Air floating platform substrate deformation online regulation method and system

Abstract

The present application belongs to the technical field of printing display, and particularly relates to a kind of air floating platform substrate deformation online regulation and control method and system, comprising: real-time synchronous acquisition preset m measuring point place substrate flying height change data;Based on each measuring point corresponding flying height change data and n mode shape function at the measuring point Value construction modal superposition equation;Through solving equation set, each mode time coordinate set under collection time is obtained;Based on the set and n mode shape function at each target point Value, the change data of the substrate flying height at the target point is obtained, and closed-loop control is carried out accordingly;n mode shape function determination method: the whole air film covered by the target substrate is regarded as an elastic foundation, the air film stiffness distribution function is constructed by fitting, and the mass matrix and stiffness matrix of the air film-substrate assembly are obtained by combining the orthogonal function satisfying the boundary condition, and n air film-substrate assembly mode shape functions are calculated. The present application can be online regulated.

Description

Technical Field

[0001] This invention belongs to the field of printed display technology, and more specifically, relates to a method and system for online control of deformation of an air-floating platform substrate. Background Technology

[0002] The novel inkjet printing technology for displays uses additive manufacturing to deposit a solution into pixel pits, forming luminescent pixels and encapsulation films. Compared to traditional vacuum evaporation processes, it effectively avoids the waste of solvents and solutes. In particular, inkjet printing allows for free patterning, making it especially suitable for large-size panels. One of the key steps in inkjet printing manufacturing of large-size flexible panels is the air-floating transport of the flexible substrate. Vibration and deformation during transport directly affect printing accuracy. Detecting and controlling the accuracy of air-floating transport during the process can significantly improve the yield of inkjet printing systems, facilitating the mass production application of inkjet printing technology in the field of new displays. This is a goal that global panel manufacturers and research institutions urgently need to achieve.

[0003] Air-floating transport of large-size flexible substrates offers advantages such as non-contact operation and light load, but it also introduces new challenges and problems. An existing patent, CN202311618114, describes a splicing air-floating platform and inkjet printing equipment for display panel processing. However, it only proposes a novel structural design scheme without providing corresponding detection and control solutions. Patent CN115435742A describes a continuous online warpage rapid measurement device for substrate glass. This method proposes a structural design scheme to measure the deformation of freely suspended glass substrates, but clearly, this method cannot be applied to moving air-floating substrates.

[0004] Further research revealed that the technologies designed in existing patents and literature still have the following shortcomings:

[0005] 1. For large-size flexible glass substrates transported by air flotation, existing mechanical designs are only suitable for substrates in a free-floating state and cannot be applied in this scenario.

[0006] 2. For high-precision air flotation conveying scenarios, the stability and reliability of air flotation conveying are also key indicators. A complete closed-loop control scheme is needed to ensure accuracy and improve the adaptability of the air flotation platform, which is a point that has not been addressed in the existing solutions.

[0007] 3. Existing solutions are mostly structural designs and improvements of air flotation platforms. These solutions are highly targeted and difficult to apply in practice. There is no detection and control solution that does not rely excessively on the structure and can be easily applied in various scenarios. Summary of the Invention

[0008] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and system for online control of the deformation of air-floating platform substrate, the purpose of which is to realize online control of the deformation of air-floating platform substrate in actual inkjet printing scenarios without relying on the platform structure.

[0009] To achieve the above objectives, according to one aspect of the present invention, a method for online control of deformation of an air-floating platform substrate is provided, comprising:

[0010] During inkjet printing, the change data of substrate height at m preset measurement points are collected in real time. Based on the change data of the height at each measurement point and the values ​​of n mode shape functions at that measurement point, a modal superposition equation is constructed. Based on the modal superposition equation of all measurement points, the set of modal time coordinates η1(t), η2(t), ..., η at the acquisition time t is obtained by solving the system of equations. n (t); Based on the time coordinate set and the values ​​of the n mode shape functions at each target point, the change data of the substrate height at the target point are obtained;

[0011] Closed-loop control is performed based on the change data of the substrate's flight height at all target points to achieve online regulation of the deformation of the air-floating platform substrate.

