High-speed paper feeding mechanism paper tension dynamic balance control method and system

Abstract

The present application relates to paper tension control technical field, disclose a high-speed paper feed mechanism paper tension dynamic balance control method and system, include: S1, obtain the paper parameter and calculate cross-sectional area, determine each tension area target tension reference;S2, gather tension signal and filter, calculate tension error;S3, gather the included angle, normal pressure, roll linear velocity, vacuum pressure, roll roughness, calculate the tension transmissibility index;S4, construct the tension dynamic model containing leakage term;S5, based on the tension error and dynamic model calculation speed difference, from bottom to top generation speed command;S6, estimate the roll diameter and combine dynamic parameter calculation feedforward torque;S7, limit speed command, adaptive adjustment convergence rate, low tension transmissibility when enable equal speed escort.The present application realizes the real-time dynamic balance control of each tension area tension in high-speed paper feed process.

Description

Technical Field

[0001] This invention belongs to the field of paper tension control technology, specifically relating to a method and system for dynamic balance control of paper tension in high-speed paper feeding mechanisms. Background Technology

[0002] In high-speed paper feeding systems, paper typically undergoes continuous transmission through tension control zones between multiple rollers to ensure smooth paper web movement and synchronized coordination between different process stages. However, under high-speed operating conditions, the inherent flexibility and susceptibility of paper, coupled with factors such as lag in the equipment drive, uneven roller surface friction, and vacuum bonding, can easily lead to uneven tension distribution, large tension fluctuations, and even paper wrinkling and breakage. Therefore, achieving continuous and stable control of paper tension under dynamic operating conditions is one of the key technical challenges currently facing high-speed paper feeding equipment.

[0003] Existing tension control technologies primarily rely on closed-loop PID control strategies, with some systems incorporating tension sensor feedback signals to adjust the main drive speed or roll diameter torque. While these approaches are effective under low-speed or stable conditions, their response speed and control accuracy are significantly insufficient at high speeds or when load fluctuations are substantial. Furthermore, traditional methods often neglect the transmission efficiency of tension across multiple control segments and its nonlinear characteristics that vary with operating conditions, failing to effectively model the dynamic evolution of actual tension and providing sufficient fault tolerance and safety guarantees under abnormal conditions. Moreover, as paper feeding processes increasingly demand higher paper quality and transmission stability, simply relying on fixed adjustment strategies or static parameter settings is insufficient to meet the personalized needs of tension adjustment under complex operating conditions. Summary of the Invention

[0004] This invention provides a method and system for dynamic balance control of paper tension in a high-speed paper feeding mechanism, which solves the technical problems in related technologies such as sluggish response of paper web tension control process to changes in traction state, inability to effectively characterize the dynamic tension process, and poor coordination of tension control under multiple driving conditions.

[0005] This invention provides a method for dynamic balance control of paper tension in a high-speed paper feeding mechanism, comprising the following steps:

[0006] S1, obtains the width, thickness, elastic modulus, length of each tension zone, allowable stress of the paper web, equivalent moment of inertia, main drive speed range, acceleration limit and final target tension, calculates the cross-sectional area, and determines and outputs the target tension reference for each tension zone;

[0007] S2, collect the raw tension signal downstream of each tension zone, obtain the tension estimate after low-pass filtering, and compare it with the target tension benchmark to obtain the tension error;

[0008] S3 collects wrap angle, normal clamping force, roller linear speed, vacuum pressure, and roller surface roughness, and calculates the tension transferability index;

[0009] S4, the tension transferability index is mapped to the leakage coefficient, and a tension dynamic model including the leakage term is established based on the paper web parameters and the upstream and downstream roller linear speeds. The tension dynamic model outputs the tension derivative in the continuous time domain.

[0010] S5, set the tension error convergence rate, calculate the target speed difference based on the leakage coefficient, tension dynamic model and tension error, and generate speed commands from bottom to top with the speed of the downstream main section as the speed anchor point.

[0011] S6 calculates the current roll diameter based on thickness, initial unwinding radius, paper web running speed and sampling period, and generates feedforward torque based on current roll diameter, tension estimate, equivalent moment of inertia, angular acceleration and friction torque;

[0012] S7 limits the speed command for each tension zone and adaptively adjusts the tension error convergence rate according to the tension transferability index. When the tension transferability index is lower than the preset minimum threshold and the duration reaches the preset time period, it enters constant speed escort and returns to execute S3.

[0013] Furthermore, the calculation process for the cross-sectional area and the target tension reference for each tension zone includes:

[0014] S21, the cross-sectional area is obtained by calculating the product of the width and thickness;

[0015] S22, the target tension upper limit is obtained by calculating the product of the allowable stress of the paper web and the cross-sectional area;

[0016] S23, take the smaller value between the final target tension and the upper limit of the target tension as the target tension benchmark for each tension zone; and perform a consistency check on the target tension benchmark and the upper limit of the target tension. If any target tension benchmark is greater than the upper limit of the target tension, reject the output and return to S22 to redetermine the upper limit of the target tension; if the consistency check is passed, output the target tension benchmark for each tension zone.

[0017] Furthermore, the wrap angle and roller surface roughness are combined to obtain the traction enhancement coefficient, and the roller surface linear velocity and vacuum pressure are combined to obtain the traction attenuation coefficient. The ratio of the traction enhancement coefficient and the traction attenuation coefficient is calculated to obtain the effective friction coefficient. The effective friction coefficient is multiplied by the current normal clamping force to obtain the tangential traction force. An exponential function is constructed by the ratio of the tangential traction force to the tension estimate, and the output value of the exponential function is subtracted to obtain the tension transmissibility index.

[0018] Furthermore, S3 also includes: when the tension transferability index does not reach the first preset threshold, the gray wolf optimization algorithm is used to iteratively optimize and obtain the final order of normal clamping force, vacuum pressure and wrap angle, and adjust them in sequence according to the final order, and recalculate the tension transferability index after each adjustment, and output it when the tension transferability index reaches the first preset threshold.

