Roll-to-roll multilayer overprinting control method based on improved simulated annealing optimization LQR

Abstract

The invention discloses a reel-to-reel multilayer printing control method based on improved simulated annealing optimization LQR, and belongs to the field of multilayer printing flexible electronics. According to the reel-to-reel multilayer printing flexible electronic control method based on the improved simulated annealing optimization LQR, initial LQR controller design is carried out on an overprinting system according to a reel-to-reel overprinting system dynamic model, and a simulated annealing algorithm is selected to carry out LQR controller optimization; and self-adaptive annealing, dynamic step length, mixed neighborhood search and other methods are used to make up for the defects of slow convergence speed, difficult temperature control and the like of the traditional simulated annealing algorithm, so as to obtain the optimal control quantity and improve the overprinting precision and control stability of the system. The control quantity optimization of the overprinting system is realized, the control stability of the overprinting system is ensured, and the overprinting precision is improved.

Description

Technical Field

[0001] The invention relates to a roll-to-roll multi-layer overprint control method based on improved simulated annealing optimization LQR, belonging to the technical field of roll-to-roll multi-layer overprint. Background Art

[0002] Roll-to-Roll (R2R) printed flexible electronics refers to the technology of printing electronic circuits and components on flexible substrates using a continuous roll-to-roll process, which has the characteristics of large-scale and large-area production. In addition, the increasing demand for wearable and flexible electronic products in recent years has accelerated the application of R2R technology in the field of printed electronics.

[0003] In the roll-to-roll printing process, the overprint error is defined as the relative distance between the reference position and the current printed pattern. When performing multi-layer printing, the overprint error should be strictly controlled to prevent device functional errors caused by overprint errors. However, most of the current overprint control is performed on traditional printed media (such as magazines and newspapers). Therefore, the overprint accuracy is determined based on the human visual discernible range, which is usually 100μm. However, when using R2R printing for flexible electronics, the overprint accuracy should be below 30μm to meet the printing requirements of functional devices.

[0004] Traditional LQR (Linear Quadratic Regulator) controller design often adopts empirical methods. It is difficult to obtain the optimal feedback gain K through this design method to make the system reach the optimal control state. At present, particle swarm optimization algorithm and genetic algorithm are mostly used to optimize LQR controllers. However, particle swarm optimization algorithm and genetic algorithm are prone to fall into local optimal solutions during the optimization process. The simulated annealing algorithm is a general probabilistic optimization algorithm. Its basic idea is to perform random search in the solution space and use the Metropolis criterion to accept poor solutions, so as to avoid falling into local optimal solutions and gradually move towards global optimal solutions. It has strong robustness. Therefore, Meng Jie proposed in the literature "Research on Optimal Control of Automobile Suspension Based on Simulated Annealing Algorithm" that the simulated annealing algorithm can be used to optimize the LQR controller. However, although the traditional simulated annealing algorithm can effectively avoid falling into local optimal solutions, its convergence speed is slow and has high requirements for temperature control. If the temperature control is improper, it may cause the algorithm to converge prematurely and fall into the local optimal solution. Summary of the invention

[0005] In order to improve the search efficiency of the algorithm and ensure that a high-quality optimal solution is found, the present invention provides a roll-to-roll multi-layer overprint control method based on improved simulated annealing optimization LQR, which uses adaptive annealing, dynamic step size and hybrid neighborhood search to make up for the defects of the traditional simulated annealing algorithm such as slow convergence speed and difficult temperature control. The method includes:

[0006] Step S1, preliminarily designing an LQR controller based on a dynamic model of a roll-to-roll overprinting system;

[0007] Step S2, taking system control accuracy and energy consumption as optimization objectives, determining a fitness function;

[0008] Step S3, optimizing the LQR controller preliminarily designed in step S1 by using an improved simulated annealing algorithm, wherein the improved simulated annealing algorithm is an algorithm obtained by improving the traditional simulated annealing algorithm by using adaptive annealing, dynamic step size and hybrid neighborhood search.

