A method for on-line identification and compensation of nonlinear error of shearing length of packaging material

Abstract

The application discloses a packaging material shearing length nonlinear error online identification and compensation method, and belongs to the technical field of industrial automation control. The method collects material tension, feeding displacement, actual shearing length and environmental temperature and humidity data, constructs a nonlinear error dynamic model containing a first-order term, a second-order term and a third-order term of the tension, adopts a recursive least square algorithm with a variable forgetting factor to identify model parameters online, predicts a next shearing cycle length error and calculates a feedforward compensation amount, simultaneously estimates a servo dynamic error additional compensation amount by using a disturbance observer, and corrects a feeding displacement set value after superposition. The application realizes online identification and active feedforward compensation of the shearing length nonlinear error, eliminates feedback lag, and controls the shearing length deviation within ±0.3 mm.

Description

Technical Field

[0001] This invention relates to the field of industrial automation control technology, and in particular to a method for online identification and compensation of nonlinear error in the shearing length of packaging materials. Background Technology

[0002] In packaging industry production, the fixed-length shearing of continuous roll materials (such as plastic film, composite film, paper, aluminum foil, etc.) is a core step in processes such as bag making, slitting, and labeling. A typical fixed-length shearing system for packaging materials consists of an unwinding mechanism, a tension adjustment mechanism, a feeding mechanism, a shearing mechanism, and a control system. During operation, the feeding mechanism feeds the roll material from the unwinding end at a set speed. After passing through the tension adjustment area, it enters the shearing area. The control system issues a shearing command according to the preset shearing length, driving the shearing mechanism to complete the cutting.

[0003] The current mainstream shear length control methods in the industry can be summarized into the following two categories:

[0004] The first type is a semi-closed-loop control method based on pulse counting. This method records the rotation angle of the feeding roller using a rotary encoder coaxially mounted on the feeding roller. The angle is converted into the feeding length based on the nominal circumference of the feeding roller. Shearing is triggered when the accumulated pulse count reaches a preset value. The fundamental drawback of this method is that the packaging material itself is a viscoelastic body, and it will elastically elongate under tensile tension during feeding. Furthermore, the elastic modulus varies between different batches of material, reducing the material roll diameter causes tension fluctuations, and there is micro-slippage between the feeding roller and the material. These factors lead to a deviation between the actual fed material length and the length calculated based on the encoder pulse count. Practice shows that the shearing length error controlled solely by pulse counting can reach ±2mm to ±5mm, which is insufficient to meet the precision requirements of high-end packaging bag making.

[0005] The second type is the fully closed-loop feedback correction control method. This method adds a length encoder or visual inspection device at the shearing exit to measure the actual shearing length, compares the measured value with the set value, and uses a proportional-integral-derivative controller or fuzzy controller to correct the feeding speed or shearing trigger time. Chinese patent document CN106325195A discloses a fully closed-loop shearing machine with calibration compensation, which achieves closed-loop compensation control by feeding back the length signal to the PLC through a length encoder. Chinese patent document CN116352171A discloses an intelligent control system for flying shears, which uses a visual recognition device to measure the actual length and optimizes the flying shear's start-up time by comparing the differences multiple times. Chinese patent document CN202310247123 discloses an automatic compensation method for film winding, which adjusts the speed reference of the film pulling unit by acquiring the swing angle of the buffer roller in real time.

[0006] While the aforementioned closed-loop feedback correction method improves shearing accuracy to some extent, it suffers from the following fundamental technical defects:

[0007] (1) Feedback correction has an unavoidable time lag. From the completion of a shearing operation to the measurement of the actual length, the calculation of the error, and the execution of the compensation command, at least one shearing cycle is required. On high-speed production lines, when material properties or operating conditions change, this lag leads to the continuous production of out-of-tolerance products over several cycles, resulting in material waste.

[0008] (2) The error model is oversimplified. Existing methods simply attribute shear length error to feeding speed deviation or triggering time deviation, without considering the deeper physical mechanisms that cause the error. The stress-strain relationship of packaging materials under tension exhibits nonlinear viscoelastic characteristics. The elastic modulus of the material varies with the amount of tension, temperature, and humidity, and there is a nonlinear coupling relationship between tension fluctuation and material elongation. These factors together cause the error to exhibit time-varying nonlinear characteristics, which cannot be accurately described by simplified linear models.

[0009] (3) Lack of predictive ability for the dynamic evolution of errors. Existing methods can only perform ex-post correction based on the errors that have occurred, and cannot predict the error trend of the next cycle. When the tension changes abruptly (e.g., during roll changing, acceleration or deceleration), the control system cannot respond in advance, resulting in a serious decrease in shearing accuracy during the transition process.

[0010] (4) Error influencing factors cannot be identified online. Factors such as changes in material batches, changes in environmental temperature and humidity, and mechanical wear can change the error characteristics of the system, but existing methods lack the ability to identify them online and cannot automatically update compensation parameters to adapt to changes in system characteristics during operation.

[0011] In summary, existing technologies suffer from shortcomings when dealing with the nonlinear, time-varying, and multi-factor coupled characteristics of packaging material shear length errors, including feedback lag, model mismatch, lack of predictive ability, and inability to identify errors online. There is an urgent need for a control method capable of identifying the nonlinear characteristics of errors in real time during production operations and performing feedforward prediction and proactive compensation for these errors. Summary of the Invention

[0012] To achieve the above objectives, the present invention provides an online identification and compensation method for nonlinear error in the shear length of packaging materials, comprising the following steps:

[0013] Step 1: In the packaging material fixed-length shearing system, material tension data is collected by tension sensor, feeding displacement data is collected by rotary encoder, actual shearing length data is collected by laser rangefinder, and ambient temperature and relative humidity data are collected by temperature and humidity sensor.

[0014] Step 2: Based on the viscoelastic mechanical properties of the packaging material under tension, construct a nonlinear error dynamic model to describe the nonlinear relationship between shear length error and material tension and feeding displacement. The nonlinear error dynamic model includes a first-order, second-order, and third-order term of the average material tension, as well as a first-order term of total feeding displacement, a first-order term of ambient temperature, and a first-order term of ambient relative humidity.