[0012] The n mode shape functions are determined as follows: the entire air film covering the target substrate is regarded as an elastic foundation. The air film stiffness distribution function is constructed by fitting and combined with orthogonal functions that satisfy the boundary conditions to obtain the mass matrix and stiffness matrix of the air film-substrate assembly. Based on the mass matrix and stiffness matrix, the mode shape functions of the n air film-substrate assembly are calculated.

[0013] Furthermore, the air film stiffness distribution function is constructed as follows:

[0014] Measure the air film stiffness of each independently supplied air flotation block of the air flotation platform;

[0015] The air film stiffness distribution function k(x,y) of the overall air film covering the target substrate is obtained by fitting the air film stiffness and coordinate position of each air float block. The air film stiffness at each position within each air float block is consistent, and the air film stiffness at the gap between air float blocks is zero.

[0016] Furthermore, the modal shape functions of the n air-film substrate components are calculated based on the mass matrix and stiffness matrix as follows:

[0017] Based on the mass matrix and stiffness matrix of the air-film-substrate assembly, the set of natural frequencies and the set of mode shape functions with respect to coordinate position of the target substrate under air-float state are determined. Then, the n mode shape functions corresponding to the n smallest natural frequencies are selected from the set of mode shape functions. A natural frequency and its corresponding mode shape function constitute a mode.

[0018] Furthermore, the air film stiffness of the air buoy is measured by using each air buoy to support and suspend substrates of different thicknesses or by adding a weight load to the suspended glass substrate; wherein, the air film stiffness of each air buoy is calculated by the following formula:

[0019]

[0020] In the formula, ΔG represents the change in gravity between the two measurements, and Δh represents the change in the height of the substrate between the two measurements.

[0021] Furthermore, the element in the i-th row and j-th column of the mass matrix M of the air-film-substrate assembly is:

[0022]

[0023] The element in the i-th row and j-th column of the stiffness matrix K is:

[0024]

[0025] In the formula, ρ is the density of the target substrate, and H is the thickness of the target substrate; when the substrate is unilaterally adsorbed during transport, φ i Let φ be the i-th modal function of the cantilever plate. j (x,y) represents the j-th order mode function of the cantilever plate; when it is bilateral adsorption, φ i Let φ be the i-th order mode function of a plate with fixed opposite sides and free opposite sides. j (x,y) represents the j-th mode function of the plate with fixed opposite sides and free opposite sides; a and b represent the length and width of the substrate, respectively. Represents the Laplace operator;

[0026] By solving the formula: The set of natural frequencies λ1,…,λ is obtained. i ,…,λ n and its corresponding set of mode functions W1(x,y),…,W i (x,y),…W n (x,y).

[0027] Furthermore, the modal superposition equations corresponding to each measuring point are as follows:

[0028] η1(t)W1(x1,y1)+η2(t)W2(x1,y1)+...+η n(t)W n (x1,y1)=w(x1,y1)

[0029] η1(t)W1(x2,y2)+η2(t)W2(x2,y2)+...+η n (t)W n (x2,y2)=w(x2,y2)

[0030]

[0031] η1(t)W1(x m ,y m )+η2(t)W2(x m ,y m )+...+η n (t)W n (x m ,y m )=w(x m ,y m )

[0032] In the formula, w(x1,y1), w(x2,y2), ..., w(x m ,y m W1(x1,y1), W2(x1,y1), and W2(x1,y1) represent the changes in the substrate height at different measuring points, respectively. n (x1, y1) represent the values ​​of different mode shape functions at the first measuring point; W1(x2, y2), W2(x2, y2), W n (x2, y2) represent the values ​​of different mode shape functions at the second measuring point; W1(x m ,y m W2(x) m ,y m W n (x m ,y m ) represent the values ​​of different mode shape functions at the m-th measuring point.