[0019] Furthermore, the final order of normal clamping force, vacuum pressure, and wrap angle is obtained by iterative optimization using the gray wolf optimization algorithm, including:

[0020] The normal clamping force, vacuum pressure and wrap angle are each assigned a sorting weight and a single-step adjustment ratio, and the order of adjustment is determined by sorting the three weights in ascending order.

[0021] Upper and lower limits, change rates, and process safety constraints are set for normal clamping force, vacuum pressure, and wrap angle, respectively. Sequences exceeding the constraints are truncated according to the upper and lower limits.

[0022] Construct a set of working conditions, execute each candidate sequence in the set of working conditions in sequence according to the single-step adjustment ratio, recalculate the tension transferability index in real time and determine whether the first preset threshold is reached, and record the time when the first preset threshold is reached, the number of parameter actions, tension over-limit and amplitude limit events.

[0023] A comprehensive evaluation index is formed by weighting the time to reach the first preset threshold, the number of parameter actions, tension overrun and amplitude limit events. The candidate order is sorted in ascending order, and the top three are selected as the alpha wolf, the second alpha wolf and the third wolf. A new candidate order and single-step adjustment ratio are generated according to the encirclement and iterative update rules of the gray wolf algorithm.

[0024] When the change in the comprehensive evaluation index within the preset algebra is less than the second preset threshold, the final order and the corresponding single-step adjustment ratio are output.

[0025] Furthermore, S4 specifically includes:

[0026] S31, obtain the paper web parameters and the upstream and downstream roller linear speeds, wherein the paper web parameters include: paper web cross-sectional area, elastic modulus, and tension zone length;

[0027] S32, subtract the tension transmissibility index from 1 and multiply it by the preset maximum leakage coefficient to obtain the corresponding leakage coefficient;

[0028] S33, divide the product of the elastic modulus and the cross-sectional area of ​​the paper web by the length of the tension zone to obtain the elastic gain term; multiply the leakage coefficient by the tension estimate to obtain the leakage term;

[0029] S34. Multiply the difference in linear velocity between the upstream and downstream rollers by the elastic gain term and subtract the leakage term to obtain the tension derivative in the continuous time domain.

[0030] Furthermore, the tension error convergence rate is set, and the target velocity difference is calculated based on the leakage coefficient, the tension dynamic model, and the tension error. A velocity command is generated from bottom to top, using the velocity of the downstream main segment as the velocity anchor point, including:

[0031] S41 sets the tension error convergence rate for each tension zone, establishes a first-order error convergence target, and uses tension error as the only error signal.

[0032] S42, solve the target velocity difference by simultaneously solving the tension dynamic model containing the leakage term and the first-order error convergence target. First, calculate the product of the leakage coefficient and the tension estimate, then calculate the product of the tension error convergence rate and the tension error. Subtract the latter from the former to obtain the tension change demand. Then, convert the tension change demand into the target velocity difference by dividing the product of the elastic modulus and the cross-sectional area of ​​the paper web by the length of the tension zone.

[0033] S43, set the speed of the downstream main section as the speed anchor point, and in the order of tension zone from downstream to upstream, set the speed of the upstream roller to its downstream roller speed minus the target speed difference of the tension zone, recursively generate the speed command of each upstream roller, and publish it as a speed command interface.

[0034] S44: When any speed command exceeds the actuator's allowed range, record the event and limit the speed at the execution layer.

[0035] Furthermore, the current roll diameter is calculated based on thickness, initial unwinding radius, paper web speed, and sampling period. A feedforward torque is generated based on the current roll diameter, tension estimate, equivalent moment of inertia, angular acceleration, and frictional torque, including:

[0036] S51, multiply the paper web running speed by the sampling period according to the sampling period and accumulate it over time to obtain the cumulative length; in the unwinding condition, subtract the product of the thickness and the cumulative length from the square of the initial unwinding radius and divide it by the constant pi to obtain the square root of the result to obtain the current unwinding radius; in the winding condition, add the square of the product of the thickness and the cumulative length to the square of the result and divide it by the constant pi to obtain the current winding radius.

[0037] S52, the angular velocity is obtained by dividing the paper web running speed by the current roll diameter, and the angular acceleration is obtained by dividing the difference between the current angular velocity and the previous angular velocity by the sampling period;

[0038] S53, multiply the current tension estimate by the current roll diameter to obtain the tension torque term, multiply the equivalent moment of inertia by the angular acceleration to obtain the inertia compensation term; combine the Coulomb friction constant and viscosity coefficient with the angular velocity to obtain the friction torque term; add the above three terms to obtain the feedforward torque, and use the feedforward torque as an external interface to superimpose with the closed-loop output to drive the unwinding or winding motor.

[0039] S54 performs engineering limiting and consistency checks on the current roll diameter and feedforward torque. When the current roll diameter exceeds the preset upper and lower limits, it is truncated and the event is recorded. When the feedforward torque exceeds the allowable upper limit, it is limited and the event is recorded.

[0040] Furthermore, S7 specifically includes:

[0041] Speed ​​commands in each tension zone are limited, cutting off speed commands that exceed the actuator's allowable range to preset upper and lower limits, and recording the limiting event;

[0042] The tension error convergence rate is adjusted in a piecewise linear manner based on the tension transmissibility index.

[0043] When the tension transferability index is lower than the preset minimum threshold but the duration has not reached the preset time period, the tension error convergence rate is fixed at the lower limit.

[0044] When the tension transferability index is lower than the preset minimum threshold and continues for a preset time period, it enters constant speed escort mode; the speed of the upstream roller and the downstream roller of the trigger tension zone are set to be the same, the speed difference recursion of the tension zone in step S5 is paused, and when the tension transferability index rises back to above the lower limit, it exits the escort mode and returns to execute S3.

