also proposes a lateral registration error model using the above-described method for constructing the lateral registration error model, the model comprising: The first calculation unit 100 is used to establish the elastic curve relationship of the roll material based on the motion control parameters and material mechanical coupling parameters of the roll substrate and printing roller of the roll-to-roll printing machine, using beam theory equations.

[0050] The second calculation unit 200 is used to determine the coefficients of the general solution of the fourth-order differential equation of the elastic curve of the roll material based on the given boundary conditions between the upstream and downstream printing rollers, and to obtain the equation of curvature at the downstream roller.

[0051] The third calculation unit 300 is used to combine the equations of the transverse velocity and transverse acceleration of the roll material with the equation of the curvature of the printing roller based on the transverse dynamics of the roll material to obtain and optimize the relationship between the transverse displacement of the printing roller and the roll substrate.

[0052] And the model verification unit 400 is used to combine the optimized relationship between the lateral displacement of the printing roller and the roll substrate with the lateral registration error formula of the printing roller to obtain the final lateral registration error model.

[0053] This application establishes a mathematical model of lateral error by using the lateral dynamics of the moving paper roll and the relative difference in lateral position between the printing roller and the paper roll passing through the printing section, revealing the error generation and propagation mechanism. By using a feedforward controller to compensate for upstream disturbances, the registration accuracy of roll-to-roll printing can be significantly improved, production costs reduced, and production efficiency increased.

[0054] like Figure 3 As shown, this application also provides a roll-to-roll printing control method based on a lateral registration error model, the method comprising: Step S10: Real-time detection of the lateral displacement of the upstream nm-th printing roller.

[0055] Step S20: Displace the upstream printing roller laterally by w n-m The input is fed to a feedforward controller, which calculates the feedforward compensation amount based on the lateral registration error model described above. U FF .

[0056] Step S30: Real-time detection of the actual lateral registration error of the nth printing unit, calculation of the difference between it and the target registration error; inputting the difference e to the PD controller to calculate the feedback control quantity. U FB .

[0057] Step S40: The feedforward compensation amount U FF With the feedback control quantity U FB Add them together to get the overall control quantity U.

[0058] Step S50: Output the comprehensive control quantity U to the actuator to drive the nth printing roller to generate a corresponding lateral displacement.

[0059] The lateral error model is used for feedforward-PD control, and the feedforward compensator input is set. U FF ( s )for:

[0060] in, w n-m Indicates the first n - m The lateral displacement of each printing roller is due to the presence of an empty roller between the two printing rollers. mThis represents the span between adjacent printing rollers. s This represents the complex field after the Laplace transform.

[0061] To optimize control performance, feedforward control is combined with traditional PD feedback control to comprehensively control the input. U ( s )for:

[0062] in, U FB ( s () is the output of the PD controller. U FF ( s ) is the output of the feedforward controller. , .

[0063]

[0064] Where U(s) is the motor input control signal, a m , k m These are the characteristic constants of the motor. θ (s) It is the angular position of the motor, k w It is a constant of the turbine ratio. w ( s ) represents the turbine angular displacement. D(S) represents the intermediate function.

[0065] like Figure 2 As shown, this flowchart describes the complete workflow of a feedforward-PD control strategy for a roll-to-roll printing system based on a lateral registration error model. Its core is the actual registration error. R y,n Error with target R y,n ref The difference e is taken as the controlled object. w n-m The lateral displacement of the upstream (n-1)th printing roller is used as a disturbance signal and is simultaneously input to the feedforward controller and the element D(s) representing the disturbance transmission characteristics of the system; the feedforward controller calculates the compensation amount based on the built-in model. U FF The control quantity generated by the PD controller in the feedback loop based on e U FB The sums are used to form the total input U(s). This is determined using the mathematical model of the transverse motor. G m ( s The total input quantity U(s) is converted into the angular position of the motor. θ,The worm gear transmission model K(s) then converts the displacement of the printing roller into the lateral displacement. w n Meanwhile, upstream disturbances w n-m Rather than influencing the system through the lateral displacement of the substrate generated by D(s), the lateral registration error is ultimately determined together with the current control. R y,n .

[0066] The overall operation process of the roll-to-roll printing press control method of this application includes: parameter update: real-time monitoring of the printing press system status (such as T, V), and updating relevant parameters in the lateral registration error model. Disturbance input: real-time detection of upstream disturbances. w n-m Model calculation: Substituting the latest parameters and disturbance inputs into the model, the model predicts the impending registration error. Feedforward compensation: The feedforward controller calculates the compensation amount U based on the predicted error. FF Feedback correction: The PD controller then fine-tunes based on the actual measured error e, eliminating prediction errors and unmodeled disturbances. Overall output: The overall control quantity U drives the actuator (motor) to adjust the lateral displacement of the current printing roller. w n This eliminates or significantly reduces registration errors.

