A paper box printing and forming linkage industrial control system

Abstract

The present application relates to the technical fields of industrial program control and multi-process linkage control, in particular to a carton printing and forming linkage industrial control system. The system establishes a workpiece identification for each paperboard, acquires a paper feeding reference phase, printing process phase observation and forming process phase observation, and constructs a paperboard space-time phase chain according to process transmission distance, running speed and execution delay. According to the residual error between the theoretical arrival phase and the actual response phase and the process influence matrix, the phase deviation is decomposed into paper feeding slip component, process transmission component and local execution lag component. The segmented compensation sequence is generated in combination with the remaining process of the paperboard, the correctable range and the relative position constraint of the printing reference and the forming reference, and the process influence matrix is updated according to the downstream response phase. The present application can reduce repeated compensation and reverse cancellation, and maintain the phase consistency between the printing position and the creasing, slotting and folding references.

Description

Technical Field

[0001] This invention relates to the field of industrial program control and multi-process linkage control technology, specifically a linkage industrial control system for carton printing and forming. Background Technology

[0002] A carton printing and forming production line typically consists of continuous processes such as paper feeding, printing, slotting, creasing, folding, and joining. Each process receives encoder phase, drive speed, action trigger time, and operating status through an industrial control system, and controls the corresponding execution process according to a pre-set process formula. Existing control methods often employ a structure of main shaft synchronization plus local closed-loop adjustment, using the paper feeding shaft or a common virtual axis as the cycle time reference. The printing process adjusts the printing action based on the printing plate phase and the arrival signal of the cardboard, while the forming process triggers slotting, creasing, or folding actions based on the theoretical conveying distance and the arrival time. When the actual phase of a process deviates from the target phase, the controller typically corrects the servo position, action advance, or local speed within the current process to bring the phase difference measured in this process back to the allowable range. This approach can maintain basic synchronization at a single workstation, but the cardboard position saved by each process is usually represented by the workstation coordinates or the overall line cycle time, lacking cross-process status records continuously bound to the same cardboard. Therefore, it is difficult to reflect the cumulative position changes of the cardboard in each conveying section after it enters from the paper feeding end.

[0003] In relatively similar linkage control schemes, the controller calculates the theoretical time for the paperboard to reach the next process based on the fixed distance between adjacent processes, the current linear speed, and the preset execution delay, and corrects the calculated value using the station detection results. Some schemes also transmit the registration deviation detected upstream to the downstream controller, allowing the downstream process to adjust the phase or action advance according to a fixed ratio; or, based on the overall line error, simultaneously implement speed compensation for multiple drive shafts. Such schemes typically treat observed deviations directly as errors generated at the current station or adjacent conveyor sections, without decomposing the sources of paper feeding slippage, inter-process transmission deviations, and local execution lags. When the operating speed changes, paperboard specifications are switched, drive gaps are released, or a response delay occurs in a certain execution process, different causes may result in phase residuals in the same direction, or residuals in opposite directions in subsequent processes. Since each process corrects independently based on its own measurement results, the same deviation may be compensated repeatedly, and compensations already implemented may continue to be treated as new errors by subsequent processes, resulting in a lack of unified constraints between upstream and downstream corrections.

[0004] Industrial control systems cannot establish a unified phase correlation across the feeding, printing, and forming processes using the same cardboard as an object, nor can they determine the location of errors and their propagation components based on cross-process phase residuals. When slippage, speed fluctuations, or execution lag occur during cardboard conveying, the controller can only acquire local deviations at each station, making it difficult to determine whether the current deviation is a continuation of upstream errors, a new deviation formed during inter-process transmission, or a local deviation caused by the execution response of this process. Consequently, when each process adjusts speed, phase, or action advance according to local closed loops, it is easy to repeatedly correct errors from the same source, or to use compensation in opposite directions to offset the results of previous control. Although the total phase deviation may decrease temporarily at individual stations, the relative position between the printing reference and the crease, slotting, and folding references will still drift as the process progresses. Furthermore, the controller cannot reverse the error propagation relationship based on the actual downstream response, making it difficult to form a stable cross-process closed loop. Summary of the Invention

[0005] The purpose of this invention is to provide an industrial control system for carton printing and forming linkage, which can solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A carton printing and forming linkage industrial control system includes an industrial controller. The industrial controller acquires the workpiece identification, paper feeding reference phase, printing process phase observation and forming process phase observation for each cardboard, and establishes a cardboard spatiotemporal phase chain based on the process transmission distance, real-time running speed and execution delay. Based on the residual between the theoretical arrival phase and the actual response phase and the preset process influence matrix, the phase deviation is decomposed into paper feeding slip component, inter-process transmission component and local execution lag component. Based on the remaining processes of the paperboard, the correctable range of each process, and the relative positional constraints of the printing reference and the forming reference, a segmented compensation sequence is generated, and speed fine-tuning amount, phase correction amount, or action advance amount is issued to the corresponding process. The process influence matrix is ​​updated according to the downstream response phase.

[0007] Preferably, the spatiotemporal phase chain takes the paper feeding reference phase as the starting node and establishes phase state nodes corresponding to the paper feeding, printing and forming processes in sequence for the same workpiece identifier; Each phase state node records the theoretical entry time, actual entry time, theoretical departure time, actual departure time, transmission distance between nodes, and velocity integral value of adjacent nodes; The industrial controller recursively calculates the theoretical arrival phase of the next phase state node based on the actual departure phase of the previous phase state node, the velocity integral value between nodes, and the execution delay of the next process, and writes the actual response phase returned by each process into the corresponding phase state node.

[0008] Preferably, the rows of the process influence matrix correspond to paper feeding slippage, inter-process transfer, and local execution lag, respectively, and the columns correspond to the residual characteristics of each phase state node. The industrial controller extracts the sign change, duration interval, propagation delay, and response slope as a function of operating speed of the residuals of adjacent phase state nodes to form a residual propagation vector. Under the constraint that the sum of all deviation components equals the total phase deviation and that the local execution lag component only acts on the corresponding process, it solves for each deviation component and its source process.

[0009] Preferably, the segmented compensation sequence includes a compensation process, compensation method, compensation direction, compensation amount, and execution window bound to the same workpiece identifier; The industrial controller establishes a feasible compensation domain based on the allowable phase change range of each remaining process, the current execution status, and the arrival time sequence. Using the relative positional deviation between the printing reference and the forming reference, the continuity of compensation changes in each process, and the consistency of cumulative compensation for the same paperboard as joint constraints, the total compensation amount is allocated as the speed fine-tuning amount, the phase correction amount, and the action advance amount, and is issued sequentially according to the execution window.

[0010] Preferably, when any phase state node lacks an actual entry phase or the actual departure phase, the industrial controller selects the nearest effective phase state node upstream of the missing node and the earliest effective phase state node downstream of the same workpiece identifier as bidirectional anchor points, performs delayed inversion of the missing phase based on the speed integral value between the two anchor points, the theoretical transmission distance, and the intermediate process, and writes a credibility flag for the inversion result. When the corresponding actual phase is subsequently obtained, the difference between the actual phase and the inverted phase is used to correct the equivalent values ​​of the transmission distance and execution delay of adjacent nodes.

