A method of flexographic press control

Abstract

The present application relates to the field of control, in particular to a kind of flexographic printing equipment control method and system, specifically, the multi-dimensional state vector of each printing unit of flexographic printing equipment is acquired, and the multi-dimensional error vector formed by the speed deviation of each servo motor;Real-time decoupling compensation matrix is generated;Real-time decoupling compensation matrix is singular value decomposed;Regularized real-time decoupling compensation matrix is obtained by reconstruction;According to the estimated time lag of each control channel, the multi-dimensional error vector is feedforward compensated, and the multi-dimensional error vector after time lag correction is obtained;Initial control increment vector is calculated;Control constraint adjustment factor is calculated based on the minimum singular value recorded, and the control increment constraint ellipsoid is adjusted using the adjustment factor;Determine whether the initial control increment vector is located in the constraint ellipsoid, if not, the initial control increment vector is projected to the ellipsoid surface, control increment is obtained, and control instruction is generated according to control increment and output to each servo driver.

Description

Technical Field

[0001] This application belongs to the field of control, and in particular relates to a control method and system for flexographic printing equipment. Background Technology

[0002] Flexographic printing technology has been widely used in the packaging printing industry due to its advantages such as high printing speed, wide range of printable substrates, and good environmental performance. In high-speed flexographic printing, to ensure print quality, it is necessary to coordinate the control of printing pressure, substrate tension, and the registration accuracy between different color groups. The servo motors of each printing unit, as the main actuators, directly affect registration accuracy with their speed adjustments. Furthermore, these changes are transmitted through the substrate, indirectly causing fluctuations in printing pressure and substrate tension. Conversely, changes in pressure and tension also affect the registration state, creating a complex relationship. When operating conditions such as equipment speed, substrate characteristics, and ink viscosity change, mismatch problems become more severe, leading to decreased performance. Under certain specific conditions, it may exhibit pathological characteristics, generating excessive control output, or even causing system oscillations, endangering equipment safety. Moreover, from sensor detection of state deviations to controller calculation and final motor response, the entire control loop has unavoidable measurement and execution time delays. Especially at high speeds, these time delays reduce the response speed and stability of the control system. Designing an advanced control method that can adaptively adjust and fully consider time delays and constraints is a technical challenge that urgently needs to be addressed to improve the automation level and printing quality of flexographic printing equipment. Summary of the Invention

[0003] To address the aforementioned problems, in the first aspect, the present invention proposes a control method for flexographic printing equipment, comprising the following steps: The system acquires a multidimensional state vector consisting of printing pressure, substrate tension, and color difference of each printing unit in the flexographic printing equipment, as well as a multidimensional error vector consisting of the speed deviation of each servo motor. Based on the detected values ​​of the current printing pressure and substrate tension, the system calculates state weighting coefficients and uses these state weighting coefficients to weight and combine a preset set of reference decoupling matrices to generate a real-time decoupling compensation matrix. The real-time decoupling compensation matrix is ​​subjected to singular value decomposition, and the minimum singular value of this decomposition is recorded. Singular values ​​in the decomposition result that are below a preset suppression threshold are replaced with preset lower limit values, and together with the remaining singular values, they form a regularized diagonal matrix to reconstruct a regularized real-time decoupling compensation matrix. Based on the estimated time delay of each control channel, the multidimensional error vector is fed forward to obtain a time delay-corrected multidimensional error vector. The initial control increment vector is calculated using the regularized real-time decoupling compensation matrix and the time delay-corrected multidimensional error vector. The control constraint adjustment factor is calculated based on the recorded minimum singular value. The control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor is adjusted using the adjustment factor. It is determined whether the initial control increment vector is located inside the constraint ellipsoid. If not, the initial control increment vector is projected onto the surface of the ellipsoid to obtain the control increment. Control commands are generated and output to each servo driver based on the control increment.

