Decoupling control method for multi-layer registration system of gravure printing machine based on disturbance observer

Abstract

The invention discloses a decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer. The method establishes a multi-layer registration system model considering the influence of the upstream printing unit; based on the decentralized control method and the decoupling control theory, combined with the radial basis function neural network, a decoupling control method based on the RBFNN disturbance observer is proposed; a genetic algorithm is used to optimize the parameters to be set; a Lyapunov function is constructed to prove the stability of the system; and the effectiveness of the control method is verified by simulation experiments. The simulation experiment results show that the fluctuation data of the longitudinal registration error value does not exceed ±0.025mm, and the method has good tracking performance, can effectively suppress the registration error fluctuation caused by the system itself and external factors, and has strong anti-interference ability.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control, and in particular relates to a decoupling control method of a multi-layer registration system of a gravure printing machine based on a disturbance observer. Background Art

[0002] Unlike traditional batch manufacturing methods, Roll-to-Roll (R2R) manufacturing enables high-speed and automated continuous processing of materials. One of the most common applications of R2R printing systems is gravure printing presses.

[0003] A typical gravure printing machine consists of an unwinding section, a multi-layer printing section, and a winding section. Registration error occurs in the multi-layer printing section and is an important factor affecting printing quality. Registration error is mainly divided into longitudinal registration error along the substrate conveying direction and transverse registration error perpendicular to the substrate conveying direction. Among them, there are many factors affecting longitudinal registration error, and substrate tension fluctuation and substrate speed fluctuation are the more important factors.

[0004] The complexity of influencing factors makes the longitudinal registration error a difficult point to control in R2R system precision printing. At the same time, the multi-layer registration system has the characteristics of strong coupling, nonlinearity, and time lag, which limits the improvement of multi-layer registration accuracy and seriously affects the quality of multi-layer printed electronic products. In general, the registration accuracy is required to be 0.1mm, and in special cases it is 0.05mm. Therefore, it is a challenge to design an algorithm for the multi-layer registration system to achieve higher accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer, which is used to solve the registration error problem caused by the system's own disturbance or external disturbance during the precision printing process of the R2R system.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer comprises the following steps:

[0008] S1: According to the printing principle and physical laws of multi-layer gravure printing press, based on the law of conservation of mass and moving coordinate system, a nonlinear model of single registration error is established, and it is linearized using the small deviation method;

[0009] S2: According to the definition of registration error, based on the linear model of the single registration error obtained in step S1, a recursive iterative derivation is performed to obtain the general form of the multi-layer registration model;

[0010] S3: For the multi-layer registration error model obtained in step S2, based on the decentralized control method and decoupling control theory, combined with the RBF neural network, a decoupling control method based on the RBFNN disturbance observer is designed;

[0011] S4: A genetic algorithm is used to optimize the undetermined parameters in the control method proposed in step S3, and a GA optimized decoupling control method based on the RBFNN disturbance observer is obtained to achieve input-output decoupling of the multi-layer registration system, which is used to effectively control the registration error of each printing unit to meet the expected performance indicators.

[0012] The beneficial effects of the present invention are:

[0013] 1) The present invention designs a decoupling control method for the multi-layer registration system of a gravure printing machine based on a disturbance observer, establishes a multi-layer registration system model considering the influence of the upstream printing unit; based on the decentralized control method and decoupling control theory, combined with the radial basis function neural network, a decoupling control method based on the RBFNN disturbance observer is proposed; a genetic algorithm is used to optimize the parameters to be set; a Lyapunov function is constructed to prove the stability of the system; and the effectiveness of the control method is verified by simulation experiments. The simulation experiment results show that the fluctuation data of the registration error value does not exceed ±0.025mm, and the method has good tracking performance, can effectively suppress the registration error fluctuation caused by the system itself and external factors, and has strong anti-interference ability.

[0014] 2) The general model of the multi-layer registration system established by the present invention takes into account the influence of all upstream printing units.