[0045] When the tension estimate exceeds the preset exit threshold and continues for a preset time period, a shutdown signal is output and a fault event flag is set.

[0046] This invention also provides a dynamic balance control system for paper tension in a high-speed paper feeding mechanism, comprising:

[0047] The tension target generation module is used to obtain the width, thickness, elastic modulus, length of each tension zone, allowable stress of the paper web, main drive speed range, acceleration limit and final target tension, calculate the cross-sectional area, and determine and output the target tension reference for each tension zone;

[0048] The tension estimation and error module is used to collect raw tension signals downstream of each tension zone, obtain tension estimates after low-pass filtering, and compare them with the target tension benchmark to obtain the tension error.

[0049] The tension transferability calculation module is used to collect data on wrap angle, normal clamping force, roller linear speed, vacuum pressure, and roller surface roughness, and to calculate the tension transferability index.

[0050] The tension dynamic modeling module is used to map the tension transferability index to the leakage coefficient and establish a tension dynamic model including the leakage term based on the paper web parameters and the upstream and downstream roller linear speeds. The tension dynamic model outputs the tension derivative in the continuous time domain.

[0051] The speed command generation module is used to set the tension error convergence rate, calculate the target speed difference based on the leakage coefficient, tension dynamic model and tension error, and generate speed commands from bottom to top with the speed of the downstream main section as the speed anchor point.

[0052] The feedforward torque calculation module is used to calculate the current roll diameter based on thickness, initial unwinding radius, paper web running speed and sampling period, and to generate feedforward torque based on the current roll diameter, tension estimate, equivalent moment of inertia, angular acceleration and friction torque.

[0053] The adaptive amplitude limiting and escort module is used to limit the speed command of each tension zone and adaptively adjust the tension error convergence rate according to the tension transferability index. When the tension transferability index is lower than the preset minimum threshold and the duration reaches the preset time period, it enters constant speed escort and returns to the tension transferability calculation module.

[0054] The beneficial effects of this invention are as follows: Based on the tension transferability index, this invention constructs a dynamic tension model including a leakage term, which can realistically reflect the dynamic changes in paper web tension during transmission, overcoming the limitation of traditional static tension control models that ignore material traction characteristics. Through tension error convergence rate control and speed command generation strategies, combined with multi-segment speed collaborative recursion and a limiting protection mechanism, the invention achieves unified tension balance control and actuator protection. Furthermore, the introduction of the Grey Wolf optimization algorithm adaptively adjusts the order of normal clamping force, vacuum pressure, and wrap angle, effectively improving tension adjustment efficiency and control effect. This invention can also enter constant speed protection and self-recover based on abnormal tension states, helping to avoid breakage and over-tension accidents, and improving the safety and continuity of equipment operation. Attached Figure Description

[0055] Figure 1 This is a flowchart of the dynamic balance control method for paper tension in the high-speed paper feeding mechanism of the present invention. Detailed Implementation

[0056] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0057] like Figure 1 As shown, the method for dynamic balance control of paper tension in a high-speed paper feeding mechanism includes the following steps:

[0058] S1, obtains the width, thickness, elastic modulus, length of each tension zone, allowable stress of the paper web, equivalent moment of inertia, main drive speed range, acceleration limit and final target tension, calculates the cross-sectional area, and determines and outputs the target tension reference for each tension zone;

[0059] S2, collect the raw tension signal downstream of each tension zone, obtain the tension estimate after low-pass filtering, and compare it with the target tension benchmark to obtain the tension error;

[0060] S3 collects wrap angle, normal clamping force, roller linear speed, vacuum pressure, and roller surface roughness, and calculates the tension transferability index;

[0061] S4, the tension transferability index is mapped to the leakage coefficient, and a tension dynamic model including the leakage term is established based on the paper web parameters and the upstream and downstream roller linear speeds. The tension dynamic model outputs the tension derivative in the continuous time domain.

[0062] S5, set the tension error convergence rate, calculate the target speed difference based on the leakage coefficient, tension dynamic model and tension error, and generate speed commands from bottom to top with the speed of the downstream main section as the speed anchor point.

[0063] S6 calculates the current roll diameter based on thickness, initial unwinding radius, paper web running speed and sampling period, and generates feedforward torque based on current roll diameter, tension estimate, equivalent moment of inertia, angular acceleration and friction torque;

[0064] S7 limits the speed command for each tension zone and adaptively adjusts the tension error convergence rate according to the tension transferability index. When the tension transferability index is lower than the preset minimum threshold and the duration reaches the preset time period, it enters constant speed escort and returns to execute S3.

[0065] In one embodiment of the present invention, the width, thickness, elastic modulus, length of each tension zone, allowable stress of the paper web, main drive speed range, acceleration limit and final target tension are obtained through a preset input interface. The allowable stress of the paper web is the maximum stress value that the paper material can withstand. The main drive speed range and acceleration limit reflect the operating capability boundary of the paper feeding mechanism. The final target tension is the ideal tension value set according to the specific paper feeding process requirements.

[0066] In one embodiment of the present invention, the calculation process for the cross-sectional area and the target tension reference for each tension zone includes:

[0067] S21, the cross-sectional area is obtained by calculating the product of the width and thickness;

[0068] S22, by calculating the product of the allowable stress of the paper web and the cross-sectional area, the target tension upper limit is obtained; the target tension upper limit limits the maximum allowable value of tension from the perspective of material strength, so as to avoid paper tearing or permanent deformation due to excessive tension.

[0069] S23, take the smaller value between the final target tension and the upper limit of the target tension as the target tension benchmark for each tension zone; and perform a consistency check on the target tension benchmark and the upper limit of the target tension. If any target tension benchmark is greater than the upper limit of the target tension, reject the output and return to S22 to redetermine the upper limit of the target tension; if the consistency check is passed, output the target tension benchmark for each tension zone.