[0004] In a second aspect, the present invention proposes a flexographic printing equipment control system, comprising the following modules: The decoupling module is used to acquire a multi-dimensional state vector consisting of printing pressure, substrate tension, and color difference of each printing unit of the flexographic printing equipment, as well as a multi-dimensional error vector consisting of the speed deviation of each servo motor; calculates state weighting coefficients based on the current printing pressure and substrate tension detection values, and generates a real-time decoupling compensation matrix by weighting and combining the preset benchmark decoupling matrix set through the state weighting coefficients. The initial increment calculation module is used to perform singular value decomposition on the real-time decoupling compensation matrix and record the minimum singular value of this decomposition; replace the singular values ​​in the decomposition result that are below a preset suppression threshold with preset lower limit values, and together with the remaining singular values, form a regularized diagonal matrix to reconstruct a regularized real-time decoupling compensation matrix; perform feedforward compensation on the multidimensional error vector according to the estimated time delay of each control channel to obtain a time delay-corrected multidimensional error vector; and calculate the initial control increment vector using the regularized real-time decoupling compensation matrix and the time delay-corrected multidimensional error vector. The control module is used to calculate the control constraint adjustment factor based on the recorded minimum singular value, adjust the control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor using the adjustment factor, determine whether the initial control increment vector is located within the constraint ellipsoid, if not, project the initial control increment vector onto the surface of the ellipsoid to obtain the control increment, and generate control commands to be output to each servo driver based on the control increment.

[0005] Compared with existing technologies, this invention generates a decoupling compensation matrix by real-time detection of printing pressure and substrate tension, improving the decoupling accuracy of the control model under different operating conditions and solving the problem of control performance degradation caused by changes in operating conditions. By regularizing the decoupling matrix, it can suppress excessive control output or oscillations caused by ill-conditioned characteristics under specific operating conditions, enhancing the operational stability of the entire control system. Simultaneously, time-delay feedforward compensation of the error vector overcomes the negative impact of inherent delays in the control loop, improving the system's response speed. This invention constructs a constraint ellipsoid that reflects multi-dimensional constraints such as the maximum torque change rate and maximum power of the motor, and adjusts the constraint boundaries according to the system state to ensure that the output control commands are always within the feasible execution domain of the servo motor. This avoids the coarse processing of traditional saturation limiting methods, making the control action more fully and safely implemented, and guaranteeing product quality under high-speed printing. Attached Figure Description

[0006] Figure 1 A flowchart of the first embodiment; Figure 2 A schematic diagram of the decoupling compensation matrix generation; Figure 3 This is a schematic diagram of singular value regularization. Detailed Implementation

[0007] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards, and corresponding operation entry points are provided for users to choose to authorize or refuse.

[0008] In the first embodiment, the present invention proposes a control method for flexographic printing equipment, such as... Figure 1 As shown, it includes the following steps: Step 1: Obtain the multi-dimensional state vector composed of printing pressure, substrate tension, and color difference of each printing unit of the flexographic printing equipment, as well as the multi-dimensional error vector composed of the speed deviation of each servo motor; calculate the state weighting coefficient based on the current printing pressure and substrate tension detection values, and generate a real-time decoupling compensation matrix by weighting and combining the preset benchmark decoupling matrix set through the state weighting coefficient. Printing pressure is measured in real time by pressure sensors installed at the impression cylinders of each printing unit, substrate tension is measured by tension sensors installed at key locations along the substrate conveying path, and the overprinting marks of each color group are captured by CCD sensors. Image processing is then used to calculate the longitudinal and transverse overprinting color difference values. Simultaneously, the actual rotational speed of each motor is acquired via servo motor encoders and compared with the target rotational speed given by the controller to obtain the speed deviation. In each control cycle, all collected pressure, tension, and overprinting color difference values ​​are combined into a column vector in a predetermined order, forming a multidimensional state vector; the rotational speed deviations of all motors are also combined into a column vector, forming a multidimensional error vector.