[0009] Optionally, the step S1 includes:

[0010] Step S11, determining a state space equation according to a dynamic model of the roll-to-roll overprinting system;

[0011] The dynamic model of the roll-to-roll overprinting system is:

[0012]

[0013] Where: e(t) is the overprint error, V * is the steady-state speed of the printing roller, T* is the steady-state tension of the printing substrate, L and M are the correlation coefficients of the printing substrate, △T1(t) is the change in the tension of the printing substrate in the printing section at time t, and △V1(t) is the change in the speed of the printing roller at time t;

[0014] According to the dynamic model of the roll-to-roll overprinting system, the state space equation of the overprinting system is:

[0015]

[0016] Among them: A is the state matrix, B is the input matrix, C is the output matrix; x1 is the overprint deviation, x2 is the change in the tension of the printing section, and u is the input of the overprint system, that is, the change in the speed of the printing roller;

[0017] Step S12, completing the preliminary design of the LQR controller based on the state space equation of the overprinting system;

[0018] The cost function J is introduced to determine the state variable weight matrix Q(t) and the control variable weight matrix R(t) of the overprinting system;

[0019]

[0020] The input u of the overprinting system is:

[0021]

[0022] The state feedback matrix K = R -1 BT P and P are obtained by solving the Riccati equation.

[0023] Optionally, the fitness function in step S2 is:

[0024]

[0025] Where: u is the control input, e is the control deviation, and t represents time.

[0026] Optionally, step S3 includes:

[0027] Step S31, setting the diagonal element values ​​of the initial weight matrices Q0 and R0 of the LQR controller to random numbers [0.1, 100];

[0028] Step S32: According to the fitness function determined in step S2, an improved simulated annealing algorithm is used to perform iterative optimization to find the optimal weight matrices Q' and R' that minimize the fitness function value, and then determine the state feedback matrix K.

[0029] Optionally, the hybrid neighborhood search method in step S32 includes multi-step neighborhood search, adding random disturbance and dynamic step size; step S32 includes:

[0030] Step S321, assuming the current solution is (a, b), generate a new solution (a', b') according to the following formula:

[0031]

[0032] b'=b+(r-0.5)×s(n)×0.1

[0033] Where: r is a random number, s(n) is the dynamic step size;

[0034]

[0035] s max Indicates the maximum step length, n max Indicates the maximum number of iterations;

[0036] Step S322, calculating the fitness function values ​​of the current solution and the new solution;

[0037] If the fitness function value F(a′, b′) of the new solution is better than the fitness function value F(a, b) of the current solution, the new solution is accepted.

[0038] If the fitness function value F(a′, b′) of the new solution is inferior to the fitness function value F(a, b) of the current solution, it is accepted according to the following probability rule:

[0039]

[0040] Where: T is the current temperature;

[0041] Step S323, after each iteration, the temperature is updated by using an adaptive annealing method. The temperature update formula proposed by the present invention is as follows:

[0042] T(n+1)=α(n)·T(n)

[0043] Where: α(n) is the adaptive cooling rate, T(n) is the current temperature, and T(n+1) is the temperature at the next iteration.

[0044] Optionally, the adaptive cooling rate α(n) formula is as follows:

[0045]

[0046] Where: n is the number of iterations, α max is the maximum cooling rate, α min is the minimum cooling rate.

[0047] Optionally, set the initial temperature T0 of the simulated annealing algorithm to 1000°C, the initial cooling rate α0 to 0.99, and the minimum cooling rate α min is 0.95, the maximum cooling rate α max is 0.999, the maximum number of iterations n max is 1000.

[0048] Optionally, in the method, the state matrix Input Matrix Output matrix C = [1 0].

[0049] The present invention also provides a roll-to-roll multi-layer overprint control system based on improved simulated annealing optimized LQR. The system is implemented based on the above method, and the system includes a detection camera, a PLC controller and a tension sensor; wherein the detection camera is used to obtain an image of the printing substrate after the first layer and the second layer are printed; the tension sensor is used to obtain the change in tension of the printing substrate; the PLC controller is used to determine the deviation between the first layer printing pattern and the second layer printing pattern according to the printing substrate image obtained by the detection camera, and calculate the control output based on the deviation to compensate for the deviation.