[0070] This embodiment scientifically determines the target tension benchmark for each tension zone by combining the physical parameters of the paper, the operating parameters of the equipment, and the process objectives. This ensures that the tension setting does not exceed the paper's bearing capacity, thus avoiding material damage, and also matches the target tension with the process requirements, providing an accurate and reliable reference benchmark for subsequent dynamic tension adjustment. At the same time, the consistency verification step further enhances the stability and safety of the system, effectively preventing tension loss of control problems caused by parameter errors or abnormalities.

[0071] In one embodiment of the present invention, tension sensors are installed downstream of each tension zone to collect the original tension signal during the paper's movement in real time. The original tension signal directly reflects the paper tension state at the current tension zone exit. To suppress high-frequency noise, the original tension signal is subjected to low-pass filtering. The signal obtained after filtering is the tension estimate, and the difference between the tension estimate and the target tension reference is used as the tension error.

[0072] In one embodiment of the present invention, the wrap angle and the roller surface roughness are combined to obtain the traction enhancement coefficient, the roller surface linear velocity and the vacuum pressure are combined to obtain the traction attenuation coefficient, and the ratio of the traction enhancement coefficient and the traction attenuation coefficient is calculated to obtain the effective friction coefficient. The effective friction coefficient is multiplied by the current normal clamping force to obtain the tangential traction force. An exponential function is constructed by the ratio of the tangential traction force to the tension estimate, and the tension transmissibility index is obtained by subtracting the output value of the exponential function.

[0073] Specifically, the formula for calculating the tension transmissibility index is:

[0074] ;

[0075] in, Let exp represent the tension transmissibility index of the i-th tension zone, where i represents the tension zone index and exp represents the exponential function. This represents the initial value of the static friction coefficient. This represents the wrap angle correction factor. Indicates the corner of the enclosure. This represents the roughness correction factor, in units of... , The roughness of the roller surface is expressed in meters (m). This represents the speed correction factor, in units of... , This represents the vacuum correction factor, in Pa. Indicates the linear velocity of the roller surface. Indicates vacuum pressure, Indicates the lower limit of vacuum. Indicates the normal compressive force. Indicates tension, This represents the tension estimate. This indicates a very small positive value.

[0076] It should be noted that in the calculation of the tension transferability index, the physical properties of increasing the wrap angle to improve the contact area between the paper and the roller, and increasing the roller surface roughness to enhance the surface friction effect are weighted and combined to obtain the traction enhancement coefficient, which characterizes the comprehensive effect of promoting tension transfer. The traction attenuation coefficient is obtained by combining the physical properties of increasing the wrap angle to improve the contact area between the paper and the roller, and increasing the roller surface roughness to enhance the surface friction effect. The effective friction coefficient, calculated by the ratio of the traction enhancement coefficient and the traction attenuation coefficient, reflects the actual friction efficiency between the paper and the roller under the current operating conditions. The tangential traction force characterizes the actual traction force that the roller can transmit to the paper. To quantify the efficiency of tension transfer, an exponential function is constructed by the ratio of the tangential traction force to the estimated tension value, and the tension transferability index is obtained by subtracting the output value of this exponential function from 1. The value ranges from 0 to 1; the closer to 1, the higher the current tension transfer efficiency, and the closer to 0, the lower the transfer efficiency.

[0077] This embodiment calculates the tension transferability index through the above process, comprehensively considering multiple working parameters such as wrap angle, roll surface roughness, linear velocity, vacuum pressure, and normal clamping force. It overcomes the limitations of traditional methods that rely on only a single factor to evaluate the traction effect. Through the nonlinear transformation of the exponential function, the value range of the tension transferability index is stabilized within the range of 0 to 1, which facilitates quantitative analysis and the design of subsequent control strategies. It can reflect the effectiveness of the current tension transfer in real time and accurately, significantly improving the response speed and control accuracy of tension balance during high-speed paper feeding.

[0078] In one embodiment of the present invention, S3 further includes: when the tension transferability index does not reach the first preset threshold, using the Grey Wolf optimization algorithm to iteratively optimize and obtain the final order of normal clamping force, vacuum pressure and wrap angle, and adjusting them sequentially according to the final order, and recalculating the tension transferability index after each adjustment, and outputting it when the tension transferability index reaches the first preset threshold.

[0079] The final order of normal clamping force, vacuum pressure, and wrap angle is obtained through iterative optimization using the Grey Wolf optimization algorithm, including:

[0080] The normal clamping force, vacuum pressure, and wrap angle are each assigned a sorting weight and a single-step adjustment ratio, and the sorting weights of the three are arranged in ascending order to determine the order of adjustment. The sorting weights are set based on historical operating data. The single-step adjustment ratio limits the adjustment range in each round of adjustment to avoid nonlinear response of the system due to sudden changes.

[0081] Upper and lower limits, change rates, and process safety constraints are set for the normal clamping force, vacuum pressure, and wrap angle, respectively. Sequences exceeding the constraints are truncated according to the upper and lower limits.

[0082] A set of working conditions covering linear velocity fluctuations, friction coefficient changes, vacuum source fluctuations, and wrap angle assembly tolerances is constructed. For each candidate sequence in the set of working conditions, the single-step adjustment ratio is executed sequentially. The tension transferability index is recalculated in real time, and it is determined whether the first preset threshold is reached. The time when the first preset threshold is reached, the number of parameter actions, tension over-limit and amplitude limit events are recorded. Among them, the number of parameter actions refers to the total number of times the normal clamping force, vacuum pressure and wrap angle are adjusted under a set of adjustment sequences.

[0083] A comprehensive evaluation index is formed based on the time to reach the first preset threshold, the number of parameter actions, the tension exceeding the limit and the amplitude limiting event weighted combination. The candidate order is sorted in ascending order, and the top three are selected as the alpha wolf, the second alpha wolf and the third wolf. A new round of candidate order and single-step adjustment ratio are generated according to the encirclement and iterative update rules of the gray wolf algorithm.