[0011] Preferably, the industrial controller groups the historical phase state nodes according to cardboard specifications, operating speed range and process combination, and selects cardboard records with similar upstream residual characteristics and different downstream control actions within each group to form a paired sample. Based on the downstream residual differences of the paired samples, the independent response components corresponding to each control action are extracted, and the matrix elements in the process influence matrix corresponding to the source process, propagation path and target phase state node are corrected with the independent response components, while keeping the matrix elements that have not been paired and verified unchanged.

[0012] Preferably, the industrial controller establishes a compensation ledger for each workpiece identifier, and the compensation ledger sequentially records the source deviation component, the action process, the compensation direction, the compensation amount, and the corresponding phase state node for which compensation has been performed; When calculating subsequent phase deviations, the compensation contribution that has not yet been completed and transferred across processes in the compensation ledger is deducted from the total phase deviation, and the net residual after deduction is used to update the segmented compensation sequence. When different processes generate candidate compensations with opposite directions for the same source deviation component, the candidate compensation with the same direction as the net residual and the earliest execution window is retained.

[0013] Preferably, the industrial controller establishes non-overlapping compensation execution windows based on the arrival time of each remaining process, and divides each execution window into an entry segment, a stabilization segment, and an exit segment; The speed fine-tuning amount is allocated only in the entry section and the exit section according to the continuous change constraint between adjacent cardboard sections; the phase correction amount remains consistent with the direction of the corresponding deviation component in the stable section; and the action advance amount is only written to the forming action that has not yet been triggered. When any execution window overlaps with the latest correctable time of the next process, the unexecuted compensation amount is transferred to the subsequent execution window that is still within the compensation feasible region.

[0014] Preferably, the industrial controller stores two sets of process influence matrices corresponding to the stable operating state and the working condition switching state for the same cardboard specification, and determines the matrix calling state based on the topological consistency between the residual propagation vector sequences formed by continuous workpiece identifications. In the aforementioned operating condition switching state, only the cardboard records that have completed upstream residual pairing, downstream response closure, and no compensation window shift have been used to update the corresponding matrix elements. After the changes in the source process judgment result and the propagation delay sequence converge simultaneously, the updated matrix elements are merged into the process influence matrix corresponding to the stable operating state.

[0015] Preferably, after the cardboard leaves any compensated process, the industrial controller writes the corresponding actual response phase in reverse along the spatiotemporal phase chain to the completed phase state node, and matches the remaining deviation calculated in reverse with the unrecovered compensation contribution in the compensation ledger item by item. When the direction of the remaining deviation is opposite to the direction of the unrecovered compensation, or when the contribution of the unrecovered compensation has been absorbed by the previous execution window, the corresponding compensation item in the subsequent execution window is cancelled, and the segmented compensation sequence is regenerated with the updated net residual, process influence matrix, and correctable range of each remaining process.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By establishing a workpiece identifier for each cardboard and writing the paper feeding reference phase, printing process phase observation, and forming process phase observation into the same spatiotemporal phase chain, the industrial control system can continuously represent the theoretical arrival phase and actual response phase of the cardboard in each process under a unified workpiece coordinate system. Combining the recursive relationship formed by process transfer distance, real-time running speed, and execution delay, the residuals of adjacent state nodes can be organized into residual propagation vectors with propagation direction and propagation delay. Then, the process influence matrix is ​​used to decompose the total phase deviation into paper feeding slip component, inter-process transfer component, and local execution lag component. The segmented compensation sequence allocates speed fine-tuning, phase correction, and action advance based on the processes the cardboard has not yet passed through, the correctable range of each process, and the relative positional constraints between the printing reference and the forming reference, ensuring that deviations from different sources are processed in the corresponding processes and execution windows. The downstream actual response phase continues to be used to update the process influence matrix, thereby reducing the situation where the same deviation is identified and compensated multiple times, maintaining the continuous correspondence between the printing position and the subsequent forming reference.

[0017] 2. The bidirectional anchor point inversion mechanism in the spatiotemporal phase chain can recover missing phases when local phase data is missing, using upstream effective nodes, downstream effective nodes, velocity integral values, transmission distances, and execution delays. After the actual phase is added, the equivalent transmission distance and equivalent execution delay are corrected, preventing single-point data interruptions from causing discontinuity in subsequent phase recursion. Paired samples constructed according to cardboard specifications, operating speed ranges, and process combinations can separate independent response components corresponding to different control actions under similar upstream residual conditions, limiting the update of the process influence matrix to the propagation relationship verified through pairing. The compensation ledger records executed compensations and compensation contributions that have not yet been transmitted. Combined with non-overlapping execution windows, it continuously verifies net residuals and unrecovered compensations. Influence matrices are stored separately for stable operating states and operating condition switching states, and the calling state is selected based on the topological consistency of the residual propagation vector. After the cardboard leaves the compensated process, the actual response phase is written in reverse along the spatiotemporal phase chain, and subsequent unexecuted and absorbed compensation items are subsequently canceled, allowing the compensation sequence to be regenerated with the actual control results. Attached Figure Description

[0018] Figure 1 This is a flowchart of the overall control process of the carton printing and forming linkage industrial control system. Figure 2 A graph showing the comparison between the theoretical arrival phase and the actual response phase; Figure 3 Flowchart for constructing the spatiotemporal phase chain of cardboard and decomposing the sources of deviation; Figure 4 Trend chart for net residuals in the accounting books; Figure 5 This is a topological consistency graph for residual propagation. Detailed Implementation

[0019] In one embodiment, please refer to Figure 1 The carton printing and forming linkage industrial control system includes an industrial controller. The industrial controller acquires the workpiece identifier, paper feeding reference phase, printing process phase observation, and forming process phase observation for each cardboard. It establishes a cardboard spatiotemporal phase chain based on process transmission distance, real-time running speed, and execution delay. Based on the residual between the theoretical arrival phase and the actual response phase and the preset process influence matrix, the phase deviation is decomposed into paper feeding slip component, inter-process transmission component, and local execution lag component. Based on the remaining processes of the cardboard, the correctable range of each process, and the relative position constraints of the printing reference and forming reference, a segmented compensation sequence is generated, and speed fine-tuning amount, phase correction amount, or action advance amount is issued to the corresponding process. The process influence matrix is ​​updated according to the downstream response phase. The industrial controller associates the paper feeding reference state, printing response state, and forming response state with the same workpiece identifier. The process influence matrix records the propagation relationship from different error sources to each phase observation position. The segmented compensation sequence limits the cardboard, process, time range, and compensation type corresponding to the compensation, so that the paper feeding, printing, and forming processes form a workpiece-level closed loop.