[0033] According to another aspect of the present invention, an online deformation control system for an air-float platform substrate is provided, comprising: a displacement sensor, a processor, and an actuator;

[0034] The displacement sensor is used to collect data on the change in the height of the substrate at m preset measuring points in real time during the inkjet printing process.

[0035] The processor is used to construct modal superposition equations based on the flight altitude change data corresponding to each measuring point and the values ​​of n mode shape functions at that measuring point; based on the modal superposition equations of all measuring points, by solving the system of equations, the set of modal time coordinates η1(t), η2(t), ..., η at the acquisition time t is obtained. n (t); Based on the time coordinate set and the values ​​of n mode shape functions at each target point, the change data of the substrate's flight height at the target point is obtained; Based on the change data of the substrate's flight height at all target points, the air pressure setting value of the target air buoy is obtained;

[0036] The actuator is used for closed-loop control based on the air pressure setpoint of each target air flotation block.

[0037] Furthermore, the actuator includes a positive pressure proportional valve for the unloading zone, a negative pressure proportional valve for the unloading zone, a positive pressure proportional valve for the precision zone, a negative pressure proportional valve for the precision zone, a positive pressure proportional valve for the loading zone, and a negative pressure proportional valve for the loading zone.

[0038] Furthermore, the displacement sensor is a laser sensor.

[0039] In summary, compared with the prior art, the technical solutions conceived by this invention have the following main advantages:

[0040] 1. This invention proposes an online method for controlling the deformation of an air-float platform substrate. By simplifying the complex dynamic system of air-float, it provides a convenient framework for the design of the control system. Air-float systems are typically multi-degree-of-freedom systems, and their dynamic behavior can be very complex. Considering that the vibration modes of this system are usually nonlinear and coupled, this invention proposes to treat the entire air film covering the target substrate as an elastic foundation. By fitting and constructing the air film stiffness distribution function and combining it with orthogonal functions satisfying boundary conditions, the mass matrix and stiffness matrix of the air film-substrate assembly are obtained. Based on the mass matrix and stiffness matrix, the modal shape functions of n air film-substrate assemblies are calculated. In other words, this invention proposes to simplify the motion (or vibration) of a complex multi-degree-of-freedom system into a series of independent, individually analyzeable and controllable "modal" vibration modes through modal decomposition. Each mode is an inherent natural vibration pattern of the system, with independent natural frequency, mode shape, and amplitude. Furthermore, by constructing a modal superposition equation, the change in substrate height at each target point is determined, thereby controlling the substrate deformation online. Therefore, this invention enables online control of the deformation of the air-floating platform substrate in actual printing scenarios without relying on the platform structure.

[0041] 2. This invention proposes a method for constructing an air film stiffness distribution function. Specifically, it measures the air film stiffness of each independently supplied air-bearing block of an air-bearing platform; then, it uses the air film stiffness and coordinate position of each air-bearing block to perform function fitting, obtaining the air film stiffness distribution function k(x,y) of the overall air film covered by the target substrate. Here, the air film stiffness at each position within each air-bearing block is consistent, while the air film stiffness at the gaps between air-bearing blocks is zero. This method is applicable to air-bearing platform systems of arbitrary arrangement, area, and structure, achieving equivalent modeling of the air-bearing platform.

[0042] 3. This invention proposes a preferred method for determining n modal shape functions based on two matrices. Specifically, it uses the mass matrix and stiffness matrix of the air-film substrate assembly to determine the set of natural frequencies of the target substrate in the air-floating state and the set of modal shape functions with respect to coordinate position. Then, it selects the n modal shape functions corresponding to the n smallest natural frequencies from the set of modal shape functions. This method ensures the effective implementation of online control. This method can flexibly determine the modal shape functions according to the target detection accuracy requirements, thereby reducing measurement costs and computational scale, and is applicable to various application scenarios. Attached Figure Description

[0043] Figure 1 This is a flowchart of an online deformation control method for an air flotation platform substrate provided in an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of the detection points provided in an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of the closed-loop control scheme provided in an embodiment of the present invention;

[0046] Figure 4 This is a schematic diagram of the air film stiffness testing scheme provided in an embodiment of the present invention;

[0047] Figure 5 This is a diagram illustrating the composition of an online deformation control system for an air-float platform substrate provided in an embodiment of the present invention.