[0084] When the change in the comprehensive evaluation index within the preset algebra is less than the second preset threshold, the final order and the corresponding single-step adjustment ratio are output.

[0085] This embodiment uses the Grey Wolf optimization algorithm to intelligently optimize the adjustment sequence, overcoming the limitation that traditional fixed adjustment sequences are difficult to adapt to complex working conditions, improving the efficiency of tension transferability index reaching the threshold, and ensuring the dynamic balance performance of the tension control system.

[0086] In one embodiment of the present invention, S4 specifically includes:

[0087] S31, acquire paper web parameters and upstream and downstream roller linear speeds. The paper web parameters include: paper web cross-sectional area, elastic modulus, and tension zone length. The upstream and downstream roller linear speeds are acquired in real time by speed sensors installed on the rollers, representing the roller linear speeds at the tension zone inlet and outlet, respectively.

[0088] S32, subtract the tension transferability index from 1 and multiply it by the preset maximum leakage coefficient to obtain the corresponding leakage coefficient. The leakage coefficient represents the normalized proportion of tension transfer loss. The preset maximum leakage coefficient is set according to the equipment characteristics and paper type.

[0089] S33, the product of the elastic modulus and the cross-sectional area of ​​the paper web is divided by the length of the tension zone to obtain the elastic gain term; the leakage coefficient is multiplied by the tension estimate to obtain the leakage term; among them, the product of the elastic modulus and the cross-sectional area of ​​the paper web is obtained according to the deformation-force relationship derived from Hooke's law, which represents the overall elastic stiffness of the paper web, and is then divided by the current tension zone length to obtain the elastic gain term characterizing the effect of the paper's elastic deformation on the tension; the tension attenuation term represents the transmission loss.

[0090] S34. Multiply the difference in linear velocity between the upstream and downstream rollers by the elastic gain term to obtain the tension change component caused by the speed difference. Then subtract the leakage term to obtain the rate of change of tension with time in the continuous time domain, i.e., the tension derivative, which reflects the dynamic change trend of tension at the current moment.

[0091] Specifically, the formula for the tension derivative is:

[0092] ;

[0093] in, Let T represent the current tension, E represent the elastic modulus, A represent the cross-sectional area of ​​the paper web, and L represent the length of the tension zone. and These represent the linear velocities of the upstream and downstream rollers, respectively. This represents the leakage coefficient, in units of... , This indicates the target tension reference.

[0094] This embodiment constructs a dynamic model that takes into account both the elastic properties of paper and the tension transmission loss, breaking through the limitations of traditional models that only consider elastic deformation and ignore transmission loss. The introduction of a leakage coefficient enables the model to accurately quantify the impact of tension transmission efficiency on tension changes. Especially in high-speed paper feeding scenarios, it can effectively compensate for tension losses caused by slippage, insufficient friction, etc. This enables refined dynamic control of tension, significantly improving the response speed and accuracy of tension control during high-speed paper feeding.

[0095] In one embodiment of the present invention, a tension error convergence rate is set, and the target velocity difference is calculated based on the leakage coefficient, the tension dynamic model, and the tension error. A velocity command is generated from bottom to top, using the velocity of the downstream main segment as the velocity anchor point, including:

[0096] S41 sets the tension error convergence rate for each tension zone, establishes a first-order error convergence target, and uses tension error as the sole error signal; wherein, the tension error convergence rate is determined based on the paper material characteristics and process requirements, and is used to control the decay rate of tension error; simultaneously, a first-order error convergence target is established, the expression of which is: , Indicates tension error. This indicates the convergence rate of the tension error. This represents the time derivative of the tension error. The target uses the tension error as the sole error signal to ensure that the control system focuses on the rapid correction of tension deviation.

[0097] S42, the tension dynamic model containing the leakage term is solved simultaneously with the first-order error convergence objective to obtain the target velocity difference. First, the product of the leakage coefficient and the tension estimate is calculated, then the product of the tension error convergence rate and the tension error is calculated. The former is subtracted from the latter to obtain the required tension change. Then, based on the proportional relationship between the product of the elastic modulus and the cross-sectional area of ​​the paper web and the length of the tension zone, the required tension change is equivalently converted into the target velocity difference. The formula for calculating the target velocity difference is: , The first-order error convergence target represents the desired evolution path of the tension error, that is, how the system hopes the tension error will gradually decrease over time until it approaches zero.

[0098] S43, set the speed of the downstream main section as the speed anchor point, and in the order of tension zone from downstream to upstream, set the speed of the upstream roller to its downstream roller speed minus the target speed difference of the tension zone, recursively generate the speed command of each upstream roller, and publish it as a speed command interface.

[0099] S44: When any speed command exceeds the actuator's allowed range, record the event and limit the speed at the execution layer.

[0100] This embodiment achieves precise matching between tension error correction and actual working conditions by simultaneously solving the first-order error convergence target and the tension dynamic model, avoiding overshoot or slow convergence problems caused by neglecting tension transmission loss in traditional control. The bottom-up recursive method with the downstream main section speed as the anchor point ensures the coordination and consistency of speeds in each tension zone, preventing speed conflicts caused by independent adjustment of multiple sections.

[0101] In one embodiment of the present invention, the current roll diameter is calculated based on thickness, initial unwinding radius, paper web running speed, and sampling period; and a feedforward torque is generated based on the current roll diameter, tension estimate, equivalent moment of inertia, angular acceleration, and frictional torque, including:

[0102] S51: Multiply the paper web running speed by the sampling period according to the sampling period and accumulate it over time to obtain the cumulative length; in the unwinding condition, subtract the product of the thickness and the cumulative length from the square of the initial unwinding radius and take the square root of the result after dividing by the constant pi to obtain the current unwinding radius; in the winding condition, add the square of the product of the winding core radius and the product of the thickness and the cumulative length and take the square root of the result after dividing by the constant pi to obtain the current winding radius; wherein, the unwinding and winding conditions are automatically identified according to the current speed direction.