[0050] The present invention also provides application of the method in the technical field of roll-to-roll multi-layer overprinting.

[0051] The beneficial effects of the present invention are:

[0052] The present invention proposes a roll-to-roll multi-layer overprint control method based on improved simulated annealing optimization LQR. According to the dynamic model of the roll-to-roll overprint system, an initial LQR controller is designed for the overprint system, and a simulated annealing algorithm is selected to optimize the LQR controller. Adaptive annealing, dynamic step size, and hybrid neighborhood search are used to compensate for the defects of traditional simulated annealing algorithms such as slow convergence speed and difficult temperature control.

[0053] The temperature attenuation and step size adjustment in the traditional simulated annealing algorithm are usually fixed. When the cooling rate and step size are not set properly, the algorithm may easily converge slowly and fall into a local optimal solution. To address this problem, the solution of the present invention adopts adaptive annealing to avoid the algorithm from stagnating and converging too early, and provides a more flexible search strategy through dynamic step size, so that the algorithm can flexibly adjust parameters according to the current search state, thereby improving search efficiency and convergence speed. At the same time, a hybrid neighborhood search is introduced in the generation of new solutions, so as to more fully explore the solution space and avoid falling into a local optimal solution due to improper temperature control. Finally, the LQR control method of the improved simulated annealing optimization proposed by the present invention is used to obtain the optimal control amount, thereby improving the overprinting accuracy and control stability of the system. The present invention realizes the optimization of the control amount of the overprinting system, ensures the control stability of the overprinting system, and improves the overprinting accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0055] Figure 1 This is a diagram showing the working principle of roll-to-roll multi-layer overprinted flexible electronics.

[0056] Figure 2 It is a flow chart of the roll-to-roll multi-layer overprinting flexible electronic control method based on improved simulated annealing optimization LQR proposed in the present invention.

[0057] Figure 3 It is a flow chart of optimizing the LQR controller by using the improved simulated annealing algorithm proposed in the present invention.

[0058] Figure 4 It is a simulation diagram comparing the fitness iterations of LQR optimization using the standard simulated annealing algorithm and the improved simulated annealing algorithm proposed in the present invention.

[0059] Figure 5 It is a simulation diagram comparing the changes in overprint deviation of an LQR without any algorithm optimization, an LQR optimized by a standard simulated annealing algorithm, and an LQR control method optimized by an improved simulated annealing algorithm proposed by the present invention.

[0060] Figure 6 It is a simulation diagram comparing the changes in control quantities of an LQR without any algorithm optimization, an LQR optimized by a standard simulated annealing algorithm, and an LQR control method optimized by the improved simulated annealing algorithm proposed by the present invention. DETAILED DESCRIPTION

[0061] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0062] Embodiment 1:

[0063] This embodiment provides a roll-to-roll multi-layer overprinting flexible electronic control method based on improved simulated annealing optimization LQR, see Figure 1 The working principle diagram of the roll-to-roll multi-layer overprint flexible electronics shown in the figure, the roll-to-roll multi-layer overprint control system is mainly composed of a line scan camera (as a detection camera), a PLC (programmable logic controller) and a C++-based overprint detection and control program. During the overprint process, the distance between the first layer of printed pattern and the second layer of printed pattern is measured by the corresponding overprint mark points. When the substrate is printed after the second layer, the printed pattern will pass through the line scan camera (i.e. Figure 1 The line scan camera sends the captured image to the deviation detection program for deviation detection. After the deviation detection is completed, the control program processes the detected deviation value, calculates the control output, and sends it to the PLC for deviation compensation.