[0009] Based on historical experimental data or mechanistic models, several baseline decoupling matrices under typical operating conditions are pre-calculated and stored offline, such as matrices corresponding to low-speed low-tension, high-speed low-tension, and high-speed high-tension operating conditions. During runtime, the currently detected printing pressure and substrate tension are used as inputs. A preset fuzzy membership function or multidimensional linear interpolation algorithm is used to calculate the degree of closeness between the current state and each baseline operating condition, resulting in a set of weighted coefficients summing to 1. These weighted coefficients are then multiplied by their corresponding baseline decoupling matrices and summed to obtain the real-time decoupling compensation matrix.

[0010] Step 2: Perform singular value decomposition on the real-time decoupling compensation matrix and record the minimum singular value of this decomposition; replace the singular values ​​in the decomposition result that are below a preset suppression threshold with preset lower limit values, and together with the remaining singular values, form a regularized diagonal matrix to reconstruct the regularized real-time decoupling compensation matrix; perform feedforward compensation on the multidimensional error vector according to the estimated time delay of each control channel to obtain the time delay corrected multidimensional error vector; use the regularized real-time decoupling compensation matrix and the time delay corrected multidimensional error vector to calculate the initial control increment vector; The singular value decomposition (SVD) algorithm is invoked to decompose the real-time decoupling compensation matrix generated in the previous step into the product of a left singular matrix, a diagonal singular value matrix, and a right singular matrix. The smallest singular value in the diagonal singular value matrix is ​​recorded. Each singular value in the diagonal singular value matrix is ​​iterated over and compared with a preset mode suppression threshold. If a singular value is less than the threshold, its value is modified to a preset lower limit value, preferably a very small positive number; if it is greater than or equal to the threshold, its value remains unchanged. This yields a new regularized diagonal matrix in which all diagonal elements are not lower than the lower limit value. A regularized real-time decoupling compensation matrix is ​​reconstructed by multiplying the original left singular matrix, the new regularized diagonal matrix, and the transpose of the right singular matrix.

[0011] Beforehand, methods such as step response testing are used to identify the state variables affected by the speed adjustment of each servo motor, such as the time required for changes in color difference during printing, i.e., the time delay of each control channel. During control, the rate of change of error is calculated using the multidimensional error vector between the current and previous moments. Then, based on the estimated time delay for each channel, a linear extrapolation prediction is performed on the current error. That is, the current error value is added to the product of the rate of change of error and the time delay to obtain an estimated value of the error after the predicted time delay occurs. Each component in the multidimensional error vector is processed in this way to obtain the time-delay-corrected multidimensional error vector.

[0012] The obtained regularized real-time decoupling compensation matrix is ​​then multiplied by a standard matrix-vector multiplication operation with the obtained time-delay corrected multidimensional error vector. The result is a new column vector, where each element corresponds to the required speed increment of the servo motor, which is the initial control increment vector.

[0013] Step 3: Calculate the control constraint adjustment factor based on the recorded minimum singular value, and use the adjustment factor to adjust the control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor; determine whether the initial control increment vector is located inside the constraint ellipsoid; if not, project the initial control increment vector onto the ellipsoid surface to obtain the control increment, and generate control commands to be output to each servo driver based on the control increment.

[0014] Based on the servo motor parameters, such as the maximum allowable acceleration and the maximum output torque at different speeds, a multi-dimensional basic control increment constraint ellipsoid equation is established. The recorded minimum singular value is substituted into a preset monotonically increasing function, such as a proportional function, to calculate a control constraint adjustment factor ranging from 0 to 1. When the minimum singular value decreases, indicating the system is approaching an ill-conditioned state, this factor also decreases accordingly. The adjustment factor is used to scale the lengths of each half-axis of the basic constraint ellipsoid, forming a dynamically adjustable constraint ellipsoid. The calculated initial control increment vector is substituted into the dynamic constraint ellipsoid equation to determine if it satisfies the inequality. If not, it means the control increment exceeds the current allowable range; in this case, the vector needs to be scaled down proportionally so that it falls exactly on the surface of the ellipsoid; the vector falling on the surface is the control increment. If satisfied, the initial control increment vector is directly used as the control increment. The control increment vector is added to the current speed command of each servo motor to generate a new speed command, which is then sent to the corresponding servo driver for execution.