[0103] S52, the angular velocity is obtained by dividing the paper web running speed by the current roll diameter, and the angular acceleration is obtained by dividing the difference between the current angular velocity and the previous angular velocity by the sampling period;

[0104] S53: Multiply the current tension estimate by the current roll diameter to obtain the tension torque term; multiply the equivalent moment of inertia by the angular acceleration to obtain the inertia compensation term; combine the Coulomb friction constant and viscosity coefficient with the angular velocity to obtain the friction torque term; add the above three terms to obtain the feedforward torque, and use this feedforward torque as an external interface to superimpose with the closed-loop output to drive the unwinding or winding motor; where, the equivalent moment of inertia represents the magnitude of the inertia of the component participating in the rotational motion against changes in the rotational motion state; the inertia compensation term is used to offset the inertial torque when the roll diameter accelerates or decelerates; the friction torque term is used to compensate for mechanical friction loss.

[0105] S54 performs engineering limiting and consistency checks on the current roll diameter and feedforward torque. When the current roll diameter exceeds the preset upper and lower limits, it is truncated and the event is recorded. When the feedforward torque exceeds the allowable upper limit, it is limited and the event is recorded.

[0106] This embodiment uses a dynamic roll diameter calculation model to track the nonlinear changes in roll diameter in real time during unwinding or rewinding, overcoming the tension control lag problem caused by the traditional fixed roll diameter assumption; the feedforward torque comprehensively considers tension balance, inertia compensation and friction loss, realizing the active prediction of the dynamic characteristics of roll diameter and significantly reducing tension fluctuations.

[0107] In one embodiment of the present invention, the speed command of each tension zone is limited, and the tension error convergence rate is adaptively adjusted according to the tension transmissibility index; when the tension transmissibility index is lower than a preset minimum threshold and the duration reaches a preset time period, constant speed escort is entered and execution S3 is returned, including:

[0108] Speed ​​commands in each tension zone are limited, cutting off speed commands exceeding the actuator's allowable range to preset upper and lower limits, and recording the limiting event; the preset upper and lower limits are determined by the motor's rated speed and the reducer characteristics.

[0109] The tension error convergence rate is adjusted in a piecewise linear manner based on the tension transmissibility index.

[0110] When the tension transferability index is lower than the preset minimum threshold but the duration has not reached the preset time period, the tension error convergence rate is fixed at the lower limit.

[0111] When the tension transferability index is lower than the preset minimum threshold and continues for a preset time period, it enters constant speed escort mode; the speed of the upstream roller and the downstream roller of the trigger tension zone are set to be the same, the speed difference recursion of the tension zone in step S5 is paused, and when the tension transferability index rises back to above the lower limit, it exits the escort mode and returns to execute S3.

[0112] When the tension estimate exceeds the preset exit threshold and continues for a preset time period, a stop signal is output and a fault event flag is set to force the equipment to stop running in order to avoid paper breakage or equipment damage.

[0113] When the tension zone enters the constant speed escort phase, an escort flag is set. A flag of 0 indicates that the upstream speed is generated normally according to the target speed difference; a flag of 1 indicates that the speed difference recursion is skipped, and the upstream roller's speed is directly made the same as its downstream roller's speed. In subsequent speed command recursion, the calculation path is determined based on the escort flag. By introducing the escort flag, the escort logic and the normal recursion logic are separated into layers, allowing for unified management of control behavior under abnormal conditions.

[0114] This embodiment directly protects the actuator from overload risks by limiting the speed command, ensuring hardware safety. It sets up three layers of safety protection: limiting, escort, and shutdown, forming a complete risk defense system and significantly improving the reliability of the high-speed paper feeding system under complex working conditions.

[0115] In one embodiment of the present invention, a dynamic balance control system for paper tension of a high-speed paper feeding mechanism is also provided, comprising:

[0116] The tension target generation module is used to obtain the width, thickness, elastic modulus, length of each tension zone, allowable stress of the paper web, main drive speed range, acceleration limit and final target tension, calculate the cross-sectional area, and determine and output the target tension reference for each tension zone;

[0117] The tension estimation and error module is used to collect raw tension signals downstream of each tension zone, obtain tension estimates after low-pass filtering, and compare them with the target tension benchmark to obtain the tension error.

[0118] The tension transferability calculation module is used to collect data on wrap angle, normal clamping force, roller linear speed, vacuum pressure, and roller surface roughness, and to calculate the tension transferability index.

[0119] The tension dynamic modeling module is used to map the tension transferability index to the leakage coefficient and establish a tension dynamic model including the leakage term based on the paper web parameters and the upstream and downstream roller linear speeds. The tension dynamic model outputs the tension derivative in the continuous time domain.

[0120] The speed command generation module is used to set the tension error convergence rate, calculate the target speed difference based on the leakage coefficient, tension dynamic model and tension error, and generate speed commands from bottom to top with the speed of the downstream main section as the speed anchor point.

[0121] The feedforward torque calculation module is used to calculate the current roll diameter based on thickness, initial unwinding radius, paper web running speed and sampling period, and to generate feedforward torque based on the current roll diameter, tension estimate, equivalent moment of inertia, angular acceleration and friction torque.

[0122] The adaptive amplitude limiting and escort module is used to limit the speed command of each tension zone and adaptively adjust the tension error convergence rate according to the tension transferability index. When the tension transferability index is lower than the preset minimum threshold and the duration reaches the preset time period, it enters constant speed escort and returns to the tension transferability calculation module.

[0123] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0124] The embodiments of the present invention have been described above, but the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of the present embodiments, all of which are within the protection scope of the present embodiments.