[0067] This application establishes a mathematical model of lateral error by using the lateral dynamics of the moving paper roll and the relative difference in lateral position between the printing roller and the paper roll passing through the printing section, revealing the error generation and transmission mechanism; based on this, a feedforward controller is designed to predict and compensate for system disturbances using the error model, thereby effectively suppressing lateral deviation.

[0068] In this application, during the roll-to-roll printing process, registration errors occur due to variations in the tension of the roll substrate and the tilt of the printing roller. Optical sensors measure the printing accuracy in each printing unit. An error detection system determines whether there is an error between the printed mark of the current printing unit and the printed mark of the previous unit. If an error exists, the control system calculates the lateral displacement of the printing roller based on this error, combined with the error measurement data of the current unit and the target error, using the control method proposed in this application. This control signal is then output to adjust the lateral displacement of the roll substrate, driving the turbine transmission mechanism and the side-mounted motor to compensate for the error while simultaneously measuring the lateral registration error of the next printing unit. In each subsequent printing unit, the error detection system determines whether there is an error between the printed mark of the current printing unit and the printed mark of the previous unit. If an error exists, the above method is followed until the lateral registration error is eliminated.

[0069] Compared with the prior art, the present invention provides a method for modeling lateral registration error and feedforward-PD control of the model in a roll-to-roll printing system, which has the following beneficial effects: 1. This invention presents a modeling method for lateral registration error in roll-to-roll printing systems, along with a feedforward-PD control method. High-precision modeling methods for lateral registration error in roll-to-roll printing systems are rare, and existing models have limited prediction accuracy and control effectiveness. This invention significantly reduces lateral registration error. It remains applicable to different threading lengths, linear speeds, and roll substrate tensions. It is not only simple and efficient to implement in practice, but also offers superior control performance, making it highly suitable for widespread use in lateral registration error modeling and control of roll-to-roll printing systems. Furthermore, it provides a more effective dynamic model foundation for the future development of other advanced control strategies for roll-to-roll printing systems.

[0070] 2. The lateral registration error modeling and feedforward control method of this roll-to-roll printing system exhibits excellent industrial performance and is applicable to situations with varying tension ranges and threading lengths in different types of printing equipment. The modeling method of this invention can be applied to lateral registration error modeling in various roll-to-roll printing equipment. Furthermore, an effective feedforward compensation mechanism to offset upstream deterministic disturbances is designed, combined with PD feedback to suppress residual errors, providing key technical support for improving registration accuracy and product yield in large-scale continuous printing.

[0071] like Figure 5 The diagram shows a typical roll-to-roll printing press. The roll material is conveyed from the unwinding section, and its tension is maintained at a stable level by a tension controller in the feeding section. Then, the roll material is fed into the multi-color printing section, where gravure rollers in each printing unit sequentially print the pattern onto the roll material. An oven is used to cure the printing material, and sensors are used to measure registration errors. The sensors transmit the measured errors to the controller, which controls the registration error, keeping the accuracy within a certain range. Finally, the printed roll material is collected in the rewinding section after passing through the unwinding section.

[0072] like Figure 6 The diagram shows a three-layer printing system structure representing a roll-to-roll printing press lateral registration error model. The length between any two adjacent printing rollers is L, and the substrate moves at a constant speed V along the machine direction. OP The process moves to the right and performs multi-color overprinting. Using the print mark of the first printing unit as a reference, both the roll material and the downstream printing roller may experience lateral displacement when the second downstream printing roller performs overprinting. Here, y represents the lateral displacement of the substrate, and w represents the lateral displacement of the printing roller. Gray squares represent the print mark of the first printing roller, and black squares represent the print mark of the second printing roller. The lateral error is recorded as the difference in lateral distance between the two print marks.

[0073] like Figure 7As shown, the horizontal axis represents time, the vertical axis represents lateral displacement, and y2 and y3 respectively represent... Figure 6 When the substrate passes through the second and third printing rollers, the lateral displacement of the substrate on the roll is 30m / min.