[0015] 3) The RBFNN disturbance observer proposed in the present invention can effectively track system disturbance data.

[0016] 4) The decoupling control method based on the RBFNN disturbance observer of the present invention has good tracking performance, can effectively suppress the registration error fluctuation caused by the system itself and external factors, and has strong anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a decoupling control method of a multi-layer registration system of a gravure printing machine based on a disturbance observer according to an embodiment of the present invention;

[0018] Figure 2 is an example diagram of registration error according to an embodiment of the present invention;

[0019] Figure 3 is a structural diagram of a multi-layer registration system according to an embodiment of the present invention;

[0020] Figure 4 4 is a diagram of the RBF neural network structure of an embodiment of the present invention.

[0021] Figure 5 It is a block diagram of the multi-layer registration control principle of the present invention;

[0022] Figure 6 is a registration error response diagram under the RDODC and DODC methods of an embodiment of the present invention;

[0023] Figure 7 is a registration error response diagram (segmented) under the RDODC and DODC methods of an embodiment of the present invention;

[0024] Figure 8 is a register error response diagram under a sine wave signal according to an embodiment of the present invention;

[0025] Fig. 9 is a registration error response diagram under a spike signal according to an embodiment of the present invention;

[0026] Fig.10 3 is a response diagram of the registration error under the sinusoidal disturbance of the embodiment of the present invention. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0028] The embodiment of the present invention is described by taking a registration system in roll-to-roll manufacturing as an example. Figure 2 The following are examples of the longitudinal registration error and transverse registration error during the printing process of the gravure printing machine. Among them, the longitudinal registration error is affected by many factors and is the difficulty of precision printing of the R2R system. The registration error is defined as: taking the first printing unit as the reference, that is, in the entire printing process, the position of the mark point generated by the first printing unit is the reference position of the mark points generated by other printing units, then the registration error is the misalignment between the subsequent printing mark point and the first printing mark point.

[0029] This embodiment takes six layers of printed material as an example. Figure 1 FIG. 1 is a flow chart of a decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0030] Step 1: Figure 3 The mathematical modeling of the single-segment substrate between two adjacent printing groups in the multi-layer registration system shown is carried out to establish the registration error model of the single-segment substrate. For the establishment of the registration model, the following assumptions are made:

[0031] 1) The substrate is an ideal elastomer, and the density and elastic modulus of a single-segment substrate remain uniform;

[0032] 2) The quality of the substrate can be ignored;

[0033] 3) There is no sliding between the substrate and the roller, and the contact surface length is much smaller than the substrate span;

[0034] 4) Ignore the influence of external environment, such as temperature, humidity, etc.;

[0035] 5) The substrate only undergoes longitudinal deformation, and lateral deformation is not considered;

[0036] 6) Ignore energy losses on the idler rollers.

[0037] First, for the registration error e between the i-th printing unit and the i+1-th printing unit i,i+1 , that is, the ith error. V i is the linear speed of the i-th printing unit, T i is the substrate tension between the i-th printing unit and the i+1-th printing unit, L i,i+1 is the substrate span between the i-th printing unit and the i+1-th printing unit, A is the cross-sectional area of ​​the substrate, E is the Young's modulus of the substrate, τ i is the delay time of the substrate being transported from the i-th printing unit to the i+1-th printing unit. Based on the law of conservation of mass and the moving coordinate system, the nonlinear registration error model of the i+1-th printing unit relative to the i-th printing unit can be obtained as shown in formula (1):

[0038]

[0039] Assume e * 、V * and T * is the stable value of registration error, speed and tension, △e i,i+1 , △V i and △T i is the small fluctuation of the registration error, speed and tension around the stable value. The small fluctuation is much smaller than the stable value. The small deviation method is used to linearize equation (1). The small deviation method is as follows:

[0040]

[0041] Due to the registration error i,i+1 The stable value of is 0, the stable value of speed is V1, and the stable value of tension is T0, so e i.i+1 =△e i.i+1 , △T0=0, △V1=0. Substituting equation (2) into equation (1) and performing Laplace transform on the result, the linear model of registration error can be obtained:

[0042]

[0043] Among them, τ i 、a i , b i The expressions of , c and d are as follows:

[0044]

[0045] Step 2: The linear model of the single registration error obtained in the first step is recursively iterated to obtain the general form of the multi-layer registration model.