[0015] In a preferred embodiment, the step of calculating state weighting coefficients based on the detected values ​​of current printing pressure and substrate tension, and then using these state weighting coefficients to weight and combine a preset set of benchmark decoupling matrices to generate a real-time decoupling compensation matrix, includes: The current printing pressure and substrate tension detection values ​​are normalized to the [0,1] interval to obtain the state parameters. and ; Four reference matrices were selected from the reference decoupling matrix set, corresponding to high pressure and high tension, high pressure and low tension, low pressure and high tension, and low pressure and low tension, respectively. , , , The real-time decoupling compensation matrix M is calculated using bilinear interpolation. .

[0016] Assuming the printing press pressure setting range is 100 N / m to 500 N / m, and the substrate tension range is 20 N / m to 100 N / m, if the currently detected printing pressure is 200 N / m and the substrate tension is 80 N / m, then normalization is performed first. The pressure state parameter α is the current value minus the minimum value and then divided by the range, i.e., 0.25. The tension state parameter β is 0.75.

[0017] Preliminary decoupling matrices were obtained through experimental calibration or model identification, corresponding to four extreme operating conditions: high pressure and high tension, high pressure and low tension, low pressure and high tension, and low pressure and low tension. Using bilinear interpolation formulas and with state parameters α and β as weights, the four reference matrices were weighted and summed, as follows: Figure 2As shown, the generated real-time decoupling compensation matrix M can reflect and adapt to changes caused by pressure and tension variations during the printing process in real time.

[0018] In a preferred embodiment, the real-time decoupling compensation matrix is ​​subjected to singular value decomposition, and the minimum singular value of this decomposition is recorded; singular values ​​in the decomposition result that are below a preset suppression threshold are replaced with preset lower limit values, which, together with the remaining singular values, form a regularized diagonal matrix, and the regularized real-time decoupling compensation matrix is ​​reconstructed, including: Singular value decomposition is performed on the real-time decoupling compensation matrix M to obtain ,in Let U be a diagonal singular value matrix, where U and V are orthogonal matrices, and record the minimum singular value of this decomposition; Iterate through all singular values ,like If the value is less than the modal suppression threshold, then the new value is... ,otherwise ; Using the new set of singular values Construct a new diagonal matrix ; pass The reconstructed matrix yields a regularized real-time decoupling compensation matrix.

[0019] To ensure the stability of the control system, the generated real-time decoupling compensation matrix M is further regularized. Assume that matrix M, after singular value decomposition, yields three singular values: 1.2, 0.8, and 0.03. The smallest singular value, 0.03, is recorded, representing the weakest controllable mode of the system. Excessively small singular values ​​indicate that the system is close to singular or ill-conditioned in that corresponding direction; even minor measurement noise or model errors can be amplified, leading to severe fluctuations in the controller output, or even instability.

[0020] To suppress the aforementioned adverse effects, a modal suppression threshold is set, for example, 0.05, and a preset lower limit value, for example, 0.01. All singular values ​​are iterated over, and singular values ​​below the threshold are replaced with the lower limit value. 0.03 is less than 0.05, so it is replaced with 0.01. The new set of singular values ​​becomes 1.2, 0.8, and 0.01, as shown below. Figure 3 As shown, a new diagonal matrix is ​​constructed using the corrected singular values, and this matrix is ​​then combined with the original left and right singular vector matrices to reconstruct a regularized real-time decoupling compensation matrix. This, in turn, limits the gain of the ill-conditioned mode.

[0021] In a preferred embodiment, the step of performing feedforward compensation on the multidimensional error vector based on the estimated time delay of each control channel to obtain the time delay-corrected multidimensional error vector includes: Obtain the estimated time delay of the i-th control channel And the multidimensional error vector e(t) at the current time t; Based on the control increment u(t-1) from the previous time step t-1 and the system model, predict the effects of u(t-1) on the future... Error change over time The predicted change is added to the corresponding component of the current error vector to obtain the time-delay corrected error vector. Its i-th component The calculation is as follows: .