[0015] Step 3: After each shearing is completed, the length error observation value is calculated based on the difference between the actual shearing length and the preset shearing length. The model parameters of the nonlinear error dynamic model are identified and updated online using a recursive least squares algorithm with a variable forgetting factor. The variable forgetting factor is dynamically adjusted according to the magnitude of the one-step prediction error.

[0016] Step 4: Using the updated model parameters and the currently collected material tension data, ambient temperature data, and ambient relative humidity data, predict the length error of the next shearing cycle, and calculate the feedforward compensation amount of the feeding displacement based on the predicted length error;

[0017] Step 5: Construct a disturbance observer for the feeding servo system, estimate the equivalent load disturbance torque referred to the motor shaft online, calculate the feeding displacement error caused by the servo dynamic error based on the equivalent load disturbance torque, and invert the feeding displacement error as the additional compensation amount for the servo dynamic error.

[0018] Step 6: Add the feedforward compensation amount of the feeding displacement to the additional compensation amount of the servo dynamic error to obtain the total feeding compensation amount. Add the total feeding compensation amount to the feeding displacement setting value of the next shearing cycle. The control system uses the corrected feeding displacement setting value as the target value of feeding control. When the cumulative value of the feeding displacement encoder reaches the corrected feeding displacement setting value, a shearing command is issued.

[0019] Preferably, in step 1:

[0020] The tension sensor is installed on the feeding path in the tension adjustment area between the unwinding mechanism and the feeding mechanism. The tension sensor outputs an analog voltage signal from 0V to 10V. The analog voltage signal is converted into a digital tension value by an analog-to-digital converter, and the digital tension value is denoted as [value missing]. The unit is Newton, and the sampling frequency of the digital tension value is set to 1000Hz. Indicates the first Each sampling time;

[0021] The rotary encoder is an incremental rotary encoder, which is mounted on the drive motor shaft of the feeding mechanism. The incremental rotary encoder outputs A-phase pulse signals and B-phase pulse signals. The control system performs a 4x frequency multiplication on the A-phase and B-phase pulse signals to obtain the encoder pulse count value. Multiplying the encoder pulse count value by the conversion factor between the nominal circumference of the feeding roller and the reduction ratio yields the feeding displacement data, which is denoted as […]. The unit is millimeters;

[0022] The laser rangefinder is installed at the exit of the shearing mechanism. After each shearing action, the laser rangefinder measures the actual length of the cut material. The actual shear length measured after the first shearing is denoted as . The unit is millimeters;

[0023] The temperature and humidity sensor is a digital temperature and humidity sensor, which is installed on the feeding path and located between the tension sensor and the feeding mechanism. The digital temperature and humidity sensor measures the ambient temperature and relative humidity of the packaging material's environment in real time. The ambient temperature at each sampling time is recorded as . The unit is Celsius, the first The relative humidity of the environment at each sampling time is recorded as follows: Expressed as a percentage;

[0024] The material tension data, the feeding displacement data, the actual shearing length data, the ambient temperature data, and the ambient relative humidity data are stored in the data buffer of the control system according to a unified timestamp.

[0025] Preferably, the process of constructing the nonlinear error dynamic model in step 2 includes:

[0026] Establish actual shear length With preset cutting length Length error Relationship:

[0027]

[0028] Establish length error The compositional relationship:

[0029]

[0030] In the formula, This represents the nonlinear error component caused by material tension, expressed in millimeters. This represents the inherent error component of the system, expressed in millimeters.

[0031] Nonlinear error components caused by material tension Described using a cubic polynomial structure:

[0032]

[0033] In the formula, For the first The average value of material tension over one shear cycle, in Newtons; The coefficient of the first term is expressed in millimeters per Newton. The coefficient of the quadratic term is expressed in millimeters per square Newton. represents the coefficient of the cubic term, measured in millimeters per cubic Newton;

[0034] No. The average material tension over one shear cycle Calculated from all material tension samples during this shear cycle:

[0035]

[0036] In the formula, For the first The starting sampling number of each shearing cycle For the first The end sampling sequence number of each shearing cycle For the first Number of sampling points within a shearing cycle;

[0037] System inherent error components The following structure is used for description:

[0038]

[0039] In the formula, For the first Total feed displacement within a shearing cycle, in millimeters; The displacement error coefficient is dimensionless. This is the temperature effect coefficient, expressed in millimeters per degree Celsius. This is the humidity influence coefficient, expressed as a percentage per millimeter.

[0040] Nonlinear error components caused by material tension With the inherent error components of the system Adding them together yields the complete expression for the nonlinear error dynamic model:

[0041]

[0042] Define parameter vector and regression vector They are respectively:

[0043]

[0044]

[0045] The nonlinear error dynamic model is then expressed in linear regression form:

[0046]

[0047] Preferably, the specific process of using a recursive least squares algorithm with a variable forgetting factor to identify and update the model parameters of the nonlinear error dynamic model online in step 3 includes:

[0048] Each time the first The actual shear length was measured after the second shearing. Then, calculate the first... Observed value of length error during secondary shearing :

[0049]

[0050] Construct the first The regression vector of the second shearing , of which Total feeding displacement within one shearing cycle The ambient temperature is calculated from the encoder pulse count value. Take the first The average value of all ambient temperature samples within each shear cycle, and the ambient relative humidity. Take the first The average value of all environmental relative humidity samples within each shearing cycle;

[0051] Calculate the gain matrix according to the following recursive update formula. Parameter estimation vector Covariance Matrix :

[0052]

[0053]

[0054]

[0055] In the formula, The variable forgetting factor is defined by the following dynamic adjustment formula:

[0056]

[0057] In the formula, The lower limit of the forgetting factor is set at 0.95; This is the prediction error for one step. The error variance reference value is set to 1.0;

[0058] covariance matrix The initial value is set to ,in It is a 6th-order identity matrix; the initial values ​​of the parameter estimation vector are set to... .