[0046] Since the speed value of each printing unit fluctuates slightly around the stable speed value, and the length of the substrate between each printing unit is equal, that is, L i,i+1 =L * , L * is the calibration value of the substrate span, so the delay time corresponding to the registration error of each layer is approximately equal, and there is:

[0047]

[0048] Combining equation (5) with equation (3) in the first step, we can recursively iterate and derive the general form of the multi-layer registration model:

[0049]

[0050] Among them, G1, G2, G3 and G i,j The expression is as follows:

[0051]

[0052] In formula (6), △V i is the system input; E i is the output of the system. It can be seen that the multi-layer registration system is a multi-input, multi-output, nonlinear, strongly coupled, time-delay system.

[0053] Step 3: Design a decoupling control method based on the coupling model of multi-layer registration errors obtained in the second step.

[0054] For any multiple-input multiple-output (MIMO) system, it can be expressed as follows:

[0055]

[0056] Where x∈R n is the system state, u∈R m is the system input, y∈R mis the system output. f′(x), g′(x) and h(x) are smooth nonlinear functions. d′ is an external disturbance and its derivative is bounded. Assuming that system (7) has a relative order r, feedback linearization is achieved by solving the Li derivative. Then the i-th output of system (7) is:

[0057]

[0058] in,

[0059]

[0060] The system coupling term and other uncertain factors are combined into the system disturbance term d i , realize the channel control method:

[0061]

[0062] Therefore, the system output term can be expressed as the sum of the input term and the system disturbance term:

[0063]

[0064] Assuming that the system disturbance term is known, the control method can be designed as follows:

[0065]

[0066] make Substituting formula (12) into formula (11), we can obtain:

[0067]

[0068] and

[0069]

[0070] in, So that the polynomial All roots of are on the left side of the complex plane and are unknown parameters. Therefore, the matrix H i is a Hurwitz matrix. Assume that there exists a positive definite symmetric matrix P i , which satisfies the following Lyapunov equation:

[0071]

[0072] Among them, Q i is a positive definite matrix with the smallest eigenvalue λ min (Q i ). i The last column is p i .

[0073] From equation (6) in the first step, we can see that the relative order of the registration system is r i = 1. Combined with formula (11) and the disturbance value estimated by the observer We can get:

[0074]

[0075]

[0076] Step 4: In most cases, the system disturbance term in step 3 cannot be obtained accurately. Therefore, a disturbance observer is used to observe its value.

[0077] like Figure 4 The radial basis function neural network (RBFNN) shown in the figure has a simple structure, simple training, fast learning convergence speed, and can approximate any nonlinear function. RBFNN is used to approximate the system disturbance term d i . Then there exists an optimal weight coefficient W of the neural network i , so that:

[0078]

[0079] Among them, |ε|≤ε min is the minimum approximation error, ε min is an arbitrarily small positive constant.

[0080] Combining formula (11) and formula (17), we get:

[0081]

[0082] Definition D i =ε+d′ as the new expansion state, formula (18) can be rewritten as:

[0083]

[0084] in D i The bounded derivative of .

[0085] Based on formula (19), the RBFNN disturbance observer of the i-th output is designed as:

[0086]

[0087] in, and is the state variable of the observer, l i,1 and l i,2 is a normal number, is the optimal weight coefficient Wi The estimated value of .