[0064] Figure 2 The flowchart of the roll-to-roll multi-layer overprinting flexible electronic control method based on improved simulated annealing optimization LQR proposed by the present invention specifically includes the following specific steps:

[0065] Step S1, preliminarily completing the design of the LQR controller based on the dynamic model of the roll-to-roll overprinting system;

[0066] Step S1 includes the following specific steps:

[0067] S11. Determine the state space equation according to the dynamic model of the roll-to-roll overprinting system:

[0068] The dynamic model of the roll-to-roll overprinting system is as follows:

[0069]

[0070] Where: e(t) is the overprint error, V *is the steady-state speed of the gravure roller, is the initial printing speed set for the system, T* is the steady-state tension of the printing substrate, is the initial tension set for the system, L and M are the correlation coefficients of the printing substrate, which are known parameters, △T1(t) is the tension change of the printing substrate in the printing section at time t, which can be measured by the tension sensor set in the printing section, △V1(t) is the speed change of the gravure roller at time t, which is the system control quantity.

[0071] According to the dynamic model of the roll-to-roll overprinting system, the state space equation of the overprinting system can be obtained as follows:

[0072]

[0073] Among them: A is the state matrix, B is the input matrix, and C is the output matrix. x1 is the overprint deviation, which is obtained by the detection program based on the image collected by the line scan camera, x2 is the tension change of the printing section, which is measured by the tension sensor, and u is the input quantity, that is, the speed change of the gravure roller.

[0074] In this embodiment, C=[1 0].

[0075] S12. Complete the preliminary design of the LQR controller based on the state space equation of the overprint system and introduce the cost function J:

[0076]

[0077] Among them: Q(t) is the state variable weight matrix, a semi-positive definite matrix; R(t) is the control variable weight matrix, a positive definite matrix.

[0078] The input u of the control system is:

[0079]

[0080] The state feedback matrix K = R -1 B T P, P can be solved by the Riccati equation, which is shown as follows:

[0081] A T P+PA-PBR -1 B T P+Q=0

[0082] The initial values ​​of k1 and k2 are 0.5 and 1.99×10 -5 .

[0083] S2. Based on the state space equation of the overprinting system, the system control accuracy and energy consumption are taken as the optimization objectives to design the fitness function. The fitness function is designed as follows:

[0084]

[0085] Where: u is the control input, e is the control deviation, and t represents time.

[0086] S3. The designed LQR controller is optimized by simulated annealing algorithm, and the traditional simulated annealing algorithm is improved by adaptive annealing, dynamic step size and hybrid neighborhood search to obtain the optimal control quantity and improve the overprinting accuracy and control stability.

[0087] Figure 3 The control flow chart of the improved simulated annealing optimization LQR is shown, and step S3 specifically includes the following steps:

[0088] S31, set the diagonal element values ​​of the initial weight matrix Q0 and R0 of the LQR controller to random numbers [0.1, 100], set the initial temperature T0 of the simulated annealing algorithm to 1000 °C, the initial cooling rate α0 to 0.99, and the minimum cooling rate α min is 0.95, the maximum cooling rate α max is 0.999, the maximum number of iterations n max is 1000;

[0089] S32, according to the fitness function in step S2, using the improved simulated annealing algorithm to iteratively search for the optimal weight matrices Q' and R' that minimize the fitness function value;

[0090] The iterative optimization process of improving the simulated annealing algorithm includes the following specific steps:

[0091] S321. Because the standard simulated annealing algorithm converges slowly during the iterative optimization process, to solve this problem, when the algorithm generates a new solution, a hybrid neighborhood search method is adopted, which mainly includes multi-step neighborhood search, adding random perturbations and dynamic step lengths. When using multi-step neighborhood search, when generating a new solution a', the algorithm has a 50% probability of selecting different step length ratios, which is equivalent to a mixed large step length and small step length search method, while taking into account the optimization problems of extensive search and fine adjustment. Large step length search is used to explore a farther solution space and jump out of the local optimal solution, and small step length search is used to search for a more detailed local optimal solution to improve the accuracy of the solution. When generating a new solution, random numbers are used to add random perturbations to the generation of the new solution, so that the algorithm generates random new solutions near the current solution, thereby avoiding falling into the local optimum and opening up a wider solution space. Adopting an adaptive dynamic step length adjustment method, the step length is adjusted dynamically with the number of iterations, so that the algorithm can conduct a large-scale search in the early stage of the search and a fine search in the later stage of the search, ensuring the global search capability and convergence accuracy of the algorithm. Assume the current solution is (a, b), the new solution (a', b') is generated by the following formula:

[0092]

[0093] b'=b+(r-0.5)×s(n)×0.1

[0094] Where: r is a random number, s(n) is the dynamic step size.