[0059] Preferably, the specific process of predicting the length error of the next shearing cycle and calculating the feedforward compensation amount of the feeding displacement using the updated model parameters in step 4 includes:

[0060] After completing the first The parameter estimation vector is obtained by shearing and updating once. Then, collect the current time, i.e., the [number]th [time]. Material tension at the beginning of each shear cycle Collect the ambient temperature at the current moment. and ambient relative humidity , obtain the The preset total feed displacement for each shearing cycle ;

[0061] Construct the first The predicted regression vector of the second shearing , due to the The second cut is not yet complete, the first... The average material tension over one shear cycle Using the material tension at the current moment As an approximation:

[0062]

[0063] Using the latest parameter estimation vector Predicting the first Length error of the second cut :

[0064]

[0065] Based on the predicted length error Calculate the feedforward compensation amount for the feed displacement :

[0066]

[0067] In the formula, For compensation gain coefficient, compensation gain coefficient The value ranges from 0.85 to 1.15.

[0068] Preferably, the specific process of constructing the disturbance observer of the feeding servo system and estimating the equivalent load disturbance torque online in step 5 includes:

[0069] Establish a simplified first-order dynamic model of the feeding servo system:

[0070]

[0071] In the formula, Feeding speed, in millimeters per second; The coefficient of viscous friction is expressed in Newton-millimeter-second (N·m·s). The equivalent moment of inertia is expressed in kilograms per square millimeter. This is the torque constant, expressed in Newton-millimeter per ampere. This refers to quadrature-axis current, measured in amperes. The equivalent load disturbance torque referred to the motor shaft is expressed in Newton-millimeter (N·mm).

[0072] The state equation for the perturbation observer is designed as follows:

[0073]

[0074] In the formula, This is an estimated feed rate, in millimeters per second. This is an estimate of the equivalent load disturbance torque, in Newton-millimeter units. The actual feeding speed is obtained by differential calculation of the feedback signal from the incremental rotary encoder, in millimeters per second. The gain coefficient of the first observer. The gain coefficient of the second observer;

[0075] First observer gain coefficient Second observer gain coefficient Tuning was performed according to the observer pole placement method, configuring the two closed-loop poles of the perturbation observer as follows: and .

[0076] Preferably, the specific process of calculating the feeding displacement error caused by the servo dynamic error based on the equivalent load disturbance torque in step 5, and then inverting the feeding displacement error as the additional compensation amount for the servo dynamic error, includes:

[0077] In the Within each shear cycle, the estimated value of the equivalent load disturbance torque The feed displacement error caused by the load disturbance is calculated by accumulating the errors. :

[0078]

[0079] In the formula, For the first The start time of each shearing cycle, For the first The end time of each shearing cycle, The control cycle of the control system, in milliseconds;

[0080] Feed displacement error caused by load disturbance Take the opposite number as the additional compensation amount for servo dynamic error. :

[0081]

[0082] Preferably, the specific process of adding the feedforward compensation amount of the feeding displacement to the additional compensation amount of the servo dynamic error in step 6 to obtain the total feeding compensation amount, and then adding the total feeding compensation amount to the feeding displacement set value of the next shearing cycle, includes:

[0083] Calculate the first Total compensation for each shearing operation :

[0084]

[0085] Calculate the corrected feed displacement setpoint :

[0086]

[0087] In the formula, Based on preset shearing length Conversion of basic feeding displacement, basic feeding displacement Based on the preset cutting length Multiply by the feed roller circumference compensation coefficient to obtain;

[0088] The control system in the In each shearing cycle, the corrected feed displacement setting value is used. As the target value for feeding control, the cumulative value of the feeding displacement fed back by the incremental rotary encoder is compared in real time with the corrected feeding displacement setpoint. When the cumulative value of the feeding displacement reaches the corrected feeding displacement set value... At that time, the control system sends a shearing command to the shearing mechanism, driving the shearing mechanism to complete the first shearing step. The next cutting action.

[0089] Preferably, the online identification and compensation method for nonlinear error in the shear length of packaging materials further includes the following steps:

[0090] Step 7: After completing the first step After the first shearing, the laser range sensor measures the first... Actual shear length of the second ,Will Updated to Then return to step 3, use the new actual shear length data to recursively update the model parameters of the nonlinear error dynamic model, and then continue to execute steps 4 to 6 to predict the next step. The length error of each shearing is calculated and the compensation amount of the feeding displacement is calculated. This process is repeated to achieve continuous online identification and successive feedforward prediction compensation of nonlinear errors during continuous fixed-length shearing of packaging materials.

[0091] During the cyclic execution process, the control system synchronously segments and stores the material tension data, feeding displacement data, ambient temperature data, and ambient relative humidity data from step 1 according to the shearing cycle. The data segment of each shearing cycle is identified by the timestamp of the first sampling time within that shearing cycle. When executing step 3, the data segment corresponding to the shearing cycle is extracted from the data buffer to calculate the average material tension, total feeding displacement, average ambient temperature, and average ambient relative humidity.

[0092] Preferably, when the type of packaging material changes, the compensation gain coefficient... Adjustments should be made based on the elastic modulus and thickness of the replaced packaging material;

[0093] For polyethylene film packaging materials with an elastic modulus of less than 500 MPa and a thickness of less than 0.1 mm, the compensation gain coefficient is... Take a value between 1.00 and 1.05;

[0094] For polyester film packaging materials with an elastic modulus between 500 MPa and 1500 MPa and a thickness between 0.1 mm and 0.3 mm, the compensation gain coefficient... Take a value between 0.95 and 1.00;

[0095] For paper-based packaging materials with an elastic modulus greater than 1500 MPa and a thickness greater than 0.3 mm, the compensation gain coefficient... Take a value between 0.90 and 0.95;

[0096] After changing the type of packaging material, the control system will estimate the parameter vector. Reset to initial value and the covariance matrix Reset to initial value This eliminates the influence of historical data from the previous type of packaging material on the current identification process, enabling the recursive least squares algorithm with a variable forgetting factor to quickly converge to new model parameters that adapt to the characteristics of the replaced packaging material within the initial few shearing cycles.

[0097] The beneficial effects of this invention are:

[0098] 1. This invention constructs a nonlinear error dynamic model that includes first, second, and third terms of material tension, accurately describing the nonlinear characteristics of the stress-strain relationship of packaging materials under tensile conditions. It also employs a recursive least squares algorithm with a variable forgetting factor to identify and update the model parameters online, overcoming the limitation of existing methods that only use linear error models. This enables the model to adaptively track changes in material properties, environmental temperature and humidity, and equipment state drift, significantly improving the prediction accuracy of shear length error.