[0048] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0049] 1 is PC1, 2 is PLC, 3 is positive pressure proportional valve in the unloading area, 4 is negative pressure proportional valve in the unloading area, 5 is positive pressure proportional valve in the precision area, 6 is negative pressure proportional valve in the precision area, 7 is laser displacement sensor, 8 is positive pressure proportional valve in the loading area, 9 is negative pressure proportional valve in the loading area, 10 is air flotation motor guide rail, 11 is substrate adsorption module, 12 is air flotation module in the unloading area, 13 is air flotation module in the precision area, and 14 is air flotation module in the loading area. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0051] Example 1

[0052] A method for online control of substrate deformation of an air-floating platform, such as Figure 1 As shown, it includes:

[0053] During inkjet printing, the change data of substrate height at m preset measurement points are collected in real time. Based on the change data of the height at each measurement point and the values ​​of n mode shape functions at that measurement point, a modal superposition equation is constructed. Based on the modal superposition equation of all measurement points, the set of modal time coordinates η1(t), η2(t), ..., η at the acquisition time t is obtained by solving the system of equations. n (t); Based on the time coordinate set and the values ​​of the n mode shape functions at each target point, the change data of the substrate height at the target point are obtained;

[0054] Closed-loop control is performed based on the change data of the substrate's flight height at all target points to achieve online regulation of the deformation of the air-floating platform substrate.

[0055] The n mode shape functions are predetermined in the following way:

[0056] The modal shape functions of n air-film-substrate assemblies are predetermined and determined as follows: the entire air film covered by the target substrate is regarded as an elastic foundation. The air film stiffness distribution function is constructed by fitting and combined with orthogonal functions that satisfy the boundary conditions to obtain the mass matrix and stiffness matrix of the air-film-substrate assembly. The modal shape functions of n air-film-substrate assemblies are calculated based on the mass matrix and stiffness matrix.

[0057] Online control is performed by pre-setting n modal vibration functions. Existing technologies often use manual initial adjustments for air flotation platforms. Under the influence of factors such as platform flatness and changes in air supply pressure, the leveling of air flotation is cumbersome and cannot adaptively and actively control the air flotation state.

[0058] In addition, there are many factors that cause substrate deformation, including the different thicknesses of the gas film beneath the target substrate, which lead to different deformations.

[0059] Regarding the selection of the number and location of measuring points, such as Figure 2 As shown, the following principles should be followed:

[0060] 1) The number of measurement points should be greater than the number of modes selected; it is recommended to select ≥4 modes.

[0061] 2) The location of the measuring points should avoid the nodes of the mode shape function; the nodes are the W modes of each order. i The zeros of the function (x,y);

[0062] 3) Measurement points should be selected from asymmetrical points on the board as much as possible, and the measurement points should be distributed as widely as possible;

[0063] 4) The more modes selected, the more accurate the reconstruction. The specific number of modes selected should be determined through actual experiments in combination with the target accuracy requirements.

[0064] This embodiment presents a closed-loop control scheme. Displacement data from various measuring points is acquired. The PC, based on stored modal functions and corresponding algorithms, combines the measured data to obtain an estimate of the deformation of the entire surface. Control commands are then sent based on the deformation to regulate the actuators, thereby controlling the deformation of the air-floating platform. Displacement sensor detection is performed in real time, forming a closed-loop feedback loop. One implementation method is as follows: Figure 3 As shown,

[0065] As a preferred implementation, the n modal shape functions are preferably determined in the following manner:

[0066] Measure the air film stiffness of each independently supplied air flotation block of the air flotation platform;

[0067] The air film stiffness and coordinate position of each air float block are used to perform function fitting to obtain the air film stiffness distribution function k(x,y) of the overall air film covered by the target substrate. Among them, the air film stiffness corresponding to each position in each air float block is consistent, and the air film stiffness corresponding to the gap between air float blocks is zero.