[0095] At present, most of the methods for improving the step size of the simulated annealing algorithm use an exponential decay step size method. This adjustment method relies on the setting of the decreasing coefficient, and the parameter adjustment is relatively sensitive. At the same time, in the later stage of iteration, the step size will become very small, which may cause the algorithm to converge too slowly. The method of dynamically adjusting the step size according to the number of iterations proposed in the present invention, on the one hand, does not need to consider the problem of setting the decreasing coefficient, and on the other hand, it is simple and easy to implement, has high computational efficiency, and converges quickly. Let the step size be s, the current number of iterations be n, and the maximum number of iterations be n. max , the step size adjustment formula adopted by the present invention is as follows:

[0096]

[0097] Among them, s max Indicates the maximum step size.

[0098] At present, most of the hybrid neighborhood search methods are combined with other optimization algorithms (such as particle swarm optimization algorithm, taboo search algorithm, etc.). This implementation method often leads to complex algorithm structure, greatly increased calculation amount, and the parameter tuning requirements of these optimization algorithms are also high. The neighborhood search method adopted by the present invention by mixing multiple step lengths, random perturbations and probability selection methods can also achieve the same effect as combining other optimization algorithms for neighborhood search, but the calculation complexity is greatly reduced, and there is no need to consider parameter setting issues; at the same time, the hybrid neighborhood search method combined with other optimization algorithms may be limited by the local search capabilities of other optimization algorithms during the algorithm optimization process, while the hybrid neighborhood search method proposed by the present invention can cover the solution space more comprehensively through the randomness and adaptability of the neighborhood, and improve the ability of the algorithm to search for the global optimal solution.

[0099] S322, calculate the fitness function values ​​of the current solution and the new solution:

[0100] If the fitness function value F(a′, b′) of the new solution is better than the fitness function value F(a, b) of the current solution, the new solution is accepted.

[0101] If the fitness function value F(a′, b′) of the new solution is inferior to the fitness function value F(a, b) of the current solution, it is accepted according to the following probability rule:

[0102]

[0103] Where: T is the current temperature.

[0104] S323. In view of the problem that improper temperature control of the standard simulated annealing algorithm may cause the algorithm to converge prematurely and fall into a local optimal solution, an adaptive annealing method is used to update the temperature after each iteration. The temperature update formula proposed by the present invention is as follows:

[0105] T(n+1)=α(n)·T(n)

[0106] Where: α(n) is the adaptive cooling rate, T(n) is the current temperature, and T(n+1) is the temperature at the next iteration.

[0107] The adaptive cooling rate α(n) refers to dynamically adjusting the cooling rate of annealing according to the changes in the currently searched optimal solution. When a better solution is found, the algorithm slightly increases the cooling rate to slowly reduce the temperature, thereby maintaining a higher temperature and continuing to explore in the neighborhood of the current solution to avoid premature convergence and falling into the local optimum; when no better solution is found, the cooling rate is slightly reduced and the cooling speed is accelerated to avoid wandering in the suboptimal solution area and accelerate convergence. During the algorithm iteration process, the cooling rate adjustment formula proposed by the present invention is as follows:

[0108]

[0109] Where: n is the number of iterations, α max is the maximum cooling rate, α min is the minimum cooling rate.

[0110] The fixed cooling rate of the traditional simulated annealing algorithm often causes the algorithm to stay in certain areas for too long, wasting computing resources. At the same time, the traditional simulated annealing algorithm usually requires manual setting of a suitable fixed cooling rate. If the cooling rate is not set properly, it will affect the optimization effect of the algorithm. The adaptive cooling rate method proposed in the present invention can automatically optimize the cooling rate during the algorithm optimization process, can better adapt to changes in the optimization process, ensure that the algorithm can maintain a certain temperature when searching for the potential optimal solution area, prevent falling into the local optimum, and optimize the use of computing resources.