[0020] In this embodiment, the workpiece identifier is generated when the cardboard enters the paper feeding process. The workpiece identifier can be formed by combining the current production batch identifier, sequence number, and entry time. The industrial controller does not rely on the encoding form of the workpiece identifier itself, but requires that each workpiece identifier remain unique before the cardboard leaves the entire linkage production line. The paper feeding reference phase represents the starting position of the leading edge of the cardboard relative to the paper feeding control cycle. The phase observations of the printing process include the arrival phase when the cardboard enters the printing process, the actual response phase of the printing action, and the departure phase when the cardboard leaves the printing process. The phase observations of the forming process include the arrival phase when the cardboard enters the forming process, the actual response phase of the forming action, and the departure phase when the cardboard leaves the forming process. The real-time running speed is associated with the workpiece identifier in the form of a time sequence. The execution delay is recorded according to the process type as the time difference from the issuance of the control command to the corresponding action entering a stable response state. The process transmission distance is represented by the equivalent path length between the control reference points of adjacent processes. The industrial controller uses the above data to arrange the discrete observation results of the same cardboard into a phase state sequence with process sequence and time sequence.

[0021] Specifically, after the cardboard leaves the previous process, the industrial controller calculates the theoretical arrival phase based on the actual departure phase of the previous process, the speed integral of the cardboard between adjacent processes, and the execution delay of the next process. The theoretical arrival phase is determined using the following formula: ; in, This represents the theoretical phase at which the cardboard with workpiece identification k arrives at the i-th process. This indicates the actual phase at which the same cardboard leaves the previous process. This represents the rate of phase change in the control cycle corresponding to the cardboard. This represents the equivalent transmission distance from the control reference point of the previous process to the control reference point of the i-th process. This represents the average running speed of the same cardboard over the equivalent conveying distance. This represents the equivalent execution delay of process i. This means mapping the calculation results to a unified phase period; for example, when the actual departure phase of the current process is 0.30, the phase change rate is 5, and the sum of the equivalent transmission time and execution delay is 0.12, the theoretical arrival phase is 0.90. If the actual arrival phase is 0.96, then the corresponding arrival residual is 0.06. The industrial controller writes the residual into the phase state node of the i-th process and retains its direction.

[0022] Please refer to Figure 2 , Figure 2 The horizontal axis represents the process nodes that the same paperboard passes through sequentially along the production line, including paper feeding, printing, slotting, creasing, folding and joining, and paper collection; the vertical axis represents the unified cycle phase, which is used to convert the arrival status and action response status of different processes to the same phase scale. Figure 2 The solid black line represents the theoretical phase, recursively derived from the actual departure phase of the previous node, the equivalent transmission distance between nodes, the integral of the cardboard running speed, and the execution delay of the next process. The dashed gray line represents the actual response phase returned by each process. The dotted line represents the residual formed between the theoretical value and the response value. Two horizontal reference lines are used to help determine whether the residual has entered the range of interest.

[0023] from Figure 2 As can be seen, the theoretical phase curve shows a continuous upward trend as the process progresses, indicating that the paperboard state under the same workpiece identification can maintain an orderly progression along the feeding to receiving direction. The actual response curve generally follows the theoretical curve, remaining close to the printing, slotting, and folding joint nodes. Near the creasing node, it shows a more significant drop below the theoretical progressive value, suggesting that there may be a local action response delay or speed integral deviation in the intermediate conveying section at this node. The residual curve does not form a large reverse oscillation near the zero axis, indicating that this set of data is suitable for further residual source decomposition, rather than directly attributing the single-point difference as a whole to the current process.

[0024] During the continuous operation of the cardboard, the industrial controller maintains a spatiotemporal phase chain for each workpiece identifier, without replacing the state of a single cardboard with the instantaneous cycle time of the entire line. When the upstream speed changes briefly, the speed change is entered into the theoretical arrival phase calculation through the integral result of the corresponding cardboard in the conveying interval, and will not be directly propagated to other cardboards that have not yet entered the conveying interval. When the printing or forming action produces a local response delay, the delay is only written into the actual response phase and departure phase of the corresponding process. This allows speed disturbances, conveying disturbances, and execution disturbances to retain their time positions for subsequent decomposition. After receiving the downstream phase observation, the industrial controller matches the actual response phase with the theoretical arrival phase corresponding to the same workpiece identifier, avoiding the incorrect writing of the observation of the later cardboard into the record of the previous cardboard due to the change in the spacing between adjacent cardboards. At the same time, the observations that exceed the reasonable process sequence are temporarily stored, and the link connection is completed after the preceding node is closed.

[0025] In this embodiment, the residual between the theoretical arrival phase and the actual response phase is not directly equivalent to the current process error. The industrial controller forms a residual vector from the residuals of continuous phase state nodes and forms an error propagation characteristic based on the location of residual occurrence, residual direction, duration interval, propagation delay, and the response relationship of residual with running speed. The paper feeding slip component represents the phase deviation that has been formed before the paperboard enters the printing process and continues to propagate in the same direction in subsequent nodes. The inter-process transfer component represents the phase deviation that is added between adjacent processes after the paperboard leaves a certain process. The local execution lag component represents the phase deviation formed by the change in the response time of the corresponding action after the paperboard arrives at the process and does not propagate in the reverse direction to the completed process. The industrial controller uses the process influence matrix to map the above error sources to each phase state node, so that the same observed residual can be interpreted in combination according to the propagation trajectory of different sources.

[0026] The error components are determined through a constrained residual fitting process, and the calculation method used is as follows:

[0027]

[0028]

[0029] in, Let represent the error component vector for workpiece identified as k. The elements in the vector correspond to the paper feeding slip component, the inter-process transfer component, and the local execution lag component of each process, respectively. Let x represent the column vector to be optimized. This represents the influence matrix of the currently invoked process. This represents the residual vector of each phase state node. The weight matrix is ​​formed based on observation completeness and phase reliability, and D represents the difference matrix that restricts abrupt changes in adjacent propagation components. The constraint coefficients represent the balance between residual fitting and propagation continuity. This means that the combined value of all components at the final observation position equals the total final residual. This indicates that a process that has not yet occurred cannot generate a local execution lag component. For example, if the residual vectors are 0.04, 0.07, and 0.09 respectively, and the matrix solution yields a paper feeding slip component of 0.04, a printing to forming transfer component of 0.03, and a forming local execution lag component of 0.02, the industrial controller retains the source location and propagation range of the three components respectively, and does not include 0.09 as a whole in the forming process.

[0030] Furthermore, the initial value of the process influence matrix is ​​constructed from stable production records. The industrial controller selects paperboard records with complete phase states and no compensation transfers. The paper feeding end residual, the new residual of adjacent processes, and the local action response difference are respectively used as candidate source quantities. The residual of each observation node is used as the result quantity. The initial influence coefficient is obtained by regression calculation with limited propagation direction. The paper feeding source can only act on the observation position after the paper feeding node. The source of any process transfer can only act on the observation position after the corresponding transfer section. The source of local execution lag can only act on the response node of this process and its subsequent departure node. The propagation direction restriction keeps the position of no physical propagation path in the matrix at 0. When solving online, the industrial controller only calls the matrix data that matches the current paperboard specifications, operating status, and process combination, avoiding the direct application of error propagation relationships under other operating conditions to the current paperboard.