[0068] Based on the air film stiffness distribution function and combined with the orthogonal function that satisfies the boundary conditions, the mass matrix and stiffness matrix of the air film-substrate assembly are calculated to determine the set of natural frequencies of the target substrate under air-float state and the set of mode shape functions with respect to the coordinate position. Then, the n mode shape functions corresponding to the first n smallest natural frequencies are selected from the set of mode shape functions. A natural frequency and its corresponding mode shape function constitute a mode.

[0069] Once all natural frequencies and mode shapes are calculated, the natural frequency results and mode shape data are stored in ascending order of natural frequency. A natural frequency and its corresponding mode shape constitute a mode. The mode shapes corresponding to the first n smallest natural frequencies are selected for online control.

[0070] This can be used as a preferred implementation method, such as Figure 4As shown, the air film stiffness of the air float is measured by using each air float to support and suspend substrates of different thicknesses or by adding a weight load to the suspended glass substrate; wherein, the air film stiffness of each air float is calculated by the following formula:

[0071]

[0072] In the formula, ΔG represents the change in gravity between the two measurements, and Δh represents the change in the height of the substrate between the two measurements.

[0073] As a preferred embodiment, the element in the i-th row and j-th column of the mass matrix M of the air-film-substrate assembly is:

[0074]

[0075] The element in the i-th row and j-th column of the stiffness matrix K is:

[0076]

[0077] In the formula, ρ is the density of the target substrate, and H is the thickness of the target substrate; when the substrate is unilaterally adsorbed during transport, φ i Let φ be the i-th modal function of the cantilever plate. j (x,y) represents the j-th order mode function of the cantilever plate; when it is bilateral adsorption, φ i Let φ be the i-th order mode function of a plate with fixed opposite sides and free opposite sides. j (x,y) represents the j-th mode function of the plate with fixed and free sides; a and b represent the length and width of the substrate, respectively, and ▽ represents the Laplace operator;

[0078] By solving the formula: The set of natural frequencies λ1,…,λ is obtained. i ,…,λ n and its corresponding set of mode functions W1(x,y),…,W i (x,y),…W n (x,y).

[0079] As a preferred implementation, the modal superposition equations corresponding to each measuring point are as follows:

[0080] η1(t)W1(x1,y1)+η2(t)W2(x1,y1)+...+η n (t)W n (x1,y1)=w(x1,y1)

[0081] η1(t)W1(x2,y2)+η2(t)W2(x2,y2)+...+η n (t)W n (x2,y2)=w(x2,y2)

[0082]

[0083] η1(t)W1(x m ,y m )+η2(t)W2(x m ,y m )+...+η n (t)W n (x m ,y m )=w(x m ,y m )

[0084] In the formula, w(x1,y1), w(x2,y2), ..., w(x m ,y m W1(x1,y1), W2(x1,y1), and W2(x1,y1) represent the changes in the substrate height at different measuring points, respectively. n (x1, y1) represent the values ​​of different mode shape functions at the first measuring point; W1(x2, y2), W2(x2, y2), W n (x2, y2) represent the values ​​of different mode shape functions at the second measuring point; W1(x m ,y m W2(x) m ,y m W n (x m ,y m ) represent the values ​​of different mode shape functions at the m-th measuring point.

[0085] For example, target point (x) a ,y a The deformation amount w(x) a ,y a )for:

[0086] w(x a ,y a )=η1(t)W1(x a ,y a )+η2(t)W2(x a ,y a )+...+η n (t)W n (x a ,y a )

[0087] The entire surface of the substrate is divided into equally spaced grids, and the deformation of the entire surface can be obtained by calculating the deformation of each grid node.