[0088] have

[0089] Combining formula (16), formula (18) and formula (20), we can get:

[0090]

[0091]

[0092] Rewriting formula (22) into the form of state equation, we have:

[0093]

[0094] in:

[0095]

[0096] Obviously, A i is a Hurwitz matrix, assuming that there exists a positive definite symmetric matrix Γ i The following Lyapunov equation is satisfied:

[0097]

[0098] where Γ i =[Γ i,1 Γ i,2 ], define the error variable as E i =y i -y d ,y d is the ideal output. The designed weight adaptive law is:

[0099]

[0100] Among them, Λ i =Λ i T >0,ρ i >0 indicates the parameter to be set.

[0101] Step 5: Conduct stability analysis on the decoupling control method for the multi-layer registration system of a gravure printing machine based on a disturbance observer designed by the present invention.

[0102] Constructing Lyapunov functions Prove the stability of the proposed control method, V i is the Lyapunov function of the i-th output.

[0103] V i =V i,1 +Vi,2 +V i,3 +V i,4 (27)

[0104] in,

[0105]

[0106]

[0107]

[0108]

[0109] Combining formulas (17) to (31), and considering the inequality By taking the derivative of the Lyapunov function (27), we can obtain:

[0110]

[0111]

[0112]

[0113]

[0114] Combining formulas (32) to (35) and simplifying them, we can obtain:

[0115]

[0116] When for all i=1,2,…,m, if the condition is satisfied:

[0117]

[0118] Then there is

[0119] Based on the Lyapunov stability principle, the system output y i , observation error Weight estimation error And the tracking error E i They are all consistent and converge in the end, and the proof is complete.

[0120] Step 6: Use genetic algorithm to optimize the parameters of the control law proposed in the third step and the observer proposed in the fourth step.

[0121] From the third and fourth steps, we can see that there are parameters to be set in the control law (15) and the RBFNN disturbance observer (20). The genetic algorithm (GA) has macroscopic search capabilities and excellent global optimization capabilities, so the genetic algorithm is selected to optimize the parameters of the control law (15) and the observer (20). The specific steps of the genetic algorithm to optimize the parameters are as follows:

[0122] 1) Population initialization. Each individual is a real number vector composed of all parameters to be set. Define the value range of each optimization parameter according to the characteristics of each parameter, determine the population number to be 30, and set the genetic generation to 50.

[0123] 2) Selection operation. Obtain the output value corresponding to each individual, and use the fitness function to select the individual with the largest fitness, which will serve as the parent individual to reproduce the next generation.

[0124] 3) Crossover and mutation operations. Set the crossover probability to 0.9, and randomly select each individual mutation probability in the interval [0.090, 0.100]. Thus, a new population is established. If the maximum genetic generation is not met, the genetic operation continues, otherwise the operation ends.

[0125] Figure 5 It is a block diagram of the multi-layer registration control principle. Figure 6 is the registration error response diagram under the RDODC and DODC methods. For the convenience of analysis, Figure 6 Segmentation according to the transport cycle, such as Figure 7 As shown in the figure, the registration error under RDODC control is significantly smaller than that under DODC control, and the convergence speed of RDODC is faster. Even in the case of system disturbance, the fluctuation data of the registration error value controlled by the RDODC method will not exceed ±0.025mm. When the number of layers increases, RDODC responds faster. The higher the number of layers, the more obvious the suppression of the registration error fluctuation caused by the speed fluctuation of the upstream printing unit, and it is significantly stronger than DODC.

[0126] Figure 8 as well as Fig. 9These are the registration error response diagrams under sine wave and spike wave signals, respectively. It can be seen that the RDODC method and the DODC method perform well in tracking periodic signals, but there are certain small tracking errors. At the same time, due to the existence of speed fluctuations of the upstream printing unit, during the periodic signal tracking process, the errors in each transmission cycle will be accumulated to the next transmission cycle, forming a cumulative error. Under the sine wave signal, only the cumulative error of the fourth layer is slightly smaller than that of the RDODC method under the DODC method. Overall, under the RDODC method, the cumulative error is significantly smaller than that of the DODC method. And the RDODC method has a stronger inhibitory effect on abrupt changes. Therefore, the RDODC method has better tracking performance and can effectively suppress cumulative errors.