[0111] In the prior art, improvements to the cooling rate of the simulated annealing algorithm are mostly made by using exponential cooling and linear decreasing methods. Although these two methods can control the speed of temperature cooling, they cannot dynamically adjust the temperature according to the state of the currently searched optimal solution, which easily causes the algorithm to stagnate and converge in the early stages of the optimization search. The adaptive cooling rate method proposed in the present invention slowly cools down when a new solution is found, retains the exploration capability, reduces the possibility of falling into a local optimal solution, and ensures a wider search. When a new solution is not found, the temperature is accelerated to avoid excessive wandering in the suboptimal solution area, thereby improving the convergence efficiency of the algorithm. The adaptive cooling rate method proposed in the present invention can well balance the algorithm's global search state at higher temperatures and the local optimization state at lower temperatures, thereby ensuring a good search effect.

[0112] S324, determine whether the termination condition is met, the termination condition is set to reach the maximum number of iterations, when the termination condition is met, output the current optimal weight matrix Q' and R'. If the termination condition is not met, repeat steps S321-S323.

[0113] Figure 4 The fitness change comparison curve of the improved simulated annealing optimization LQR controller and the standard simulated annealing optimization LQR controller shows that the initial fitness value of the improved simulated annealing optimization algorithm proposed in this invention is 4.35×10 -6 , while the initial fitness value of the standard simulated annealing optimization algorithm is 6.46×10 -6 ; This shows that in the early stage of optimization, the global optimization ability of the improved simulated annealing algorithm proposed in the present invention is significantly stronger than that of the standard simulated annealing algorithm. After 101 iterations, the improved simulated annealing algorithm proposed in the present invention found a global optimal solution of 1.15×10 -6 , while the standard simulated annealing algorithm found the global optimal solution after 683 iterations. -6 ,These results show that the improved simulated annealing algorithm proposed in ,the present invention performs better in both detection efficiency and the ,quality of the optimal solution searched.

[0114] Under the initial overprint deviation interference, the overprint deviation changes under the standard LQR control strategy, the standard simulated annealing optimized LQR control strategy and the improved simulated annealing optimized LQR control strategy are shown in Figure 2. Figure 5 As shown. Figure 5 From the comparison of the overprint deviation changes shown, it can be seen that the maximum overshoot of the standard LQR control strategy is 14μm, the maximum overshoot of the standard simulated annealing optimized LQR control strategy is 11μm, and the maximum overshoot of the improved simulated annealing optimized LQR control strategy proposed in the present invention is 6μm, that is, the maximum overshoot of the improved simulated annealing proposed in the present invention is lower, and the control accuracy of the system is higher.

[0115] Figure 6 The control amount change curves under the standard LQR control strategy, the standard simulated annealing optimized LQR control strategy and the improved simulated annealing optimized LQR control strategy are shown. By observing the control amount changes under the three control strategies, it can be seen that the peak control amount under the standard LQR control strategy is 2.5×10 -4 m / s, and the peak control amount of the standard simulated annealing optimized LQR control strategy is 1.6×10 -4 m / s, while the overshoot of the improved simulated annealing optimized LQR control strategy proposed in this invention is 9.5×10 -5m / s, it can be seen that compared with the other two control strategies, the improved simulated annealing optimized LQR control strategy proposed in the present invention has lower system energy consumption, smoother control output and more stable system.

[0116] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0117] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A roll-to-roll multi-layer overprint control method based on improved simulated annealing optimization LQR, characterized in that: The method comprises: Step S1, preliminarily designing an LQR controller based on a dynamic model of a roll-to-roll overprinting system; Step S2, taking system control accuracy and energy consumption as optimization objectives, determining a fitness function; Step S3, optimizing the LQR controller preliminarily designed in step S1 by using an improved simulated annealing algorithm, wherein the improved simulated annealing algorithm is an algorithm obtained by improving the traditional simulated annealing algorithm by using adaptive annealing, dynamic step size and hybrid neighborhood search.