Claims

1. A method for dynamically balancing the tension of paper in a high speed paper feed mechanism, characterized by, The method comprises the following steps: S1, obtaining the width, thickness, elastic modulus, length of each tension zone, allowable stress of the paper web, equivalent moment of inertia, main transmission speed range, acceleration limit and final target tension, calculating the cross-sectional area, determining and outputting the target tension reference of each tension zone; S2, collecting the original tension signal downstream of each tension zone, obtaining the tension estimation value through low-pass filtering, and comparing the tension estimation value with the target tension reference to obtain the tension error; S3, collecting the wrap angle, normal pressure, linear speed of the roller, vacuum pressure and roughness of the roller surface, calculating the tension transmissibility index; Wherein, the wrap angle and the roughness of the roller surface are combined to obtain the traction enhancement coefficient, the linear speed of the roller surface and the vacuum pressure are combined to obtain the traction attenuation coefficient, the traction enhancement coefficient and the traction attenuation coefficient are calculated by ratio to obtain the effective friction coefficient; the effective friction coefficient is multiplied by the current normal pressure to obtain the tangential traction force, an index function is constructed by the ratio of the tangential traction force to the tension estimation value, and the output value of the index function is subtracted to obtain the tension transmissibility index; The calculation formula of the tension transmissibility index is: ； wherein, represents the tension transmissibility index of the i-th tension zone, i represents the tension zone index, and exp represents the exponential function, represents the static friction coefficient initial value, represents the wrap angle correction coefficient, represents the wrap angle, represents the roughness correction coefficient, represents the roll surface roughness, represents the speed correction coefficient, represents the vacuum correction coefficient, represents the roll surface linear speed, represents the vacuum pressure, represents the vacuum lower limit value, represents the normal pressure force, represents the tension, represents the tension estimate value, represents the minimum positive value; S4, mapping the tension transmissibility index to the leakage coefficient, and establishing a tension dynamic model containing a leakage term according to the paper web parameters and the linear speeds of the upstream and downstream rollers, the tension dynamic model outputs the tension derivative in the continuous time domain; S5, setting the tension error convergence rate, calculating the target speed difference according to the leakage coefficient, the tension dynamic model and the tension error, and generating the speed command from bottom to top with the speed of the most downstream main section as the speed anchor point; S6, calculating the current roll radius based on the thickness, the initial radius of unwinding, the paper web running speed and the sampling period, and generating the feed-forward torque based on the current roll radius, the tension estimation value, the equivalent moment of inertia, the angular acceleration and the friction torque; S7, limiting the speed command of each tension zone, and adaptively adjusting the tension error convergence rate according to the tension transmissibility index; when the tension transmissibility index is lower than the preset minimum threshold and the duration reaches the preset time period, entering the constant speed escort and returning to execute S3.

2. The paper-tension-dynamic-balance control method for a high-speed paper feed mechanism according to claim 1, characterized by, The calculation process of the cross-sectional area and the target tension reference of each tension zone comprises: S21, obtaining the cross-sectional area by calculating the product of the width and the thickness; S22, obtaining the target tension upper limit by calculating the product of the allowable stress of the paper web and the cross-sectional area; S23, taking the smaller value of the final target tension and the target tension upper limit as the target tension reference of each tension zone; and performing consistency check on the target tension reference and the target tension upper limit, if any target tension reference is greater than the target tension upper limit, rejecting the output and returning to S22 to re-determine the target tension upper limit; passing the consistency check and outputting the target tension reference of each tension zone.

3. The paper-tension-dynamic-balancing control method for a high-speed paper feed mechanism according to claim 1, characterized by, S3 further comprises: when the tension transmissibility index does not reach the first preset threshold, using the grey wolf optimization algorithm to iteratively optimize the final order of the normal pressure, the vacuum pressure and the wrap angle, and adjusting them in turn according to the final order, and recalculating the tension transmissibility index after each adjustment, and outputting the tension transmissibility index when it reaches the first preset threshold.

4. The paper-tension-dynamic-balancing control method of the high-speed paper feed mechanism according to claim 3, characterized by, The grey wolf optimization algorithm is used to iteratively optimize the final order of the normal pressure, the vacuum pressure and the wrap angle, comprising: The normal compression force, the vacuum pressure and the wrap angle are respectively set with an order weight value and a single-step adjustment ratio, and the order weight values of the three are determined in the order from small to large to determine the adjustment sequence; The normal compression force, the vacuum pressure and the wrap angle are respectively set with upper and lower limits, a change rate and a process safety constraint, and the order exceeding the constraint is truncated according to the upper and lower limits; A working condition set is constructed, and each candidate sequence in the working condition set is executed in turn according to the single-step adjustment ratio, the real-time re-calculation of the tension transmissibility index is performed, and it is judged whether the preset minimum threshold is reached, and the time reaching the first preset threshold, the parameter action frequency, the tension overrun and the limiting event are recorded; According to the weighted combination of the time reaching the first preset threshold, the parameter action frequency, the tension overrun and the limiting event, a comprehensive evaluation index is formed, the candidate sequences are sorted in ascending order, the first three are selected as the first wolf, the second wolf and the third wolf, and the new candidate sequence and the single-step adjustment ratio are generated according to the hunting and iterative updating rules of the grey wolf algorithm; When the change of the comprehensive evaluation index within the preset number of generations is less than the second preset threshold, the final sequence and the corresponding single-step adjustment ratio are output.

5. The paper-tension-dynamic-balancing control method for a high-speed paper feed mechanism according to claim 1, characterized by, S4 specifically comprises: S31, obtaining paper web parameters and upstream and downstream roll linear speeds, wherein the paper web parameters include paper web cross-sectional area, elastic modulus and tension zone length; S32, obtaining a corresponding leakage coefficient by multiplying 1 minus the tension transmissibility index by a preset maximum leakage coefficient; S33, obtaining an elastic gain term by dividing the product of the elastic modulus and the paper web cross-sectional area by the tension zone length, and obtaining a leakage term by multiplying the leakage coefficient by the tension estimate value; S34, obtaining a tension derivative in a continuous time domain by multiplying the difference between the upstream roll and the downstream roll linear speeds by the elastic gain term and subtracting the leakage term.