[0099] 2. This invention utilizes the nonlinear error model obtained through online identification to predict the length error of the next shearing cycle and calculate the feedforward compensation amount of the feeding displacement before each shearing begins. This transforms the traditional passive feedback correction into active feedforward prediction compensation, completely eliminating the inherent time lag problem of feedback correction. It can still maintain stable and high-precision shearing length control under transitional conditions such as sudden changes in material tension, roll changing, or acceleration and deceleration.

[0100] 3. Based on the material domain nonlinear error feedforward compensation, this invention further constructs a disturbance observer for the feeding servo system, estimates the equivalent load disturbance torque referred to the motor shaft online, and calculates the additional compensation amount for servo dynamic error, forming a dual-domain collaborative compensation mechanism of the material domain and servo domain. The superposition of the two produces a synergistic effect, which controls the shearing length deviation within ±0.3 mm, improving the accuracy by more than 50% compared with existing methods. Attached Figure Description

[0101] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0102] Figure 1 This is a schematic diagram of the structure and data acquisition device arrangement of the packaging material fixed-length shearing system of the present invention;

[0103] Figure 2 This is a flowchart of the steps of the method of the present invention. Detailed Implementation

[0104] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0105] Please see Figures 1-2 This invention provides an online identification and compensation method for nonlinear error in the shearing length of packaging materials. This method is applicable to a fixed-length shearing device for packaging materials that includes an unwinding mechanism, a tension adjustment mechanism, a feeding mechanism, a shearing mechanism, and a control system.

[0106] System composition and data acquisition device

[0107] Prior to implementing this method, the packaging material fixed-length shearing system was equipped with the following data acquisition devices.

[0108] A tension sensor is installed in the tension adjustment area between the unwinding mechanism and the feeding mechanism. The tension sensor is used to detect the tensile tension of the packaging material on the feeding path in real time, and outputs an analog voltage signal from 0V to 10V. This analog voltage signal is converted into a digital quantity by an analog-to-digital converter to obtain the material tension data. The material tension data at the k-th sampling time is denoted as (T(k)), with the unit being N, and the sampling frequency is set to 1000Hz.

[0109] An incremental rotary encoder is coaxially mounted on the drive motor shaft of the feeding mechanism. The incremental rotary encoder outputs A-phase pulse signals and B-phase pulse signals. The control system performs a 4x frequency multiplication on the A-phase pulse signals and B-phase pulse signals to obtain the encoder pulse count value. The encoder pulse count value is multiplied by the conversion factor between the nominal circumference of the feeding roller and the reduction ratio to obtain the feeding displacement data. The feeding displacement data at the k-th sampling time is denoted as (x(k)), in mm.

[0110] A laser rangefinder is installed at the exit of the shearing mechanism. After each shearing action, the laser rangefinder measures the actual length of the cut packaging material. The actual shearing length measured after the i-th shearing action is denoted as . The unit is mm.

[0111] A digital temperature and humidity sensor is installed on the feeding path between the tension sensor and the feeding mechanism. The digital temperature and humidity sensor measures the ambient temperature and relative humidity of the environment surrounding the packaging material in real time. The ambient temperature at the k-th sampling time is denoted as... The unit is ℃; the relative humidity of the environment at the kth sampling time is denoted as (H(k)), expressed as a percentage.

[0112] The aforementioned material tension data, feeding displacement data, actual shearing length data, ambient temperature data, and ambient relative humidity data are stored in the data buffer of the control system according to a unified timestamp for subsequent steps to access.

[0113] Step 1: Collect multi-source operational data of the packaging material fixed-length shearing system

[0114] During the continuous operation of the packaging material fixed-length shearing system, the control system synchronously acquires material tension data (T(k)) and feeding displacement data (x(k)) at a sampling frequency of 1000Hz. The material tension data is obtained by analog-to-digital conversion from the output signal of the tension sensor, and the feeding displacement data is obtained by frequency multiplication and conversion from the feedback pulses of the incremental rotary encoder. Simultaneously, a digital temperature and humidity sensor acquires ambient temperature data at the same sampling frequency. And ambient relative humidity data (H(k)). After each shearing operation, the laser rangefinder measures the actual shearing length. This data is stored in relation to the index number i of the current cut.

[0115] The above data acquisition process provides a basic data source for subsequent error modeling and online identification. Material tension data is used to calculate the average tension during the shearing cycle, reflecting the tensile state of the material; feed displacement data is used to determine the start and end times of the shearing cycle and the total feed displacement; ambient temperature data and ambient relative humidity data are used to correct for changes in the material's elastic modulus due to environmental factors; actual shearing length data is used to calculate the length error observation value, driving the recursive update of the model parameters.

[0116] Step 2: Construct a nonlinear error dynamic model describing the nonlinear relationship between shear length error, material tension, and feed displacement.

[0117] During the feeding process, packaging materials undergo elastic elongation under tension, exhibiting a viscoelastic nonlinear stress-strain relationship. When the tension varies within a small range, the elongation is approximately linearly related to the tension; however, when the tension fluctuates significantly or reaches a high level, the material enters the nonlinear deformation region. Furthermore, factors such as manufacturing tolerances of the feeding roller diameter, encoder quantization errors, and mechanical transmission clearances introduce inherent system errors. Changes in environmental temperature and humidity causing a shift in the material's elastic modulus also affect these error characteristics.

[0118] Based on the above physical mechanism, the actual shear length is established. With preset cutting length The relationship between them:

[0119]

[0120] Among them, length error Nonlinear error components caused by material tension and system inherent error components Superposition composition:

[0121]

[0122] Nonlinear error components caused by material tension Described using a cubic polynomial structure:

[0123]

[0124] In the formula, The average material tension during the i-th shear cycle is calculated using the following formula:

[0125]

[0126] in Let be the starting sampling number of the i-th shearing cycle. Let be the end sampling number of the i-th shearing cycle. This represents the number of sampling points within that period.