[0031] In this embodiment, the segmented compensation sequence is bound to the workpiece identifier. Each compensation item in the sequence records at least the source deviation component, compensation process, compensation method, compensation direction, compensation amount, start time, end time, and revocable state. The industrial controller determines the set of remaining processes based on the processes that the paperboard has completed, and determines the correctable range from the current control state of each remaining process, whether the action has been triggered, and the allowable phase change range. For paperboard that has not yet entered the printing process, the paper feeding slip component can be allocated as the paper feeding speed fine-tuning amount or the printing phase correction amount. For paperboard that has completed printing but has not yet triggered the forming action, the still propagating transmission component can be allocated as the forming action advance amount. For paperboard that has triggered the forming action, no new advance amount is written to the action, but the unexecuted compensation is retained as the basis for subsequent error model updates.

[0032] The speed fine-tuning amount, phase correction amount, and action advance amount are obtained through joint constraint calculation, and the calculation form is as follows: ; in, This represents the compensation vector for the corresponding cardboard, where u represents the compensation vector, and the vector elements represent the speed fine-tuning amount, printing phase correction amount, and forming action advance amount, respectively. This represents the feasible compensation region formed by the remaining steps, the allowable phase change range, the action trigger state, and the latest correctable time. This represents the residual between the printing reference and the paperboard reference. denoted by , where represents the residual between the forming reference and the cardboard reference, and b represents the mapping vector of different compensation amounts to the relative position of the printed forming. Let G denote the transpose, and let G denote the matrix constraining the continuity of changes in adjacent compensation terms. This represents the compensation vector that was planned in the previous control cycle for the same cardboard. , and This indicates a preset weight; for example, if the printing residual is 0.05, the molding residual is 0.01, and the molding action has not yet been triggered, the solution result can allocate 0.02 to the printing phase correction and 0.02 to the molding action advance, so that the correction of the two processes revolves around the same relative position constraint.

[0033] When the industrial controller issues compensation amounts to the corresponding process, it does not overwrite the existing control state with a single abrupt command. Instead, it determines the timing of writing based on a segmented compensation sequence. The speed fine-tuning amount is written before the cardboard enters the target conveying interval and is withdrawn after the cardboard leaves. The printing phase correction amount is written when the printing action allows adjustment and has not yet entered the irreversible response stage. The forming action advance amount is written when the forming action triggering condition has not yet been met. Once a compensation item is executed, the actual issued value and execution completion mark are recorded. When subsequent nodes calculate the theoretical phase, they read the actual issued value instead of the planned value to avoid inconsistencies between planned and actual compensation due to limited control output or execution interruption. If a compensation item fails to be completed within the execution window, the industrial controller will re-include the unexecuted part in the net residual instead of considering it as an eliminated error.

[0034] When updating the process influence matrix based on the downstream response phase, the industrial controller compares the actual response phase with the predicted response phase before compensation, identifies the independent response direction and magnitude of the current control action to the downstream residual, and locates the matrix elements to be updated according to the source deviation component, propagation path, and target phase state node. The matrix update does not use the method of correcting the entire matrix at the same time, but only adjusts the elements with actual propagation chains and complete response records. For paperboard records with missing observations, shifted compensation windows, or indistinguishable multiple control actions, they are retained for state verification but do not participate in the matrix element update. This allows the downstream feedback to enter the error decomposition process of subsequent paperboards, while avoiding unclosed records from changing the already verified propagation relationship.

[0035] In the continuous control process of this embodiment, the industrial controller combines cardboard events and fixed control cycles to process data. Cardboard entering and leaving the process and action responses form event records. Real-time running speed, control output and execution confirmation are written to the cache according to the control cycle. When an event arrives, the speed sequence and control sequence corresponding to the workpiece identifier are extracted from the cache. If the event is delayed, the phase state node is written back according to the time of the event and the subsequent theoretical phase is recalculated. The control output that has been completed is not retrospectively modified. The recalculated difference is written to the compensation ledger and matrix verification record, so that the observed events, cycle data and control outputs maintain a unified time base. The node version, control version and ledger version of the cardboard before and after the event are retained so that the original calculation conditions can be restored according to the version when writing back later.

[0036] Furthermore, the industrial controller sets three states for the closed-loop records of the same workpiece identifier: forming state, executing state, and closing state. The forming state indicates that the paper feeding reference phase has been written but the subsequent process has not yet been completed. The executing state indicates that at least one compensation item has been issued and there are still unrecognized contributions. The closing state indicates that the paperboard has left the final forming process and all compensation contributions have been canceled or marked as unabsorbed residuals. Records in the forming state are used for phase recursion, records in the executing state are used for net residual calculation and window management, and records in the closing state are used for paired sample screening and process influence matrix updates. Records that have not entered the closing state are not used as the basis for verifying stable propagation relationships, so that online control data and historical learning data have clear boundaries.

[0037] In a preferred embodiment, please refer to Figure 3 The spatiotemporal phase chain starts with the paper feeding reference phase as the starting node, and establishes phase state nodes corresponding to the paper feeding, printing and forming processes in sequence for the same workpiece identifier. Each phase state node records the theoretical entry time, actual entry time, theoretical exit time, actual exit time, inter-node transmission distance and the velocity integral value of adjacent nodes. The industrial controller recursively calculates the theoretical arrival phase of the next phase state node according to the actual exit phase of the previous phase state node, the velocity integral value between nodes and the execution delay of the next process, and writes the actual response phase returned by each process into the corresponding phase state node. The phase state node is stored using a combination key of workpiece identifier and process identifier. The theoretical entry time and theoretical exit time are generated recursively from the preceding node, and the actual entry time and actual exit time are written by the process observation event. The velocity integral value between nodes is obtained by integrating the velocity sequence from the paperboard leaving the preceding node to entering the following node. If the same process contains multiple controlled actions, the response time of the main action that determines the positional relationship of the paperboard is used as the node response phase, and other action states are written as auxiliary states into the same node.

[0038] Preferably, when establishing a phase state node, the industrial controller simultaneously records a data source marker and a time consistency marker. The data source marker is used to distinguish between direct observations, recursive values, and inverse values. The time consistency marker is used to indicate whether the node time satisfies the process constraint that the departure time of the preceding sequence is not later than the entry time of the subsequent sequence. When the actual entry time corresponding to the same workpiece identifier is earlier than the actual departure time of the preceding sequence, the industrial controller temporarily does not use the observation value for error decomposition, but checks the observation order of adjacent workpiece identifiers and rematches them. When the process order is still not satisfied after rematching, the node is marked as an abnormal observation node and its weight in the residual fitting is reduced. This processing method maintains the process directionality of the spatiotemporal phase chain, so that the error propagation vector will not form a backpropagation feature due to a single out-of-order observation.