6. The paper-tension-dynamic-balancing control method for a high-speed paper feed mechanism according to claim 1, wherein A tension error convergence rate is set, a target speed difference is calculated according to the leakage coefficient, a tension dynamic model and a tension error, and a speed command is generated from the bottom to the top with the speed of the most downstream main section as a speed anchor point, including: S41, setting a tension error convergence rate for each tension zone, establishing a first-order error convergence target, and taking the tension error as the only error signal; S42, solving the target speed difference by simultaneously solving the tension dynamic model with the leakage term and the first-order error convergence target, wherein the product of the leakage coefficient and the tension estimate value is calculated first, then the product of the tension error convergence rate and the tension error is calculated, and the tension change demand is obtained by subtracting the latter from the former; and the tension change demand is equivalent to the target speed difference according to the proportional relationship that the product of the elastic modulus and the paper web cross-sectional area is divided by the tension zone length; S43, setting the speed of the most downstream main section as the speed anchor point, and in the order of the tension zone from downstream to upstream, setting the speed of the upstream roll as the speed of the downstream roll minus the target speed difference of the tension zone, recursively generating the speed command of each upstream roll, and publishing it as a speed command interface; S44, when any speed command exceeds the allowed range of the actuator, recording the event and limiting in the execution layer.

7. The paper-tension-dynamic-balancing control method for a high-speed paper feed mechanism according to Claim 1, wherein A current roll radius is calculated based on the thickness, the initial radius of unwinding, the paper web running speed and the sampling period, and a feedforward torque is generated based on the current roll radius, the tension estimate value, the equivalent moment of inertia, the angular acceleration and the friction torque, including: S51, multiply the paper running speed by the sampling period and accumulate the length over time; in the unwinding working condition, square the result of subtracting the product of the thickness and the accumulated length from the square of the unwinding initial radius and dividing by the constant of pi to obtain the current unwinding radius; in the winding working condition, square the result of adding the product of the thickness and the accumulated length to the square of the winding core radius and dividing by the constant of pi to obtain the current winding radius; S52, divide the paper running speed by the current winding diameter to obtain the angular velocity, divide the difference between the current angular velocity and the angular velocity at the last time by the sampling period to obtain the angular acceleration; S53, multiply the current tension estimation value by the current winding diameter to obtain the tension torque item, multiply the equivalent moment of inertia by the angular acceleration to obtain the inertia compensation item, and multiply the coulomb friction constant and the viscous coefficient by the angular velocity to obtain the friction torque item; add the above three items to obtain the feedforward torque, and use the feedforward torque as an external interface to superimpose the driving of the unwinding or winding motor with the closed-loop output; S54, perform engineering limiting and consistency checking on the current winding diameter and the feedforward torque, and when the current winding diameter exceeds the preset upper and lower limits, the current winding diameter is truncated and an event is recorded, and when the current feedforward torque exceeds the allowed upper limit, the current feedforward torque is limited and an event is recorded.

8. The paper-tension-dynamic-balancing control method for a high-speed paper feed mechanism according to Claim 1, wherein S7 specifically includes: limiting the speed command of each tension zone, truncating the speed command that exceeds the allowed range of the actuator to the preset upper and lower limits, and recording the limiting event; adjusting the tension error convergence rate in a piecewise linear manner according to the tension transmissibility index; when the tension transmissibility index is below the preset minimum threshold but the duration has not reached the preset time period, fixing the tension error convergence rate at the lower limit; when the tension transmissibility index is below the preset minimum threshold and continuously reaches the preset time period, entering the constant speed escort mode; set the speed of the upstream roll of the tension zone and the speed of the downstream roll of the tension zone to be the same, pause the speed difference recursion of the tension zone in S5, and when the tension transmissibility index rises above the lower limit, exit the escort mode and return to execute S3; when the tension estimation value exceeds the preset exit threshold and continuously reaches the preset time period, output a stop signal and set a fault event marker.

9. A high speed paper feed mechanism paper tension dynamic balance control system, characterized in that, The high-speed paper feeding mechanism paper tension dynamic balance control method comprises: a tension target generation module for obtaining the width, thickness, elastic modulus, length of each tension zone, paper allowable stress, main drive speed range, acceleration limit and final target tension, calculating the cross-sectional area, determining and outputting the target tension reference of each tension zone; a tension estimation and error module for collecting tension original signals downstream of each tension zone, obtaining tension estimation values through low-pass filtering, and obtaining tension errors by comparing the tension estimation values with the target tension reference; a tension transmissibility calculation module for collecting the wrap angle, normal pressing force, roll linear speed, vacuum pressure and roll surface roughness, and calculating the tension transmissibility index; a tension dynamic modeling module for mapping the tension transmissibility index to a leakage coefficient, and establishing a tension dynamic model containing a leakage term according to the paper width and the linear speeds of the upstream and downstream rolls, wherein the tension dynamic model outputs the tension derivative in the continuous time domain; The speed instruction generation module is configured to set a tension error convergence rate, calculate a target speed difference according to a leakage coefficient, a tension dynamic model and the tension error, and generate a speed instruction from the lowermost main section to the uppermost main section with the speed of the lowermost main section as an anchor point; The feedforward torque calculation module is configured to calculate a current roll radius based on a thickness, an initial unwinding radius, a paper web running speed and a sampling period, and generate a feedforward torque based on the current roll radius, a tension estimation value, an equivalent rotational inertia, an angular acceleration and a friction torque; The adaptive limiting and escorting module is configured to limit the speed instruction of each tension zone, and adaptively adjust the tension error convergence rate according to a tension transmissibility index; when the tension transmissibility index is lower than a preset minimum threshold and a duration reaches a preset time period, enter a constant speed escorting and return to execute the tension transmissibility calculation module.

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