[0127] System inherent error components Described as a linear combination of total feed displacement, ambient temperature, and ambient relative humidity:

[0128]

[0129] In the formula, The total feeding displacement during the i-th shearing cycle is determined by the cumulative value of the feeding displacement data during that cycle. The displacement error coefficient is dimensionless. This is the temperature influence coefficient, with units of mm / ℃; The humidity influence coefficient is expressed in mm / %.

[0130] Combining the above two equations, we obtain the complete expression for the nonlinear error dynamic model:

[0131]

[0132] To facilitate the implementation of the recursive estimation algorithm, a parameter vector is defined. and regression vector

[0133]

[0134]

[0135] The nonlinear error dynamic model can then be expressed in linear regression form:

[0136]

[0137] This model incorporates the nonlinear deformation characteristics of packaging materials, inherent system biases, and environmental influencing factors into a unified parameterized framework, providing a structural basis for subsequent online identification.

[0138] Step 3: Use a recursive least squares algorithm with a variable forgetting factor to identify and update the model parameters of the nonlinear error dynamic model online.

[0139] Each time, the i-th cut is completed and the actual cut length is obtained. Then, immediately perform a recursive update of the model parameters. First, calculate the length error observation value for the i-th shearing:

[0140]

[0141] Construct the regression vector for the i-th shearing .in, The average tension is calculated using the formula in step 2. The value is obtained by subtracting the initial value from the final value of the feed displacement data within the shearing cycle; ambient temperature. The arithmetic mean of all ambient temperature samples within the shearing cycle is taken; the ambient relative humidity (H(i)) is taken as the arithmetic mean of all ambient relative humidity samples within the shearing cycle.

[0142] The parameter estimation vector is updated using a recursive least squares algorithm with a variable forgetting factor. The recursive formula is as follows:

[0143]

[0144]

[0145]

[0146] In the formula, Here is the gain matrix. Let covariance matrix be the variance matrix. It is a variable forgetting factor.

[0147] Variable forgetting factor The prediction error is dynamically adjusted based on the magnitude of the one-step prediction error. The adjustment formula is as follows:

[0148]

[0149] In the formula, The lower limit of the forgetting factor is set at 0.95; This is the prediction error for one step. The error variance reference value is set to 1.0.

[0150] covariance matrix The initial value is set to ,in It is a 6th-order identity matrix. The initial values ​​of the parameter estimation vector are set to... .

[0151] The dynamic adjustment mechanism of the variable forgetting factor ensures that the forgetting factor approaches 1 when the system is stable, maintaining the smoothness and stability of parameter estimation. When a sudden change occurs in the system, leading to an increase in prediction error, the forgetting factor decreases, accelerating the forgetting of outdated data and improving parameter tracking speed. The recursive nature of the recursive least squares algorithm allows parameter updates to be completed quickly within each shearing cycle, eliminating the need to store large amounts of historical data and meeting the real-time requirements of industrial sites.

[0152] Step 4: Predict the length error of the next shearing cycle and calculate the feedforward compensation amount of the feed displacement.

[0153] After completing the i-th shearing and updating the parameter estimation vector Then, at the start of the (i+1)th shear cycle, the current material tension is collected. Ambient temperature and ambient relative humidity And obtain the preset total feeding displacement for the (i+1)th shearing cycle. .

[0154] Since the (i+1)th shearing has not yet been performed, the average tension within this shearing cycle cannot be obtained. This method uses the material tension at the current moment. As an approximation of the average tension, construct the predicted regression vector for the (i+1)th shear:

[0155]

[0156] Using the latest parameter estimation vector Predicting the length error of the (i+1)th shear:

[0157]

[0158] The feedforward compensation amount for the feeding displacement is calculated based on the predicted length error.

[0159]

[0160] In the formula, This is the compensation gain coefficient. The compensation gain coefficient is used to correct the proportional deviation between the prediction error and the actual compensation effect, and its value is related to the type of packaging material. For plastic film packaging materials, the compensation gain coefficient is 0.95 to 1.05; for paper packaging materials, the compensation gain coefficient is 0.90 to 1.10.

[0161] This step achieves a shift from passive feedback correction to active feedforward compensation by predicting the length error that will occur in the next shearing cycle in advance and converting it into a feedforward correction amount for the feeding displacement, thus eliminating the inherent time lag in feedback control.

[0162] Step 5: Construct a disturbance observer for the feeding servo system and estimate the equivalent load disturbance torque online, and calculate the additional compensation for servo dynamic error.

[0163] During the feeding process, dynamic deviations in the servo drive system caused by load disturbances and speed tracking errors can also affect the cutting length accuracy. To compensate for this error, a disturbance observer is constructed to estimate the equivalent load disturbance torque referred to the motor shaft in real time.

[0164] The simplified first-order dynamic model of the feeding servo system is as follows:

[0165]

[0166] In the formula, (v(t)) is the feeding speed, in mm / s; (B) is the viscous friction coefficient, in N·mm·s; (J) is the equivalent moment of inertia, in kg·mm². This is the torque constant, expressed in N·mm / A. This refers to the quadrature-axis current, measured in amperes (A). The equivalent load disturbance torque referred to the motor shaft is expressed in N·mm.

[0167] The state equation for the perturbation observer is designed as follows:

[0168]

[0169] In the formula, This is an estimated value for the feeding speed; This is the estimated value of the equivalent load disturbance torque; The actual feeding speed is obtained by differential calculation from the feedback signal of the incremental rotary encoder; The gain coefficient of the first observer. This is the gain coefficient of the second observer.

[0170] Observer gain coefficient and The pole placement method is used for tuning. The two closed-loop poles of the disturbance observer are set to -50 rad / s and -100 rad / s, respectively, to ensure the convergence speed and stability of the equivalent load disturbance torque estimation. Based on the desired pole locations and system parameters, the following calculations are performed: , .

[0171] The estimated value of the equivalent load disturbance torque during the (i+1)th shear cycle. The resulting feed displacement error is calculated cumulatively:

[0172]

[0173] In the formula, This represents the start time of the (i+1)th shearing cycle. This represents the end time of the (i+1)th shearing cycle. This represents the control cycle of the control system, with a value of 1ms.

[0174] The opposite of the above displacement error is taken as the additional compensation amount for servo dynamic error:

[0175]

[0176] The disturbance observer performs online estimation of the equivalent load disturbance torque that cannot be directly measured, and incorporates the displacement error caused by the disturbance into the compensation system, thereby realizing feedforward correction of servo dynamic error.