[0039] Furthermore, when the industrial controller calculates the average operating speed based on the speed sequence of the cardboard between nodes, it does not use the speed at a single moment to represent the state of the entire conveying interval. Instead, it performs piecewise integration at the speed abrupt changes when entering and leaving the interval. If the speed sequence maintains the same direction of change within the interval, the average operating speed is obtained by dividing the integral of the entire interval by the duration. If the speed sequence undergoes continuous adjustments in opposite directions within the interval, the displacement contribution is calculated and summed using the duration of each adjustment segment as the weight. The actual time for the cardboard to pass through the interval is determined by the actual departure time of the preceding sequence and the actual entry time of the following sequence. The theoretical passage time is determined by the conveying distance between nodes and the average operating speed. The difference between the two is written as the conveying delay residual into the corresponding node edge data. The edge data and the node residual jointly participate in the subsequent source decomposition.

[0040] In another preferred embodiment, the rows of the process influence matrix correspond to paper feeding slippage, inter-process transmission, and local execution lag, respectively, and the columns correspond to the residual characteristics of each phase state node. The industrial controller extracts the sign change, duration interval, propagation delay, and response slope of the residuals of adjacent phase state nodes to form a residual propagation vector. Under the constraint that the sum of each deviation component equals the total phase deviation and the local execution lag component only acts on the corresponding process, the controller solves for each deviation component and its source process. The sign change of the residual is used to indicate whether the deviation maintains its direction, decays to 0, or reverses between adjacent processes. The duration interval is used to indicate the number of processes continuously covered by the same-direction residual. The propagation delay is determined by the time difference from the first occurrence of the upstream residual to the first occurrence of the downstream same-direction residual. The response slope is obtained by dividing the residual change of similar paperboards at different operating speeds by the speed change. The industrial controller writes the above features into the residual propagation vector in a fixed column order and shields non-existent propagation paths according to the current process combination.

[0041] Specifically, when a positive residual appears at the paper feeding node and both the printing entry node and the forming entry node have positive residuals after their corresponding propagation delays, the process influence matrix allows the paper feeding slip component to explain multiple node residuals simultaneously. When the residual at the printing exit node is close to the residual at the paper feeding node and a new positive difference is added at the forming entry node, the new difference is explained by the process transfer component from printing to forming. When the residual at the forming entry node is small and a new positive residual appears at the forming action response node, the new residual is explained by the forming local execution lag component. If different source components can explain the same node residual, the industrial controller selects a combined solution based on the residual duration interval, the degree of propagation delay matching, and the observation weight, and avoids discontinuous jumps in the source components of adjacent cardboards when there are no changes in operating conditions through differential constraints.

[0042] In a preferred embodiment, the segmented compensation sequence includes compensation processes, compensation methods, compensation directions, compensation amounts, and execution windows bound to the same workpiece identifier. The industrial controller establishes a feasible compensation domain based on the allowable phase change range of each remaining process, the current execution status, and the arrival time sequence. Using the relative positional deviation between the printing reference and the forming reference, the continuity of compensation changes in each process, and the cumulative compensation consistency of the same paperboard as joint constraints, the total compensation amount is allocated as speed fine-tuning amount, phase correction amount, and action advance amount, and issued sequentially according to the execution window. The feasible compensation domain is generated based on the processes that the paperboard has not yet completed. Control variables corresponding to completed processes are deleted from the feasible domain. Control variables that have entered the irreversible action stage are locked at their current values. Control variables that are still in the correctable state form upper and lower bounds according to the allowable direction and remaining time. The cumulative compensation consistency of the same paperboard is calculated by combining the executed amount and the current planned amount in the compensation ledger to prevent subsequent compensation from forming unfounded reverse adjustments with the executed compensation.

[0043] When determining the execution window, the industrial controller uses the moment when the cardboard is expected to enter the correctable range as the starting point of the window and the latest time when the corresponding control action can be written as the ending point of the window. The window also retains the logical margin required for instruction transmission and status confirmation. The execution window is only used to limit the allowable writing range of software control instructions and does not limit the structural parameters of the actuator. When multiple compensation items act on the same process, the industrial controller arranges the compensation items according to the propagation order of the source deviation components. It first processes the components that will continue to propagate after the current process, and then processes the local execution lag components that only act on the current process. If two compensation items are in opposite directions in the same window, they are merged into a single control quantity according to the net residual and the relative position constraints of printing and forming, so as to avoid issuing opposite instructions continuously in the same control cycle.

[0044] In another preferred embodiment, when any phase state node lacks an actual entry phase or an actual departure phase, the industrial controller selects the nearest effective phase state node upstream and the earliest effective phase state node downstream of the missing node as bidirectional anchor points. Based on the velocity integral value between the two anchor points, the theoretical transmission distance, and the intermediate process execution delay, the missing phase is inverted, and a confidence flag is written to the inversion result. When the corresponding actual phase is subsequently obtained, the difference between the actual phase and the inverted phase is used to correct the equivalent transmission distance and execution delay values ​​of adjacent nodes. The bidirectional anchor point inversion uses a weighted combination of upstream forward recursion results and downstream reverse recursion results. The forward recursion weight decreases as the process distance from the missing node to the upstream anchor point increases, and the reverse recursion weight decreases as the process distance from the missing node to the downstream anchor point increases. If only a single anchor point exists, the inverted value is marked as low confidence and its participation in matrix updates is restricted.

[0045] The inversion value of the missing phase can be calculated using the following formula:

[0046] ; in, This represents the inversion phase of the cardboard with workpiece identification k at the missing node j. This represents the phase obtained by forward recursion using the upstream anchor point, velocity integral, theoretical transmission distance, and intermediate execution delay. This represents the phase obtained by subtracting the corresponding transmission amount and execution delay from the downstream anchor point in reverse. This indicates the process distance between the missing node and the upstream anchor point. This indicates the process distance between the missing node and the downstream anchor point. This indicates the forward recursion weight. For example, when the missing node is 1 process away from the upstream anchor and 2 processes away from the downstream anchor, the forward recursion weight is 2 / 3. If the forward recursion value is 0.42 and the backward recursion value is 0.45, then the inversion phase is 0.43. The industrial controller writes 0.43 into the node and adds an inversion source marker.

[0047] After the actual phase of the missing node is filled in by the subsequent buffer, the industrial controller calculates the difference between the actual phase and the inverted phase, and allocates it according to the theoretical time ratio of the difference in the two transmission paths before and after the missing node. The part allocated to the front of the node is used to correct the equivalent transmission distance or equivalent execution delay from the previous node to the missing node, and the part allocated to the back of the node is used to correct the equivalent transmission distance or equivalent execution delay from the missing node to the next node. If multiple consecutive cardboards have the same inversion difference in the same direction at the same node, the equivalent execution delay is corrected first. If the inversion difference changes accordingly with the running speed, the equivalent transmission distance is corrected first. The corrected data is only used for subsequent recursion under the same cardboard specifications and the same process combination.