[0127] Fig.10 It is the registration error response diagram under sinusoidal disturbance. By comparing the fluctuation data of each registration error separately, it can be seen that only the fluctuation range of E3 under the control of the RDODC method is higher than that of the DODC method. But overall, the RDODC method more effectively suppresses the registration error fluctuation caused by external periodic disturbances, ensuring the stable operation of the entire high-precision printing process.

[0128] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0129] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are 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 in the protection scope of the present invention.

Claims

1. A decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer, characterized in that: The following steps are involved: S1: According to the printing principle and physical law of multi-layer gravure printing machine, based on the law of conservation of mass and moving coordinate system, a nonlinear model of single registration error is established, and the linear model of single registration error is obtained by linearizing it using the small deviation method; S2: According to the definition of registration error, based on the linear model of single registration error, recursive iterative derivation is performed to obtain a multi-layer registration error model; S3: For the multi-layer registration error model, based on the decentralized control method and decoupling control theory, combined with RBF neural network, a decoupling control method based on RBFNN disturbance observer is designed; S4: A genetic algorithm is used to optimize the undetermined parameters in the decoupling control method, and a GA optimized decoupling control method based on RBFNN disturbance observer is obtained to achieve input-output decoupling of the multi-layer registration system to effectively control the registration error of each printing unit.

2. The decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to claim 1 is characterized in that: The nonlinear model of a single registration error includes: For the registration error e between the i-th printing unit and the i+1-th printing unit i,i+1 , that is, the i-th error; Let V i is the linear speed of the i-th printing unit, T i is the substrate tension between the i-th printing unit and the i+1-th printing unit, L i,i+1 is the substrate span between the i-th printing unit and the i+1-th printing unit, A is the cross-sectional area of ​​the substrate, E is the Young's modulus of the substrate, τ i is the delay time of the substrate being transported from the i-th printing unit to the i+1-th printing unit. Based on the law of conservation of mass and the moving coordinate system, the nonlinear registration error model of the i+1-th printing unit relative to the i-th printing unit is obtained as shown in formula (1): Where t is time.

3. The decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to claim 2 is characterized in that: The following assumptions are made for model building: 1) The substrate is an ideal elastomer, and the density and elastic modulus of a single-segment substrate remain uniform; 2) The quality of the substrate is negligible; 3) There is no sliding between the substrate and the roller, and the contact surface length is much smaller than the substrate span; 4) Ignore the influence of the external environment; 5) The substrate only undergoes longitudinal deformation, and lateral deformation is not considered; 6) Ignore energy losses on the idler rollers.

4. The decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to claim 2 is characterized in that: The linear model of a single registration error obtained by linearizing it using the small deviation method includes: Assume e * 、V * and T * are the stable values ​​of registration error, speed and tension, △e i,i+1 , △V i and △T i are the small fluctuations of the registration error, speed and tension near the stable value, respectively. The small fluctuations are much smaller than the stable value. The small deviation method is used to linearize equation (1), and the small deviation method is as follows: Due to the registration error i,i+1 The stable value of is 0, the stable value of speed is V1, and the stable value of tension is T0, so e i.i+1 =△e i.i+1 , △T0=0, △V1=0; Substitute equation (2) into equation (1) and perform Laplace transform on the result to obtain the linear model of registration error: Among them, τ i 、a i , b i The expressions of , c and d are as follows: This results in a nonlinear model of the single registration error.

5. The decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to claim 4 is characterized in that: Step S2 is specifically as follows: Since the speed value of each printing unit fluctuates slightly around the stable speed value, and the length of the substrate between each printing unit is equal, that is, L i,i+1 =L * , L * is the calibration value of the substrate span, so the delay time corresponding to the registration error of each layer is approximately equal, and there is: Combining formula (5) with formula (3), we can recursively iterate and derive the multi-layer registration error model: Among them, G1, G2, G3 and G i,j The expression is as follows: In the formula, the small fluctuation △V i is the input of the system, E i is the output of the system.