[0177] Step 6: Calculate the total feed compensation and perform feedforward prediction compensation.

[0178] The feed forward compensation amount obtained in step 4 Additional compensation amount for servo dynamic error obtained in step 5 Adding them together, we get the total feed compensation for the (i+1)th shear:

[0179]

[0180] Calculate the corrected feed displacement setpoint

[0181]

[0182] In the formula, Based on preset shearing length The calculated basic feeding displacement is obtained by multiplying the preset shearing length by the feeding roller circumference compensation coefficient, which is determined through offline calibration.

[0183] During the (i+1)th shearing cycle, the control system uses the corrected feed displacement setpoint. As the target value for feeding control, the cumulative value of the feeding displacement fed back by the incremental rotary encoder is compared in real time with... When the cumulative value of the feeding displacement reaches the corrected feeding displacement setpoint, the control system issues a shearing command to drive the shearing mechanism to complete the cutting action.

[0184] This step combines nonlinear error compensation in the material domain with dynamic error compensation in the servo domain to form a feedforward compensation mechanism that integrates the two domains of material domain and servo domain.

[0185] Step 7: Repeatedly perform online identification and compensation.

[0186] After the (i+1)th shearing operation, the laser rangefinder measures the actual shearing length of the (i+1)th shearing operation. The index i is updated to i+1, and the process returns to step 3 to execute a new round of model parameter recursive update and subsequent prediction compensation. This process is repeated to achieve continuous online identification and successive feedforward prediction compensation of nonlinear errors during continuous fixed-length shearing of packaging materials.

[0187] During the cyclic execution, the control system synchronously segments and stores the material tension data, feeding displacement data, ambient temperature data, and ambient relative humidity data collected in step 1 according to the shearing cycle. Each data segment of the shearing cycle is identified by the timestamp of the first sampling time in that cycle. Step 3 extracts the corresponding data segment from the data buffer to calculate the average tension, total feeding displacement, average ambient temperature, and average ambient relative humidity.

[0188] When the type of packaging material changes, the compensation gain coefficient Adjustments are made based on the elastic modulus and thickness of the replaced packaging material. For polyethylene film packaging materials with an elastic modulus less than 500 MPa and a thickness less than 0.1 mm, the compensation gain coefficient is set to 1.00 to 1.05; for polyester film packaging materials with an elastic modulus between 500 MPa and 1500 MPa and a thickness between 0.1 mm and 0.3 mm, the compensation gain coefficient is set to 0.95 to 1.00; and for paper packaging materials with an elastic modulus greater than 1500 MPa and a thickness greater than 0.3 mm, the compensation gain coefficient is set to 0.90 to 0.95. After material replacement, the control system estimates the parameter vector... Covariance Matrix Reset to initial values ​​respectively and This eliminates the interference of historical data on the identification of new material properties, enabling the algorithm to quickly converge to model parameters that adapt to the properties of the new material.

[0189] Technical Effect Description

[0190] This method accurately characterizes the nonlinear stress-strain relationship of packaging materials under tension by establishing a nonlinear error dynamic model that includes a cubic tension nonlinear term, overcoming the limitations of existing linear error compensation models. The recursive least squares algorithm with a variable forgetting factor enables the model parameters to adaptively track the slow changes in material properties, environmental conditions, and equipment status online, without requiring manual intervention or downtime calibration.

[0191] The prediction and feedforward compensation of the error in the next shearing cycle based on the online identification model completely eliminates the time delay problem that cannot be eliminated in traditional feedback correction methods. The introduction of the perturbation observer further compensates for the influence of the dynamic error of the servo drive system on the shearing length, forming a synergistic effect with the nonlinear error compensation in the material domain.

[0192] Industrial field applications show that this method can control the shearing length deviation within ±0.3mm, which is significantly higher than the accuracy level achievable by existing semi-closed-loop control methods and fully closed-loop feedback correction methods, effectively reducing material waste and scrap rate in the packaging production process.

[0193] Example

[0194] This embodiment uses a typical vertical packaging machine roll film fixed-length feeding and shearing system as an application scenario. This system is used to cut rolls of composite plastic film to a preset length for subsequent bag-making processes. The system consists of an unwinding mechanism, a tension adjustment mechanism with a tension swing arm, a servo motor-driven feeding roller pair, a rotary cutter shearing mechanism, and a programmable logic controller. The preset shearing length... The setting is 200.0mm, and the production line operating speed is set to 120 shearing cycles per minute.

[0195] Step 1: Collect multi-source operational data of the packaging material fixed-length shearing system

[0196] A strain gauge tension sensor is installed on the feeding path in the tension adjustment area between the unwinding mechanism and the feeding mechanism. The tension sensor has a range of 0N to 200N and outputs an analog voltage signal of 0V to 10V. This analog voltage signal is converted into a digital tension value by a 16-bit analog-to-digital converter. The digital tension value at the (k)th sampling time is denoted as (T(k)), with units of N, and the sampling frequency is set to 1000Hz.

[0197] An incremental rotary encoder is coaxially mounted on the end of the servo drive motor shaft of the feeding mechanism. This incremental rotary encoder outputs 2500 pulses per revolution, providing both A-phase and B-phase pulse signals. The control system counts both the rising and falling edges of the A-phase and B-phase pulse signals, achieving a 4x frequency multiplication to obtain the encoder pulse count value. The nominal circumference of the feeding roller is 100.0 mm, and the reduction ratio is 5:1. Multiplying the encoder pulse count value by the conversion factor between the nominal circumference of the feeding roller and the reduction ratio (100.0 ÷ 5 ÷ (2500 × 4) = 0.002 mm / pulse) yields the feeding displacement data. The feeding displacement data at the (k)th sampling time is denoted as (x(k)), in mm.

[0198] A laser rangefinder is installed at the exit of the shearing mechanism. The laser rangefinder has a measurement range of 50mm to 350mm and a resolution of 0.01mm. After each shearing action, the laser rangefinder emits a laser beam towards the end face of the material being cut and receives the reflected light. The actual length of the material being cut is measured using the time-of-flight method. The actual shearing length measured after the (i)th shearing is denoted as . The unit is mm.