[0048] In a preferred embodiment, the industrial controller groups historical phase state nodes according to cardboard specifications, operating speed ranges, and process combinations. Within each group, cardboard records with similar upstream residual characteristics and different downstream control actions are selected to form paired samples. Independent response components corresponding to each control action are extracted based on the downstream residual differences of the paired samples. The independent response components are used to correct the matrix elements in the process influence matrix corresponding to the source process, propagation path, and target phase state node, while keeping the matrix elements that have not been paired and verified unchanged. Similar upstream residual characteristics mean that the residual directions of the paired cardboards at the same source position are consistent, the residual amplitude difference is within a preset neighborhood, and the propagation delay difference does not exceed the control cycle of the same process. Different control actions mean that the paired cardboards use different compensation methods or compensation amounts in the target process, and the remaining compensation states are kept comparable.

[0049] The independent response components corresponding to paired samples are extracted according to the following formula: ; in, Let represent the independent response components of the target control action in the p-th paired sample group. and These represent the residuals of the paired cardboard pieces at the same downstream node. and This represents a state vector that differs from the target control action. The value represents the verified influence coefficient of the state difference on the downstream residual, and 'a' represents the sample index of the control group. For example, the downstream residuals of the paired cardboard are 0.08 and 0.05, respectively. When the non-target state difference is converted to 0.01, the independent response component is 0.02. The industrial controller corrects the matrix element corresponding to the target control action with 0.02, without changing other propagation elements that are unrelated to the pairing record.

[0050] Furthermore, the industrial controller maintains a verification state for each matrix element. The verification state includes at least unverified, single-pair verification, continuous pair verification, and stable verification. Single-pair samples are only used to form candidate update quantities. Only after multiple consecutive groups obtain independent response components with the same direction will the candidate update quantity be written into the online matrix. If the subsequent downstream response is inconsistent with the update direction, the update quantity that has not yet entered the stable verification state will be withdrawn. When the cardboard specifications or process combinations change, the matrix elements in the stable verification state will not be directly migrated, but will be used as the prior values ​​of the new group matrix and re-verified through the new group pair samples, thereby maintaining the correspondence between the influence matrix update and the actual control response.

[0051] In another preferred embodiment, the industrial controller establishes a compensation ledger for each workpiece identifier. The compensation ledger sequentially records the source deviation component, the action process, the compensation direction, the compensation amount, and the corresponding phase status node for each compensation performed. When calculating subsequent phase deviations, the compensation contribution that has not yet been completed and transferred across processes in the compensation ledger is deducted from the total phase deviation, and the net residual after deduction is used to update the segmented compensation sequence. When different processes form candidate compensations with opposite directions for the same source deviation component, the candidate compensation with the same direction as the net residual and the earliest execution window is retained. Each record in the compensation ledger also includes a planned value, an actual issued value, an execution confirmation value, an expected propagation endpoint, and a cancellation status. Compensation records that have not obtained execution confirmation are not included in the executed compensation contribution, and compensation records that have reached the expected propagation endpoint and have been absorbed by the actual response are converted to a cancellation status.

[0052] Net residuals are calculated using the following formula: ; in, This represents the net residual of the cardboard with workpiece identification k at the i-th phase state node. This represents the total phase residual of the node. This represents the set of compensation records in the compensation ledger that have been executed and are expected to propagate to the i-th node but have not yet been written off. This represents the actual execution amount of the m-th compensation record. This represents the influence coefficient of the corresponding compensation propagating from the action process to the i-th node; for example, if the total phase residual is 0.07, and there are 2 compensation records in the ledger that have not yet been cleared, with propagation contributions of 0.02 and 0.01 respectively, the net residual is 0.04. Subsequent compensation sequences are generated only around 0.04, and the already executed 0.03 is no longer reassigned.

[0053] Please refer to Figure 4 , Figure 4The horizontal axis represents the continuous paperboard sequence, arranged by Chinese paperboard serial number according to production time; the vertical axis represents the phase residual. The curves represent the total residual, the unrecovered contribution, and the net residual after deducting the ledger contribution, respectively. The total residual comes from the closed-loop observation of the current phase state node, the unrecovered contribution comes from the compensation terms that have been executed but not yet fully absorbed by the downstream nodes, and the net residual is the remaining bias actually used when the subsequent compensation sequence is regenerated.

[0054] from Figure 4 As can be seen, the total residual curve gradually approaches the zero axis and then turns slightly negative as the continuous paperboard progresses, indicating that the direction of deviation in the production process is shifting. The amplitude of the unrecovered contribution curve is consistently smaller than that of the total residual, indicating that the ledger records do not replace on-site observations, but rather deduct the expected propagation contribution of the implemented controls. The net residual curve is generally closer to the zero axis than the total residual, indicating that the compensation ledger can reduce the double allocation of the same deviation; when the net residual turns negative, subsequent compensation should focus on whether there is overcompensation or a reversal of direction.

[0055] When different processes generate candidate compensations with opposite directions for the same source deviation component, the industrial controller first reads the unverified records of the same source deviation component in the compensation ledger, and then calculates the net residual direction after each candidate compensation reaches the target node. If a candidate compensation is opposite to the net residual direction but causes the residual to cross 0 and form a reverse deviation, the candidate compensation is deleted. If multiple candidate compensations are consistent with the net residual direction, the compensation item with the earlier execution window and less impact on the relative position constraint of printing and forming is selected. The remaining compensation amount is retained to be recalculated in the next correctable process. This processing method keeps the executed compensation, in-transit compensation and planned compensation in the same ledger, and does not repeatedly cover the historical control contribution with the current observed residual.

[0056] In a preferred embodiment, the industrial controller establishes non-overlapping compensation execution windows based on the arrival time of each remaining process, and divides each execution window into an entry segment, a stabilization segment, and an exit segment. The speed fine-tuning amount is allocated only in the entry and exit segments according to the continuous change constraint between adjacent cardboards. The phase correction amount remains consistent with the direction of the corresponding deviation component in the stabilization segment, and the action advance amount is only written to the forming action that has not yet been triggered. When any execution window overlaps with the latest correctable time of the next process, the unexecuted compensation amount is transferred to the subsequent execution window that is still within the compensation feasible domain. The entry segment starts from the control cycle before the cardboard enters the correctable conveying interval, the stabilization segment covers the time range during which the cardboard is continuously affected by the current control amount, and the exit segment starts from the control cycle before the cardboard leaves the interval. All three segments are bound to the workpiece identifier to avoid adjacent cardboards sharing the same compensation window.

[0057] Preferably, the continuous change constraint between adjacent cardboards uses the actual execution amount of the previous cardboard as the initial value of the current cardboard entering the segment, and the planned compensation amount of the current cardboard as the target value of the stable segment. The exit segment transitions the control amount of the current cardboard to the initial value of the entry segment of the next cardboard. If the next cardboard has not yet formed a compensation plan, the exit segment transitions the control amount to the reference value. The industrial controller does not change the phase correction direction in the stable segment. When the net residual reverses in the stable segment, the reverse part is recorded as a new source of residual and left for processing in the next execution window. The action advance amount is locked immediately after the forming action is triggered, and any subsequent reverse compensation cannot cover the already triggered action parameters.