6. The decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to claim 5 is characterized in that: Step S3 is specifically as follows: S31: For any multi-input multi-output system, it can be expressed as follows: Where x∈R n is the system state, u∈R m is the system input, y∈R m is the system output; f′(x), g′(x) and h(x) are smooth nonlinear functions; d′ is the external disturbance and its derivative is bounded; Assuming that the system has a relative order r, feedback linearization is achieved by solving the Li derivative; then the i-th output of the system is: in: The system coupling term and other uncertain factors are combined into the system disturbance term d i , realize the channel control method: Therefore, the system output term is expressed as the sum of the input term and the disturbance term: Assume that the system disturbance term d i It is known that the design control method is as follows: make Substituting formula (12) into formula (11), we can obtain: and in, So that the polynomial All roots of are on the left side of the complex plane and are unknown parameters, so the matrix H i is the Hurwitz matrix; Assume there exists a positive definite symmetric matrix P i , which satisfies the following Lyapunov equation: Among them, Q i is a positive definite matrix with the smallest eigenvalue λ min (Q i ), P i The last column is p i ; From formula (6), we know that the relative order of the registration system is r i =1, combined with formula (11) and the disturbance value estimated by the observer have to: S32: Using RBFNN to approximate the system disturbance term d i , then there exists an optimal weight coefficient W of the neural network i , so that: Among them, |ε|≤ε min is the minimum approximation error, ε min is an arbitrarily small positive constant; Combining formula (11) and formula (17), we get: Definition D i =ε+d′ as the new expansion state, formula (18) is rewritten as: in D i The bounded derivative of ; Based on formula (19), the RBFNN disturbance observer of the i-th output is designed as: in, and is the state variable of the observer, l i,1 and l i,2 is a normal number, is the optimal weight coefficient W i The estimated value of Combining formula (16), formula (18) and formula (20), we get: Rewriting formula (22) into the form of state equation, we have: in: Obviously, A i is a Hurwitz matrix, assuming that there exists a positive definite symmetric matrix Γ i The following Lyapunov equation is satisfied: where Γ i =[Γ i,1 Γ i,2 ], define the error variable as E i =y i -y d ,y d is the ideal output; the design weight adaptive law is: Among them, Λ i =Λ i T >0,ρ i >0 is the parameter to be set; S33: Constructing Lyapunov functions Prove the stability of the control method proposed in step S32, V i is the Lyapunov function of the i-th output, we have: V i =V i,1 +V i,2 +V i,3 +V i,4 (27) in, Combining formulas (17) to (31), and considering the inequality Derivative of the Lyapunov function (27) yields: Combining formulas (32) to (35) and simplifying them, we can obtain: When for all i=1,2,…,m, if the condition is satisfied: Then there is Based on the Lyapunov stability principle, the system output y i , observation error Weight estimation error And the tracking error E i are consistent and eventually converge.

7. The decoupling control method for a multi-layer registration system of a gravure printing machine based on a disturbance observer according to claim 6 is characterized in that: Step S4 is specifically as follows: From step S3, it is known that there are parameters to be set in the control law (15) and the RBFNN disturbance observer (20). A genetic algorithm is selected to optimize the parameters of the control law (15) and the observer (20). The specific steps of optimizing the parameters by the genetic algorithm are as follows: 1) Population initialization: Each individual is a real number vector composed of all parameters to be set. The value range of each optimization parameter is defined according to the characteristics of each parameter. The population size is determined to be 30, and the genetic generation is set to 50; 2) Selection operation: Obtain the output value corresponding to each individual, use the fitness function to select the individual with the largest fitness, and use it as the parent individual to reproduce the next generation; 3) Crossover and mutation operations: Set the crossover probability to 0.9, and randomly select each individual mutation probability in the interval [0.090, 0.100] to establish a new population; if the maximum genetic generation is not met, continue the genetic operation, otherwise the operation ends.

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