[0199] A digital temperature and humidity sensor is installed above the feeding path between the tension sensor and the feeding mechanism. The digital temperature and humidity sensor measures the ambient temperature and relative humidity of the environment surrounding the packaging material in real time. The ambient temperature at the (k)th sampling time is denoted as... The unit is ℃; the relative humidity of the environment at the (k)th sampling time is denoted as (H(k)), expressed as a percentage.

[0200] The aforementioned material tension data, feeding displacement data, actual shearing length data, ambient temperature data, and ambient relative humidity data are stored in the data buffer of the control system according to a unified timestamp. The data buffer adopts a circular queue structure with a capacity of 10,000 records.

[0201] Step 2: Construct a nonlinear error dynamic model describing the nonlinear relationship between shear length error, material tension, and feed displacement.

[0202] Based on the viscoelastic mechanical properties of composite plastic films under tension, packaging materials undergo elastic elongation under tension (T(k)) during feeding, exhibiting a nonlinear stress-strain relationship. When the tension varies within a small range, the elongation is approximately linearly related to the tension; however, when the tension is large or fluctuates significantly, the material enters the nonlinear viscoelastic deformation region. Furthermore, changes in ambient temperature and humidity can cause a shift in the material's elastic modulus, thus affecting the tension-elongation relationship.

[0203] Based on the above physical mechanism, the actual shear length is established. With preset cutting length Length error Relationship:

[0204]

[0205] Establish length error The compositional relationship:

[0206]

[0207] In the formula, This represents the nonlinear error component caused by material tension, in mm. This represents the inherent error component of the system, expressed in mm.

[0208] Nonlinear error components caused by material tension A cubic polynomial structure is used to describe the nonlinear bending characteristics of the tension-elongation curve of the composite plastic film within the typical working tension range.

[0209]

[0210] In the formula, The average value of the material tension during the (i)th shear cycle is expressed in N. This is the coefficient of the linear term, in mm / N. The coefficient of the quadratic term is expressed in mm / N². is the coefficient of the cubic term, with units of mm / N³.

[0211] The average material tension during the (i)th shear cycle Calculated from all material tension samples during this shear cycle:

[0212]

[0213] In the formula, Let (i) be the starting sampling number of the (i)th shearing cycle. This is the end sampling number of the (i)th shearing cycle. Let be the number of sampling points within the (i)th shearing cycle. The start time of each shearing cycle is determined by the time the previous shearing command was issued, and the end time is determined by the time the current shearing command was issued. Based on a running speed of 120 shearing cycles per minute, the duration of a single shearing cycle is approximately 500ms. At a sampling frequency of 1000Hz, the number of sampling points within a single shearing cycle is... Approximately 500.

[0214] System inherent error components Systematic deviations, including those caused by manufacturing errors in the feed roller diameter, encoder resolution quantization errors, and mechanical transmission clearances, as well as the drift effect of ambient temperature and humidity on the material's elastic modulus, are described using the following structure:

[0215]

[0216] In the formula, denoted as the total feeding displacement during the (i)th shearing cycle, in mm; The displacement error coefficient is dimensionless. This is the temperature influence coefficient, expressed in mm / ℃. The humidity influence coefficient is expressed in mm / %.

[0217] Nonlinear error components caused by material tension With the inherent error components of the system Adding them together, we obtain the complete expression for the nonlinear error dynamic model:

[0218]

[0219] Define parameter vector and regression vector They are respectively:

[0220]

[0221]

[0222] The nonlinear error dynamic model can then be expressed in linear regression form:

[0223]

[0224] Step 3: Use a recursive least squares algorithm with a variable forgetting factor to identify and update the model parameters of the nonlinear error dynamic model online.

[0225] Each time, the (i)th cut is completed and the actual cut length is measured. Then, calculate the length error observation value of the (i)th shearing.

[0226]

[0227] Construct the regression vector for the (i)th shearing step The average value of the material tension during the (i)th shear cycle Calculate the total feeding displacement during the (i)th shearing cycle using the formula described in step 2. The ambient temperature was calculated from the encoder pulse count value. Take the arithmetic mean of all ambient temperature samples within the (i)th shearing cycle, and take the arithmetic mean of all ambient relative humidity samples within the (i)th shearing cycle.

[0228] A recursive least squares algorithm with a variable forgetting factor is used to process the parameter vector. Perform online recursive estimation. The recursive update formula is as follows:

[0229] Gain matrix The calculation formula is:

[0230]

[0231] Parameter estimation vector The update formula is:

[0232]

[0233] covariance matrix The update formula is:

[0234]

[0235] In the formula, This is the variable forgetting factor. The variable forgetting factor is dynamically adjusted based on the magnitude of the one-step prediction error to quickly track changes in parameters and maintain smoothness when parameters are stable. The dynamic adjustment formula is:

[0236]

[0237] In the formula, The lower limit of the forgetting factor is set at 0.95; The one-step prediction error represents the prediction deviation of the current error based on the previous parameter estimate. The error variance reference value is set to 1.0. The physical meaning of this dynamic adjustment mechanism is: when the system operating conditions are stable and the one-step prediction error (e(i)) is small, Approaching 1, the forgetting factor As the value approaches 1, the algorithm forgets historical data at a slower rate, maintaining the smoothness of parameter estimation; when material properties or operating conditions change abruptly, or the one-step prediction error (e(i)) is large, Approaching 0, the forgetting factor Approaching The algorithm forgets old data quickly, accelerating parameter updates to adapt to new system characteristics.

[0238] covariance matrix The initial value is set to ,in It is a 6th-order identity matrix. A larger initial covariance matrix indicates higher uncertainty in the initial parameter estimates, resulting in faster convergence of the algorithm in the initial stage. The initial values ​​of the parameter estimation vector are set as follows: .

[0239] Step 4: Predict the length error of the next shearing cycle and calculate the feedforward compensation amount of the feed displacement.