[0058] When the execution window overlaps with the latest correctable time of the next process, the industrial controller calculates the remaining time of the current window, the amount of unexecuted compensation, and the action coefficient of the subsequent process on the source deviation component. If the subsequent process is still within the compensation feasible region, the unexecuted compensation is converted into a phase correction or action advance that the subsequent process can accept according to the action coefficient, and the source of the window transfer is recorded in the compensation ledger. If the subsequent process does not have the correctable conditions, the automatic transfer is terminated and the unexecuted part is retained as the model residual. The window transfer record does not participate in the pairing update of the process influence matrix to avoid incorrectly classifying the response change caused by cross-window conversion into a single control action.

[0059] In the subsequent control cycle after the window transfer, the industrial controller simultaneously retains the mapping relationship between the original compensation item and the converted compensation item. The unexecuted part of the original compensation item is marked as transferred, and the converted compensation item records its conversion coefficient and receiving process. After the actual response arrives, the response contribution is traced back to the original source deviation component according to the mapping relationship. If the converted compensation item is only partially executed, the unexecuted part will not return to the original window again, but will re-enter the compensation feasible region for calculation based on the current remaining process. If the cardboard has crossed all correctable processes, the conversion chain is terminated and the remaining amount is used as the unabsorbed residual in the closed record. The mapping relationship ensures that cross-process compensation can still maintain the consistency of the source and avoids the same deviation forming independent duplicate records in the ledger after the window transfer.

[0060] In another preferred embodiment, the industrial controller stores two sets of process influence matrices corresponding to the stable operating state and the working condition switching state for the same paperboard specification, and determines the matrix call state based on the topological consistency between the residual propagation vector sequences formed by the continuous workpiece identifiers. In the working condition switching state, only paperboard records that have completed upstream residual pairing, downstream response closure, and no compensation window shift have been used to update the corresponding matrix elements. After the changes in the source process judgment result and the propagation delay sequence converge simultaneously, the updated matrix elements are merged into the process influence matrix corresponding to the stable operating state. The stable operating state indicates that the process combination, speed range, and main residual propagation path of the continuous paperboard remain consistent, while the working condition switching state indicates that the speed range, paperboard specification, or process execution state has changed, resulting in a rearrangement of the residual propagation path.

[0061] Topological consistency is calculated using the following formula: ; in, This indicates the topological consistency up to the nth workpiece identifier, where N represents the number of consecutive cardboard pieces involved in the judgment. Let represent the set of directed edges in the residual propagation vector of the k-th cardboard that are determined to be actual propagation relationships. Let represent the set of directed edges in the residual propagation vector of the (k-1)th cardboard sheet that are determined to be actual propagation relationships. This represents the propagation edge shared by adjacent cardboard pieces. This represents all propagation edges of adjacent cardboard sheets. For example, the propagation edge sets of continuous cardboard sheets are paper feeding to printing, printing to forming, and paper feeding to forming. When there are 2 propagation edges of adjacent cardboard sheets and a total of 3 propagation edges after merging, the corresponding consistency term is 2 / 3. The industrial controller calculates the average of the continuous consistency terms and, in combination with the source process judgment results and the propagation delay changes, decides to call the stability matrix or the switching matrix.

[0062] Please refer to Figure 5 , Figure 5 The horizontal axis represents the continuous paperboard window, and the vertical axis represents the residual propagation topology consistency index. This index is calculated from the set of directed edges of residual propagation between adjacent paperboards and is used to measure whether the error propagation paths of feeding, printing, slotting, creasing, and forming nodes between continuous paperboards are consistent. The closer the curve is to the upper region, the higher the degree of overlap of the propagation edges in adjacent windows, and the more suitable it is to continue using the process influence matrix under the current working condition; a downward curve indicates that the propagation edge set has been rearranged, requiring a working condition switch or matrix re-verification process.

[0063] from Figure 5As can be seen, the consistency index of the front window remains at a high level, indicating that the main propagation path of the continuous cardboard is relatively stable, and the system can call the process influence matrix corresponding to the stable operating state; the middle window shows a certain decline and then recovers, indicating that the short-term disturbance did not immediately destroy the overall structure; the rear window drops to a lower level, indicating that the propagation relationship may be rearranged due to changes in speed range, cardboard specifications or execution state.

[0064] During the switching state, the industrial controller writes the newly generated matrix update into an independent switching matrix cache, without directly overwriting the stable matrix. Only when the source process judgment results of the continuous paperboard are consistent, the change in the propagation delay sequence enters the allowable convergence range, and all paperboard records used have completed upstream residual pairing, downstream response closure, and no compensation window shift has occurred, will the corresponding matrix elements be merged into the stable matrix according to the verification state. Matrix elements that do not meet the merging conditions continue to be retained in the switching matrix. If the working condition returns to the original stable state, the switching matrix cache is stopped but its grouping identifier is retained for re-verification when the same switching state occurs again.

[0065] In a preferred embodiment, after the cardboard leaves any compensated process, the industrial controller writes the corresponding actual response phase backward along the spatiotemporal phase chain to the completed phase state node, and matches the residual deviation calculated in reverse with the unrecovered compensation contribution in the compensation ledger item by item. When the direction of the residual deviation is opposite to the direction of the unrecovered compensation, or when the unrecovered compensation contribution has been absorbed by the previous execution window, the corresponding compensation item in the subsequent execution window is canceled, and the segmented compensation sequence is regenerated with the updated net residual, process influence matrix, and correctable range of each remaining process. The reverse writing starts with the actual response phase of the current compensated process as the endpoint, and calculates the equivalent phase of the preceding node under the current control result segment by segment according to the known execution delay, actual speed integral, and equivalent transfer distance between processes. It is then compared with the original actual phase of the preceding node, and the difference is used to determine whether the compensation contribution has been absorbed in the preceding or current window.

[0066] Specifically, the industrial controller matches the remaining deviation calculated in reverse with the unrecovered compensation contribution sequentially according to the source deviation component and the expected propagation endpoint recorded in the compensation ledger. The matching order is arranged according to the actual execution time of the compensation. If the remaining deviation is in the same direction as an unrecovered compensation and the magnitude still covers the compensation contribution, the corresponding compensation record is retained and continues to wait for subsequent node verification. If the remaining deviation is in the opposite direction, the compensation record is marked as overcompensation and compensation items of the same source and direction in subsequent execution windows are canceled. If the remaining deviation is close to 0 and the previous execution window has produced a response change equivalent to the unrecovered compensation, the corresponding compensation record is changed to the verified state, and the subsequent sequence no longer references the compensation contribution.