[0088] This embodiment treats the entire air film covering the target substrate as an elastic foundation and models and constructs modal superposition equations. Theoretically, any solution can be achieved through a set of orthogonal bases. Modal decoupling is an intrinsic property of the system. This embodiment, starting from the foundation of modal theory, proposes a superior operation process and calculation method for this scenario.

[0089] Example 2

[0090] An online deformation control system for an air-floating platform substrate includes a displacement sensor, a processor, and an actuator. The displacement sensor is used to synchronously collect data on the change in substrate height at m preset measurement points during inkjet printing. The processor is used to construct a modal superposition equation based on the change in height at each measurement point and the values ​​of n mode shape functions at that point. Based on the modal superposition equations for all measurement points, the system of equations is solved to obtain the set of modal time coordinates η1(t), η2(t), ..., η at acquisition time t. n (t); Based on the time coordinate set and the values ​​of n modal vibration functions at each target point, the change data of the substrate flight height at the target point is obtained; Based on the change data of the substrate flight height at all target points, the air pressure setting value of the target air flotation block is obtained; The actuator is used to perform closed-loop control based on the air pressure setting value of each target air flotation block.

[0091] As a preferred embodiment, the actuator includes a positive pressure proportional valve for the unloading zone, a negative pressure proportional valve for the unloading zone, a positive pressure proportional valve for the precision zone, a negative pressure proportional valve for the precision zone, a positive pressure proportional valve for the loading zone, and a negative pressure proportional valve for the loading zone. These can be flexibly configured in different zones according to actual conditions.

[0092] As a preferred embodiment, the displacement sensor is a laser sensor.

[0093] A specific implementation plan, such as Figure 5 As shown, the system consists of PC1, PLC (controller) 2, positive pressure proportional valve 3 for the unloading area, negative pressure proportional valve 4 for the unloading area, positive pressure proportional valve 5 for the precision area, negative pressure proportional valve 6 for the precision area, laser displacement sensor 7, positive pressure proportional valve 8 for the loading area, negative pressure proportional valve 9 for the loading area, air flotation motor guide rail 10, substrate adsorption module 11, air flotation module 12 for the unloading area, air flotation module 13 for the precision area, and air flotation module 14 for the loading area.

[0094] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online control of deformation of an air-floating platform substrate, characterized in that, include: During the inkjet printing process, the change data of the substrate's height at m preset measuring points are collected in real time. Based on the altitude variation data corresponding to each measuring point and the values ​​of the mode shape functions of n air-film substrate assemblies at that measuring point, a modal superposition equation for the air-film substrate assemblies is constructed. Based on the modal superposition equation for all measuring points, by solving the system of equations, the set of modal time coordinates η1(t), η2(t), ..., η at the acquisition time t is obtained. n (t); Based on the time coordinate set and the values ​​of the n mode shape functions at each target point, the change data of the substrate height at the target point are obtained; Closed-loop control is performed based on the change data of the substrate's flight height at all target points to achieve online regulation of the deformation of the air-floating platform substrate. The n mode shape functions are determined as follows: the entire air film covering the target substrate is regarded as an elastic foundation. The air film stiffness distribution function is constructed by fitting and combined with orthogonal functions that satisfy the boundary conditions to obtain the mass matrix and stiffness matrix of the air film-substrate assembly. Based on the mass matrix and stiffness matrix, the mode shape functions of the n air film-substrate assembly are calculated.

2. The method for online control of deformation of an air-floating platform substrate as described in claim 1, characterized in that, The gas film stiffness distribution function is constructed as follows: Measure the air film stiffness of each independently supplied air flotation block of the air flotation platform; The air film stiffness distribution function k(x,y) of the overall air film covering the target substrate is obtained by fitting the air film stiffness and coordinate position of each air float block. The air film stiffness at each position within each air float block is consistent, and the air film stiffness at the gap between air float blocks is zero.