[0074] like Figure 8 As shown, the horizontal axis represents time, and the vertical axis represents the lateral registration error. The substrate speed is 30 m / min. Ry2 represents the lateral registration error between the second and first printing rollers, and Ry3 represents the lateral registration error between the third and second printing rollers. Feedforward PD control is applied to Ry2 and Ry3. After a period of time, the registration error decreases significantly, indicating that the proposed feedforward control scheme is effective.

[0075] This application also provides a printing press, which is a roll-to-roll printing press, including: an unwinding section, a rewinding section, an infeed section, an outfeed section, a multi-color printing unit, a registration error detection system, and a tension control system. The roll-to-roll printing press further includes: a lateral registration error control system, which includes: a feedforward controller, a side-mounted motor, a motor driver, and an optical sensor for measuring registration error. The motor driver receives control commands and drives the side-mounted motor to move laterally. The side-mounted motor is used to drive the corresponding printing roller to move laterally. The feedforward controller includes: a lateral registration error model constructed as described above. The model generates control commands based on the calculated prediction results and real-time errors. The feedforward controller outputs the control commands to the motor driver.

[0076] Optical sensors are installed at corresponding positions after each printing unit and before the next printing unit to detect registration marks printed on the roll material in real time and transmit the measured actual lateral registration error signal to the feedforward controller. The feedforward controller is the "brain" of the system; it receives the error signal from the optical sensors and has a built-in lateral registration error model. Based on the predicted results calculated by the model and the real-time error, the controller generates control commands. The feedforward controller outputs the control commands (comprehensive control quantity U) to the motor driver. The motor driver receives the control commands and drives the side-mounted motor. The side-mounted motor is typically connected to the bearing housing of the printing roller or the plate cylinder shaft via a precision transmission mechanism such as a worm gear mechanism or ball screw. After receiving the commands from the motor driver, it generates precise lateral displacement, thereby directly driving the corresponding printing roller to perform lateral fine-tuning to compensate for registration errors.

[0077] The roll-to-roll printing system used in this application mainly consists of modules such as an unwinding section, a rewinding section, a feeding section, an unwinding section, a multi-color printing unit, a registration error detection system, a tension control system, and a lateral registration error control system. The tension controller and drive motor control the roll material to travel at a constant speed and tension, ensuring the substrate to be printed passes precisely through each printing unit. The lateral registration error control system consists of a side-mounted motor, a motor driver, and an optical sensor for measuring registration error, providing a complete system.

[0078] In another aspect, this application provides a computer program product, including a computer program that, when executed by a processor, implements the method steps described above.

[0079] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for constructing a lateral registration error model for a roll-to-roll printing press, characterized in that, The method includes: Based on the motion control parameters of the roll substrate and printing roller of the roll-to-roll printing press, as well as the material mechanical coupling parameters, the elastic curve relationship of the roll material is established using beam theory equations. Based on the given boundary conditions of the roll material between the upstream and downstream printing rollers, the coefficients of the general solution of the fourth-order differential equation of the roll material elasticity curve are determined, and the equation of the curvature at the downstream roller is obtained. Based on the transverse dynamics of the roll material, the equations for the transverse velocity and transverse acceleration of the roll material are combined with the equation for the curvature of the printing roller to obtain and optimize the relationship between the transverse displacement of the printing roller and the roll substrate. By combining the optimized relationship between the lateral displacement of the printing roller and the roll substrate with the lateral registration error formula of the printing roller, the final lateral registration error model is obtained.

2. The method according to claim 1, characterized in that, The motion control parameters include: the lateral displacement parameters of the roll substrate and the lateral displacement parameters of the printing roller; the material mechanical coupling parameters include: the tension and bending stiffness parameters of the roll substrate. The process involves establishing the elastic curve relationship of the roll material based on the motion control parameters and material mechanical coupling parameters of the roll substrate and printing roller of the roll-to-roll printing machine, using beam theory equations, including: Using beam theory equations, a fourth-order equation is established to establish the elastic curve relationship of the roll material based on the lateral displacement parameters of the roll substrate, the lateral displacement parameters of the printing roller, and the tension and bending stiffness parameters of the roll substrate. Solving the fourth-order equation yields the general solution of the fourth-order linear differential equation relating the elastic curves of the roll material.

3. The method according to claim 2, characterized in that, The process of determining the coefficients of the general solution of the fourth-order differential equation for the elastic curve of the roll material based on the given boundary conditions between the upstream and downstream printing rollers, and obtaining the equation for the curvature at the downstream roller, includes: Based on the given displacement and rotation boundaries of the roll material between the upstream and downstream printing rollers, the coefficients of the general solution of the fourth-order differential equation of the roll material elasticity curve are obtained, and the displacement function of the roll material elasticity curve is determined. The curvature of the roll material is obtained from the second derivative of the displacement function, and the equation for the curvature of the downstream roller is derived.