[0022] In complex servo control systems, there is an inherent time delay between the controller issuing a command and the actuator generating a response that is detected by the sensor. The time delays often differ between different control channels; for example, the estimated time delay for a tension control channel is 10 milliseconds, while the time delay for an overlay control channel is 15 milliseconds. If the measured error vector is used directly for control calculations at the current time t, the controller is actually reacting to an outdated system state, which degrades control performance and may even lead to oscillations.

[0023] To compensate for the effects of time delay, based on the control output increment at the previous time t-1 and the system model, the error change that the control action will produce within the corresponding time delay in the future can be predicted. For example, it can be predicted that the error of the tension channel will decrease by 1 unit within the next 10 milliseconds, and the error of the overprinting channel will increase by 0.5 units within the next 15 milliseconds. The predicted changes are then superimposed on the error component measured at the current time to obtain the time-delay-corrected error vector. For example, if the current tension error is 5 units, the corrected error will be 4 units. This overcomes the negative impact of time delay and improves the system's response speed and stability.

[0024] In a preferred embodiment, the step of calculating the initial control increment vector using the regularized real-time decoupling compensation matrix and the time-delay corrected multidimensional error vector includes: The regularized real-time decoupling compensation matrix pseudo-reversal With time-delay corrected multidimensional error vector Multiplying them together yields the initial control increment vector. .

[0025] Ideally, the control increment is multiplied by the system matrix. This should equal the error vector, i.e., solving a system of linear equations. However, direct inversion can be numerically unstable, especially when the system is close to ill-conditioned. This invention further uses the matrix... The pseudo-inverse is multiplied by the time-delay-corrected error vector. Assuming the corrected error vector obtained after the previous steps is 4 units for tension error and -1.5 units for overprinting error, it is multiplied by... The initial control increment vector is obtained by performing matrix-vector multiplication on the pseudo-inverse matrix. For example, the calculation result is a vector with components of 0.5 and 0.2. Each component of this vector corresponds to a control adjustment value for a servo motor, which is the theoretically optimal control adjustment scheme under the current operating conditions after eliminating coupling effects and compensating for time delays.

[0026] In a preferred embodiment, calculating the control constraint adjustment factor based on the recorded minimum singular value includes: Determine the baseline singular values and sensitivity parameter k; The control constraint adjustment factor is calculated using an exponential function. : .

[0027] When in a near-singular pathological condition, i.e., the minimum singularity... When the value is very small, the controller should be more conservative to ensure stability. This is achieved by controlling the constraint adjustment factor. This allows for adjustment of the control output amplitude. For example, a baseline singular value representing the system's health status. The value is 0.1, and the sensitivity parameter k is 0.5. Assume the minimum singular value recorded is... The value is 0.03. The ratio of the baseline value to the current minimum value is approximately 3.33. This ratio reflects the degree of ill-conditioning of the current system state compared to the ideal state. The adjustment factor is calculated using the above exponential function. Calculated The value is approximately 0.32.

[0028] Furthermore, during the equipment commissioning phase, the equipment is operated at multiple stable and representative operating points. At each operating point, a small perturbation is applied and data is collected to identify the local linear model of the system, thus obtaining the decoupling compensation matrix under that operating condition. Singular value decomposition is then performed on the matrix under representative operating conditions to obtain a series of minimum singular values. A benchmark is selected from the smallest singular values ​​representing the state of a healthy system; for example, their average, median, or value under a most commonly used operating condition can be used. The k value needs to minimize the impact on normal control performance while ensuring system safety and stability, and is determined through verification and fine-tuning on actual equipment.

[0029] In a preferred embodiment, adjusting the control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor using the adjustment factor includes: Obtain the semi-axis length vector of the defined datum constraint ellipsoid ,in Each constraint corresponds to a servo motor; Adjust the control constraint factor with reference half-axis length vector Multiplying them together yields the adjusted half-axis length vector. , generated by Defined constraint ellipsoid.