3. The method for online control of deformation of an air-floating platform substrate as described in claim 1, characterized in that, The modal shape functions of n air-film substrate assemblies are calculated based on the mass matrix and stiffness matrix as follows: Based on the mass matrix and stiffness matrix of the air-film-substrate assembly, the set of natural frequencies and the set of mode shape functions with respect to coordinate position of the target substrate under air-float state are determined. Then, the n mode shape functions corresponding to the n smallest natural frequencies are selected from the set of mode shape functions. A natural frequency and its corresponding mode shape function constitute a mode.

4. The method for online control of deformation of an air-floating platform substrate as described in claim 2, characterized in that, The air film stiffness of the air float is measured by using each air float to support and suspend substrates of different thicknesses, or by adding a weight load to the suspended glass substrate; the air film stiffness of each air float is calculated by the following formula: In the formula, ΔG represents the change in gravity between the two measurements, and Δh represents the change in the height of the substrate between the two measurements.

5. The method for online control of deformation of an air-floating platform substrate as described in claim 3, characterized in that, The element in the i-th row and j-th column of the mass matrix M of the air-film-substrate assembly is: The element in the i-th row and j-th column of the stiffness matrix K is: In the formula, ρ is the density of the target substrate, and H is the thickness of the target substrate; when the substrate is unilaterally adsorbed during transport, φ i Let φ be the i-th modal function of the cantilever plate. j (x,y) represents the j-th order mode function of the cantilever plate; when it is bilateral adsorption, φ i Let φ be the i-th order mode function of a plate with fixed opposite sides and free opposite sides. j (x,y) represents the j-th mode function of the plate with fixed and free sides; a and b represent the length and width of the substrate, respectively, and ▽ represents the Laplace operator; By solving the formula: The set of natural frequencies λ1,…,λ is obtained. i ,…,λ n and its corresponding set of mode functions W1(x,y),…,W i (x,y),…W n (x,y).

6. The method for online control of deformation of an air-floating platform substrate as described in claim 1, characterized in that, The modal superposition equations corresponding to each measuring point are as follows: In the formula, w(x1,y1), w(x2,y2), ..., w(x m ,y m W1(x1,y1), W2(x1,y1), and W2(x1,y1) represent the changes in the substrate height at different measuring points, respectively. n (x1, y1) represent the values ​​of different mode shape functions at the first measuring point; W1(x2, y2), W2(x2, y2), W n (x2, y2) represent the values ​​of different mode shape functions at the second measuring point; W1(x m ,y m W2(x) m ,y m W n (x m ,y m ) represent the values ​​of different mode shape functions at the m-th measuring point.

7. An online deformation control system for an air-floating platform substrate, characterized in that, include: Displacement sensors, processors, and actuators; The displacement sensor is used to collect data on the change in the height of the substrate at m preset measuring points in real time during the inkjet printing process. The processor is used to construct modal superposition equations based on the flight altitude change data corresponding to each measuring point and the values ​​of n mode shape functions at that measuring point; based on the modal superposition equations of all measuring points, by solving the system of equations, the set of modal time coordinates η1(t), η2(t), ..., η at the acquisition time t is obtained. n (t); Based on the time coordinate set and the values ​​of n mode shape functions at each target point, the change data of the substrate's flight height at the target point is obtained; Based on the change data of the substrate's flight height at all target points, the air pressure setting value of the target air buoy is obtained; The actuator is used for closed-loop control based on the air pressure setpoint of each target air flotation block.

8. The online deformation control system for an air-floating platform substrate as described in claim 7, characterized in that, The actuator includes a positive pressure proportional valve for the unloading zone, a negative pressure proportional valve for the unloading zone, a positive pressure proportional valve for the precision zone, a negative pressure proportional valve for the precision zone, a positive pressure proportional valve for the loading zone, and a negative pressure proportional valve for the loading zone.

9. The online deformation control system for an air-floating platform substrate as described in claim 7, characterized in that, The displacement sensor is a laser sensor.

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