[0067] When regenerating the segmented compensation sequence, the industrial controller reads the updated net residual, the currently invoked process influence matrix, the processes that the paperboard has not yet completed, and the correctable range of each remaining process. It deletes expired execution windows and triggered action variables, retains compensation items that are still within the feasible region and consistent with the direction of the net residual, and redistributes the compensation amount. If there are no remaining correctable processes on the paperboard, it stops generating new control outputs and writes the remaining deviation and its source components into the closed-loop record of the current paperboard for subsequent matrix pairing and working condition judgment. The entire data chain is closed by workpiece identification, phase state nodes, error components, compensation ledger, execution windows, and downstream responses, enabling the industrial control system to continuously distinguish error sources, control contributions, and remaining deviations.

Claims

1. A carton printing and forming linkage industrial control system, characterized in that, The industrial controller acquires the workpiece identification, paper feeding reference phase, printing process phase observation and forming process phase observation for each piece of paperboard, and establishes a paperboard spatiotemporal phase chain based on process conveying distance, real-time running speed and execution delay. Based on the residual between the theoretical arrival phase and the actual response phase and the preset process influence matrix, the phase deviation is decomposed into paper feeding slip component, inter-process transmission component and local execution lag component. Based on the remaining processes of the paperboard, the correctable range of each process, and the relative positional constraints of the printing reference and the forming reference, a segmented compensation sequence is generated, and speed fine-tuning amount, phase correction amount, or action advance amount is issued to the corresponding process. The process influence matrix is ​​updated according to the downstream response phase.

2. The industrial control system for carton printing and forming linkage according to claim 1, characterized in that, The spatiotemporal phase chain takes the paper feeding reference phase as the starting node and establishes phase state nodes corresponding to the paper feeding, printing and forming processes in sequence for the same workpiece identifier. Each phase state node records the theoretical entry time, actual entry time, theoretical departure time, actual departure time, transmission distance between nodes, and velocity integral value of adjacent nodes; The industrial controller recursively calculates the theoretical arrival phase of the next phase state node based on the actual departure phase of the previous phase state node, the velocity integral value between nodes, and the execution delay of the next process, and writes the actual response phase returned by each process into the corresponding phase state node.

3. The industrial control system for carton printing and forming linkage according to claim 1, characterized in that, The rows of the process influence matrix correspond to paper feeding slippage, inter-process transmission, and local execution lag, respectively, and the columns correspond to the residual characteristics of each phase state node. The industrial controller extracts the sign change, duration interval, propagation delay, and response slope as a function of operating speed of the residuals of adjacent phase state nodes to form a residual propagation vector. Under the constraint that the sum of all deviation components equals the total phase deviation and that the local execution lag component only acts on the corresponding process, it solves for each deviation component and its source process.

4. The industrial control system for carton printing and forming linkage according to claim 3, characterized in that, The segmented compensation sequence includes the compensation process, compensation method, compensation direction, compensation amount, and execution window that are bound to the same workpiece identifier; The industrial controller establishes a feasible compensation domain based on the allowable phase change range of each remaining process, the current execution status, and the arrival time sequence. Using the relative positional deviation between the printing reference and the forming reference, the continuity of compensation changes in each process, and the consistency of cumulative compensation for the same paperboard as joint constraints, the total compensation amount is allocated as the speed fine-tuning amount, the phase correction amount, and the action advance amount, and is issued sequentially according to the execution window.

5. The industrial control system for carton printing and forming linkage according to claim 2, characterized in that, When any phase state node lacks an actual entry phase or the actual departure phase, the industrial controller selects the nearest effective phase state node upstream of the missing node and the earliest effective phase state node downstream of the same workpiece identifier as bidirectional anchor points. Based on the speed integral value between the two anchor points, the theoretical transmission distance, and the intermediate process, it performs a delayed inversion of the missing phase and writes a credibility flag to the inversion result. When the corresponding actual phase is subsequently obtained, the difference between the actual phase and the inverted phase is used to correct the equivalent values ​​of the transmission distance and execution delay of adjacent nodes.

6. The industrial control system for carton printing and forming linkage according to claim 3, characterized in that, The industrial controller groups the historical phase state nodes according to cardboard specifications, operating speed range, and process combination. Within each group, cardboard records with similar upstream residual characteristics and different downstream control actions are selected to form a paired sample. Based on the downstream residual differences of the paired samples, the independent response components corresponding to each control action are extracted, and the matrix elements in the process influence matrix corresponding to the source process, propagation path and target phase state node are corrected with the independent response components, while keeping the matrix elements that have not been paired and verified unchanged.

7. The industrial control system for carton printing and forming linkage according to claim 4, characterized in that, The industrial controller establishes a compensation ledger for each workpiece identifier. The compensation ledger sequentially records the source deviation component, the action process, the compensation direction, the compensation amount, and the corresponding phase state node for each compensation performed. When calculating subsequent phase deviations, the compensation contribution that has not yet been completed and transferred across processes in the compensation ledger is deducted from the total phase deviation, and the net residual after deduction is used to update the segmented compensation sequence. When different processes generate candidate compensations with opposite directions for the same source deviation component, the candidate compensation with the same direction as the net residual and the earliest execution window is retained.

8. The industrial control system for carton printing and forming linkage according to claim 4, characterized in that, The industrial controller establishes non-overlapping compensation execution windows based on the arrival time of each remaining process, and divides each execution window into an entry segment, a stabilization segment, and an exit segment. The speed fine-tuning amount is allocated only in the entry section and the exit section according to the continuous change constraint between adjacent cardboard sections; the phase correction amount remains consistent with the direction of the corresponding deviation component in the stable section; and the action advance amount is only written to the forming action that has not yet been triggered. When any execution window overlaps with the latest correctable time of the next process, the unexecuted compensation amount is transferred to the subsequent execution window that is still within the compensation feasible region.

9. The industrial control system for carton printing and forming linkage according to claim 1, characterized in that, The industrial controller stores two sets of process influence matrices corresponding to the stable operating state and the working condition switching state for the same cardboard specification, and determines the matrix calling state based on the topological consistency between the residual propagation vector sequences formed by continuous workpiece identification. In the aforementioned operating condition switching state, only the cardboard records that have completed upstream residual pairing, downstream response closure, and no compensation window shift have been used to update the corresponding matrix elements. After the changes in the source process judgment result and the propagation delay sequence converge simultaneously, the updated matrix elements are merged into the process influence matrix corresponding to the stable operating state.

10. The industrial control system for carton printing and forming linkage according to claim 7, characterized in that, After the cardboard leaves any compensated process, the industrial controller writes the corresponding actual response phase in reverse along the spatiotemporal phase chain to the completed phase state node, and matches the remaining deviation calculated in reverse with the unrecovered compensation contribution in the compensation ledger item by item. When the direction of the remaining deviation is opposite to the direction of the unrecovered compensation, or when the contribution of the unrecovered compensation has been absorbed by the previous execution window, the corresponding compensation item in the subsequent execution window is cancelled, and the segmented compensation sequence is regenerated with the updated net residual, process influence matrix, and correctable range of each remaining process.

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