[0030] Each servo motor's control increment is constrained by limits, such as the maximum permissible rate of torque change and peak power. These multi-dimensional constraints collectively define a permissible operating region in the control increment space. This permissible operating region is represented by a baseline constraint ellipsoid, where the lengths of each half-axis are represented by a vector A, where each component, such as... and These correspond to the maximum control increments of the first and second motors under normal operating conditions, respectively. For example, the components of vector A can be 1 and 1.2, representing the respective reference constraint boundaries of the two motors.

[0031] Using the control constraint adjustment factor calculated in the previous step The value is 0.32, which adjusts the size of the constraint ellipsoid. The factor is... Multiplying by each component of the reference semi-axis length vector A yields a new semi-axis length vector. The calculation result is The components are 0.32 and 0.384. The new vector The constraint ellipsoid is designed for a smaller volume. When the system is under sensitive conditions, the controller is required to operate within a smaller safety margin, with its maximum permissible control increment reduced to 32% of the normal value.

[0032] In a preferred embodiment, determining whether the initial control increment vector lies within the constraint ellipsoid, and if not, projecting the initial control increment vector onto the ellipsoid surface to obtain the control increment, includes: Obtain the initial control increment vector The i-th component is ; Calculate the scalar used to determine the location. ; like Then control the increment ; like Then control the increment .

[0033] After calculating the initial control increment vector Then, it must be ensured that the control command does not exceed the real-time safety boundary defined by the constraint ellipsoid. Assume the components of the initial control increment vector are 0.5 and 0.2, while the semi-axis length components of the constraint ellipsoid are 0.32 and 0.384. To determine if the vector is inside the ellipsoid, a scalar value S is calculated, where S is approximately 2.71 > 1, indicating that the initial control increment vector is outside the dynamic constraint ellipsoid and is an unexecutable command. To obtain a final control command that is both effective and safe, this out-of-bounds vector is projected back onto the surface of the ellipsoid. Control Increment Vector It is the initial vector It was shortened to approximately 60.6% of its original length. Thus, without violating the current system stability constraints, the maximum error correction was achieved.

[0034] In the second embodiment, the present invention proposes a flexographic printing equipment control system, comprising the following modules: The decoupling module is used to acquire a multi-dimensional state vector consisting of printing pressure, substrate tension, and color difference of each printing unit of the flexographic printing equipment, as well as a multi-dimensional error vector consisting of the speed deviation of each servo motor; calculates state weighting coefficients based on the current printing pressure and substrate tension detection values, and generates a real-time decoupling compensation matrix by weighting and combining the preset benchmark decoupling matrix set through the state weighting coefficients. The initial increment calculation module is used to perform singular value decomposition on the real-time decoupling compensation matrix and record the minimum singular value of this decomposition; replace the singular values ​​in the decomposition result that are below a preset suppression threshold with preset lower limit values, and together with the remaining singular values, form a regularized diagonal matrix to reconstruct a regularized real-time decoupling compensation matrix; perform feedforward compensation on the multidimensional error vector according to the estimated time delay of each control channel to obtain a time delay-corrected multidimensional error vector; and calculate the initial control increment vector using the regularized real-time decoupling compensation matrix and the time delay-corrected multidimensional error vector. The control module is used to calculate the control constraint adjustment factor based on the recorded minimum singular value, adjust the control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor using the adjustment factor, determine whether the initial control increment vector is located within the constraint ellipsoid, if not, project the initial control increment vector onto the surface of the ellipsoid to obtain the control increment, and generate control commands to be output to each servo driver based on the control increment.