2. The method according to claim 1, characterized in that The step S1 comprises: Step S11, determining a state space equation according to a dynamic model of the roll-to-roll overprinting system; The dynamic model of the roll-to-roll overprinting system is: Where: e(t) is the overprint error, V * is the steady-state speed of the printing roller, T* is the steady-state tension of the printing substrate, L and M are the correlation coefficients of the printing substrate, △T1(t) is the change in the tension of the printing substrate in the printing section at time t, and △V1(t) is the change in the speed of the printing roller at time t; According to the dynamic model of the roll-to-roll overprinting system, the state space equation of the overprinting system is: Among them: A is the state matrix, B is the input matrix, C is the output matrix; x1 is the overprint deviation, x2 is the change in the tension of the printing section, and u is the input of the overprint system, that is, the change in the speed of the printing roller; Step S12, completing the preliminary design of the LQR controller based on the state space equation of the overprinting system; The cost function J is introduced to determine the state variable weight matrix Q(t) and the control variable weight matrix R(t) of the overprinting system; The input u of the overprinting system is: The state feedback matrix K = R -1 B T P and P are obtained by solving the Riccati equation.

3. The method according to claim 2, characterized in that The fitness function in step S2 is: Where: u is the control input, e is the control deviation, and t represents time.

4. The method according to claim 3, characterized in that The step S3 comprises: Step S31, setting the diagonal element values ​​of the initial weight matrices Q0 and R0 of the LQR controller to random numbers [0.1, 100]; Step S32: According to the fitness function determined in step S2, an improved simulated annealing algorithm is used to perform iterative optimization to find the optimal weight matrices Q' and R' that minimize the fitness function value, and then determine the state feedback matrix K.

5. The method according to claim 4, characterized in that The hybrid neighborhood search method in step S32 includes multi-step neighborhood search, adding random disturbance and dynamic step size; step S32 includes: Step S321, assuming the current solution is (a, b), generate a new solution (a', b') according to the following formula: b'=b+(r-0.5)×s(n)×0.1 Where: r is a random number, s(n) is the dynamic step size; s max Indicates the maximum step length, n max Indicates the maximum number of iterations; Step S322, calculating the fitness function values ​​of the current solution and the new solution; If the fitness function value F(a′, b′) of the new solution is better than the fitness function value F(a, b) of the current solution, the new solution is accepted; If the fitness function value F(a′, b′) of the new solution is inferior to the fitness function value F(a, b) of the current solution, it is accepted according to the following probability rule: Where: T is the current temperature; Step S323: After each iteration, the temperature is updated by using an adaptive annealing method. The temperature update formula is as follows: T(n+1)=α(n)·T(n) Where: α(n) is the adaptive cooling rate, T(n) is the current temperature, and T(n+1) is the temperature at the next iteration.

6. The method according to claim 5, characterized in that The adaptive cooling rate α(n) formula is as follows: Where: n is the number of iterations, α max is the maximum cooling rate, α min is the minimum cooling rate.

7. The method according to claim 6, characterized in that In the method, the initial temperature T0 of the simulated annealing algorithm is set to 1000°C, the initial cooling rate α0 is set to 0.99, and the minimum cooling rate α min is 0.95, the maximum cooling rate α max is 0.999, the maximum number of iterations n max is 1000.

8. The method according to claim 7, characterized in that In the method, the state matrix Input Matrix 9. A roll-to-roll multi-layer overprint control system based on improved simulated annealing optimization LQR, characterized in that: The system is implemented based on the method described in any one of claims 1 to 8, and the system comprises a detection camera, a PLC controller and a tension sensor; wherein the detection camera is used to obtain an image of the printing substrate after the first layer of printing and the second layer of printing; and the tension sensor is used to obtain a change in tension of the printing substrate; The PLC controller is used to determine the deviation between the first layer printing pattern and the second layer printing pattern according to the printing substrate image acquired by the detection camera, and calculate the control output based on the deviation to compensate for the deviation.

10. Application of the method according to any one of claims 1 to 8 in the field of roll-to-roll multi-layer overprinting technology.

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