4. The method according to any one of claims 1 to 3, characterized in that, The method based on the transverse dynamics of the roll material combines the equations for the transverse velocity and acceleration of the roll material with the equation for the curvature of the printing roller to obtain and optimize the relationship between the transverse displacement of the printing roller and the roll substrate, including: Based on the transverse dynamics of the roll material, the equations for the transverse velocity and transverse acceleration of the roll material are obtained; By combining the equations for the transverse velocity and transverse acceleration of the roll material with the equation for the curvature of the downstream printing roller, the relationship between the transverse displacement of the printing roller and the roll substrate is obtained. Lateral registration error is controlled only by the translational motion of the printing roller. After removing terms related to the tilt of the printing roller, the optimized relationship between the lateral displacement of the roll substrate and the translational motion of the printing roller is obtained.

5. The method according to any one of claims 1 to 4, characterized in that, The optimized relationship between the lateral displacement of the printing roller and the roll substrate is combined with the lateral registration error formula of the printing roller to obtain the final lateral registration error model, including: The optimized relationship between the lateral displacement of the printing roller and the roll substrate was subjected to a Laplace transform to obtain the frequency domain relationship formula between the lateral displacement of the printing roller and the lateral displacement of the roll substrate. By assuming that all spans between printing rollers have the same length, the lateral displacement of the roll substrate can be expanded. Combining the lateral registration error equation of the printing rollers and the relationship formula between the lateral displacement of the printing rollers and the lateral displacement of the roll substrate after the change, the expanded lateral registration error model is obtained. Based on the idle roller, the lateral registration error model is further extended to obtain the final lateral registration error model.

6. The method according to any one of claims 1 to 5, characterized in that, Lateral registration error is the difference in relative position between the markings of the pattern printed on the upstream printing roller and the markings of the pattern printed on the downstream printing roller.

7. A lateral registration error model constructed using any one of the lateral registration error models of claims 1 to 6, characterized in that, The lateral registration error model includes: The first calculation unit is used to establish the elastic curve relationship of the roll material based on the motion control parameters of the roll substrate and printing roller of the roll-to-roll printing press and the material mechanical coupling parameters, using beam theory equations. The second calculation unit is used to determine the coefficients of the general solution of the fourth-order differential equation of the elastic curve of the roll material based on the given boundary conditions between the upstream and downstream printing rollers, and to obtain the equation of curvature at the downstream roller. The third calculation unit is used to combine the equations of the transverse velocity and transverse acceleration of the roll with the equation of the curvature of the printing roller based on the transverse dynamics of the roll to obtain and optimize the relationship between the transverse displacement of the printing roller and the roll substrate. And a model verification unit, which combines the optimized relationship between the lateral displacement of the printing roller and the roll substrate with the lateral registration error formula of the printing roller to obtain the final lateral registration error model.

8. A roll-to-roll printing control method based on a lateral registration error model, characterized in that, The method includes: Real-time detection of the lateral displacement of the upstream nm-th printing roller w n-m ; The lateral displacement w n-m The input is sent to a feedforward controller, which is configured with the lateral registration error model as described in claim 7. The feedforward controller calculates the feedforward compensation amount U based on the aforementioned lateral registration error model. FF ; The actual lateral registration error of the nth printing unit is detected in real time, and the difference between it and the target registration error is calculated; the difference e is input to the PD controller to calculate the feedback control quantity U. FB ; The feedforward compensation amount U FF With the feedback control quantity U FB Add them together to obtain the overall control quantity U; The comprehensive control quantity U is output to the actuator to drive the nth printing roller to generate a corresponding lateral displacement.

9. A printing press, said printing press being a roll-to-roll printing press, comprising: The roll-to-roll printing press comprises an unwinding section, a rewinding section, an infeed section, an outfeed section, a multi-color printing unit, a registration error detection system, and a tension control system. The roll-to-roll printing press further includes a lateral registration error control system, comprising a feedforward controller, a side-mounted motor, a motor driver, and an optical sensor for measuring registration error. The motor driver receives control commands and drives the side-mounted motor to move laterally. The side-mounted motor drives the corresponding printing roller to move laterally. The feedforward controller includes a lateral registration error model constructed according to claims 1 to 6. The model generates control commands based on the calculated prediction results and real-time errors. The feedforward controller outputs the control commands to the motor driver.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 6 or the steps of the method according to claim 8.

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