[0035] In a preferred embodiment, the step of calculating state weighting coefficients based on the detected values ​​of current printing pressure and substrate tension, and then using these state weighting coefficients to weight and combine a preset set of benchmark decoupling matrices to generate a real-time decoupling compensation matrix, includes: The current printing pressure and substrate tension detection values ​​are normalized to the [0,1] interval to obtain the state parameters. and ; Four reference matrices were selected from the reference decoupling matrix set, corresponding to high pressure and high tension, high pressure and low tension, low pressure and high tension, and low pressure and low tension, respectively. , , , The real-time decoupling compensation matrix M is calculated using bilinear interpolation. .

[0036] In a preferred embodiment, the real-time decoupling compensation matrix is ​​subjected to singular value decomposition, and the minimum singular value of this decomposition is recorded; singular values ​​in the decomposition result that are below a preset suppression threshold are replaced with preset lower limit values, which, together with the remaining singular values, form a regularized diagonal matrix, and the regularized real-time decoupling compensation matrix is ​​reconstructed, including: Singular value decomposition is performed on the real-time decoupling compensation matrix M to obtain ,in Let U be a diagonal singular value matrix, where U and V are orthogonal matrices, and record the minimum singular value of this decomposition; Iterate through all singular values ,like If the value is less than the modal suppression threshold, then the new value is... ,otherwise ; Using the new set of singular values Construct a new diagonal matrix ; pass The reconstructed matrix yields a regularized real-time decoupling compensation matrix.

[0037] In a preferred embodiment, the step of performing feedforward compensation on the multidimensional error vector based on the estimated time delay of each control channel to obtain the time delay-corrected multidimensional error vector includes: Obtain the estimated time delay of the i-th control channel And the multidimensional error vector e(t) at the current time t; Based on the control increment u(t-1) from the previous time step t-1 and the system model, predict the effects of u(t-1) on the future... Error change over time The predicted change is added to the corresponding component of the current error vector to obtain the time-delay corrected error vector. Its i-th component The calculation is as follows: .

[0038] In a preferred embodiment, the step of calculating the initial control increment vector using the regularized real-time decoupling compensation matrix and the time-delay corrected multidimensional error vector includes: The regularized real-time decoupling compensation matrix pseudo-reversal With time-delay corrected multidimensional error vector Multiplying them together yields the initial control increment vector.

[0039] In a preferred embodiment, calculating the control constraint adjustment factor based on the recorded minimum singular value includes: Determine the baseline singular values and sensitivity parameter k; The control constraint adjustment factor is calculated using an exponential function. : .

[0040] In a preferred embodiment, adjusting the control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor using the adjustment factor includes: Obtain the semi-axis length vector of the defined datum constraint ellipsoid , among which Constraints corresponding to each servo motor; Adjust the control constraint factor with reference half-axis length vector Multiplying them together yields the adjusted half-axis length vector. , generated by Defined constraint ellipsoid.

[0041] In a preferred embodiment, determining whether the initial control increment vector lies within the constraint ellipsoid, and if not, projecting the initial control increment vector onto the ellipsoid surface to obtain the control increment, includes: Obtain the initial control increment vector The i-th component is ; Calculate the scalar used to determine the location. ; like Then control the increment ; like Then control the increment .

[0042] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, compact disc read-only memory (CD-ROM), optical storage, etc.) containing computer-usable program code.

[0043] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0044] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A control method for flexographic printing equipment, characterized in that, Includes the following steps: The multidimensional state vector consisting of printing pressure, substrate tension, and registration color difference of each printing unit of the flexographic printing equipment, as well as the multidimensional error vector consisting of the speed deviation of each servo motor, are obtained. Based on the detected values ​​of current printing pressure and substrate tension, a state weighting coefficient is calculated. The preset benchmark decoupling matrix set is then weighted and combined using the state weighting coefficient to generate a real-time decoupling compensation matrix. Perform singular value decomposition on the real-time decoupling compensation matrix and record the minimum singular value of this decomposition; The singular values ​​in the decomposition results that are below the preset suppression threshold are replaced with preset lower limit values, and together with the remaining singular values, they form a regularized diagonal matrix, and the regularized real-time decoupling compensation matrix is ​​reconstructed; according to the estimated time delay of each control channel, the multidimensional error vector is fed forward to obtain the time delay corrected multidimensional error vector. The initial control increment vector is calculated using the regularized real-time decoupling compensation matrix and the time-delay corrected multidimensional error vector. The control constraint adjustment factor is calculated based on the recorded minimum singular value. The control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor is adjusted using the adjustment factor. It is determined whether the initial control increment vector is located inside the constraint ellipsoid. If not, the initial control increment vector is projected onto the surface of the ellipsoid to obtain the control increment. Control commands are generated and output to each servo driver based on the control increment.

2. The method according to claim 1, characterized in that, The process involves calculating state weighting coefficients based on the detected values ​​of current printing pressure and substrate tension, and then using these state weighting coefficients to weight and combine a preset set of benchmark decoupling matrices to generate a real-time decoupling compensation matrix. This includes: The current printing pressure and substrate tension detection values ​​are normalized to the [0,1] interval to obtain the state parameters. and ; Four reference matrices were selected from the reference decoupling matrix set, corresponding to high pressure and high tension, high pressure and low tension, low pressure and high tension, and low pressure and low tension, respectively. , , , The real-time decoupling compensation matrix M is calculated using bilinear interpolation. 。 3. The method according to claim 1, characterized in that, The process involves performing singular value decomposition on the real-time decoupling compensation matrix and recording the minimum singular value in this decomposition. Singular values ​​in the decomposition result that are below a preset suppression threshold are replaced with preset lower limits, and these lower limits, together with the remaining singular values, form a regularized diagonal matrix. This reconstructs the regularized real-time decoupling compensation matrix, including: Singular value decomposition is performed on the real-time decoupling compensation matrix M to obtain ,in Let U be a diagonal singular value matrix, where U and V are orthogonal matrices, and record the minimum singular value of this decomposition; Iterate through all singular values ,like If the value is less than the modal suppression threshold, then the new value is... ,otherwise ; Using the new set of singular values Construct a new diagonal matrix ; pass The reconstructed matrix yields a regularized real-time decoupling compensation matrix.

4. The method according to claim 1, characterized in that, The step of performing feedforward compensation on the multidimensional error vector based on the estimated time delay of each control channel to obtain the time delay-corrected multidimensional error vector includes: Obtain the estimated time delay of the i-th control channel And the multidimensional error vector e(t) at the current time t; Based on the control increment u(t-1) from the previous time step t-1 and the system model, predict the effects of u(t-1) on the future... Error change over time The predicted change is added to the corresponding component of the current error vector to obtain the time-delay corrected error vector. Its i-th component The calculation is as follows: .

5. The method according to claim 1, characterized in that, The initial control increment vector is calculated by using the regularized real-time decoupling compensation matrix and the time-delay corrected multidimensional error vector, including: The regularized real-time decoupling compensation matrix pseudo-reversal With time-delay corrected multidimensional error vector Multiplying them together yields the initial control increment vector. .

6. The method according to claim 1, characterized in that, The calculation of the control constraint adjustment factor based on the recorded minimum singular value includes: Determine the baseline singular values and sensitivity parameter k; The control constraint adjustment factor is calculated using an exponential function. : 。 7. The method according to claim 6, characterized in that, The adjustment of the control increment constraint ellipsoid defined by the maximum torque change rate and maximum power of the motor using the adjustment factor includes: Obtain the semi-axis length vector of the defined datum constraint ellipsoid , among which Constraints corresponding to each servo motor; Adjust the control constraint factor with reference half-axis length vector Multiplying them together yields the adjusted half-axis length vector. , generated by Defined constraint ellipsoid.

8. The method according to claim 7, characterized in that, The step of determining whether the initial control increment vector lies within the constraint ellipsoid, and if not, projecting the initial control increment vector onto the ellipsoid surface to obtain the control increment, includes: Obtain the initial control increment vector The i-th component is ; Calculate the scalar used to determine the location. ; like Then control the increment ; like Then control the increment .

Images