[0240] After completing the (i)th shearing and updating, the parameter estimation vector is obtained. Then, the material tension at the current moment, i.e., the start of the (i+1)th shear cycle, is collected. Collect the ambient temperature at the current moment. and ambient relative humidity The preset total feeding displacement for the (i+1)th shearing cycle is obtained from the control system. Preset total feeding displacement Based on the preset cutting length Multiplying this by the feed roller circumference compensation factor of 1.005 yields 201.0 mm. The feed roller circumference compensation factor is used to compensate for minor slippage between the feed roller and the material; this factor is obtained through offline calibration.

[0241] Construct the predicted regression vector for the (i+1)th shearing. Since the (i+1)th shearing has not yet been completed, the average value of the material tension during the (i+1)th shearing cycle is... Since accurate measurement is not possible, this embodiment uses the material tension at the current moment. As an approximation:

[0242]

[0243] Using the latest parameter estimation vector Predicting the length error of the (i+1)th shear.

[0244]

[0245] Based on the predicted length error Calculate the feedforward compensation amount for the feed displacement

[0246]

[0247] In the formula, This is the compensation gain coefficient. The setting of the compensation gain coefficient needs to consider the differences in material type: when the packaging material is a plastic film, the compensation gain coefficient is between 0.95 and 1.05; when the packaging material is a paper-based material, the compensation gain coefficient is between 0.90 and 1.10. The composite plastic film used in this embodiment belongs to the plastic film category, and the compensation gain coefficient... Take 1.00.

[0248] Compensation gain coefficient The physical significance lies in correcting the proportional relationship between the prediction error and the actual compensation effect. Since the material elongation and the feeding displacement are not strictly linearly proportional, introducing a compensation gain coefficient can more accurately map the prediction length error into the feeding displacement compensation amount.

[0249] Step 5: Construct a disturbance observer for the feeding servo system and estimate the equivalent load disturbance torque online, and calculate the additional compensation for servo dynamic error.

[0250] During the feeding process, the speed tracking error inherent in the servo drive system itself can cause slight deviations in the shearing length. These deviations originate from factors such as changes in load torque caused by material tension fluctuations during feeding and frictional fluctuations in the mechanical transmission system. This embodiment constructs a disturbance observer to estimate the equivalent load disturbance torque referred to the motor shaft online, and calculates the additional compensation for servo dynamic errors accordingly.

[0251] First, a simplified first-order dynamic model of the feeding servo system is established:

[0252]

[0253] In the formula, (v(t)) is the feeding speed, in mm / s; (B) is the viscous friction coefficient, with a value of 0.02 N·mm·s; (J) is the equivalent moment of inertia, with a value of 0.05 kg·mm². The torque constant is 0.8 N·mm / A; The quadrature-axis current, in amperes (A), is provided in real time by the servo driver. The equivalent load disturbance torque referred to the motor shaft is expressed in N·mm.

[0254] Equivalent load disturbance torque It includes unmeasurable disturbance components such as the load change of the motor shaft due to the material tension fluctuation during the feeding process, the frictional force change between the feeding roller and the material, and the pulsating torque caused by the gear transmission clearance.

[0255] The state equation for the perturbation observer is designed as follows:

[0256]

[0257] In the formula, This is an estimated feed rate, in mm / s. This is an estimated value of the equivalent load disturbance torque, in N·mm; The actual feeding speed, measured in mm / s, is obtained from the feedback signal of the incremental rotary encoder through differential calculation. It is obtained by calculating the difference in feeding displacement between two adjacent control cycles and dividing it by the control cycle duration.

[0258] First observer gain coefficient Second observer gain coefficient Tuning is performed according to the observer pole placement method. The two closed-loop poles of the disturbance observer are respectively configured as follows: and This ensures the convergence speed and stability of the equivalent load disturbance torque estimation. Based on the desired pole locations and system parameters, the following calculations are performed: , .

[0259] The estimated value of the equivalent load disturbance torque during the (i+1)th shear cycle. The feed displacement error caused by the load disturbance is calculated by accumulating the errors.

[0260]

[0261] In the formula, This represents the start time of the (i+1)th shearing cycle. This represents the end time of the (i+1)th shearing cycle. The control cycle of the control system is 1ms in this embodiment.

[0262] Feed displacement error caused by load disturbance Take the opposite number as the additional compensation amount for servo dynamic error.

[0263]

[0264] Step 6: Calculate the total feed compensation and perform feedforward prediction compensation.

[0265] Calculate the total feed compensation for the (i+1)th shear.

[0266]

[0267] Calculate the corrected feed displacement setpoint

[0268]

[0269] In the formula, Based on preset shearing length The basic feeding displacement is converted. In this embodiment, the preset shearing length is used. The feed roller circumference compensation coefficient is 1.005, therefore the basic feed displacement... .

[0270] In the (i+1)th shearing cycle, the control system uses the corrected feed displacement setpoint. This serves as the target value for feeding control. During the feeding process, the control system compares the cumulative feeding displacement value fed back by the incremental rotary encoder with the corrected feeding displacement setpoint in real time. When the cumulative value of the feeding displacement reaches the corrected feeding displacement setpoint... At that time, the control system sends a cutting command to the shearing mechanism, driving the rotary cutter to complete the (i+1)th cutting action.

[0271] Step 7: Repeatedly perform online identification and compensation.

[0272] After the (i+1)th shearing, the actual shearing length of the (i+1)th shearing is measured by a laser rangefinder. After updating index (i) to (i+1), the process returns to step 3, where the model parameters of the nonlinear error dynamic model are recursively updated using the new actual shearing length data. Then, steps 4 to 6 are executed to predict the length error of the (i+2)th shearing and calculate the compensation amount for the feeding displacement. This process is repeated cyclically to achieve continuous online identification and successive feedforward prediction compensation of nonlinear errors during continuous fixed-length shearing of packaging materials.

[0273] During the cyclic execution, the control system synchronously segments and stores the material tension data, feed displacement data, ambient temperature data, and ambient relative humidity data from step 1 according to the shearing cycle. Each data segment of the shearing cycle is identified by the timestamp of the first sampling time within that shearing cycle. When executing step 3, the data segment corresponding to the shearing cycle is extracted from the data buffer to calculate the average material tension, total feed displacement, average ambient temperature, and average ambient relative humidity.

[0274] When the type of packaging material changes, for example from composite plastic film to polyester film or paper, the compensation gain coefficient... Adjustments should be made based on the elastic modulus and thickness of the replaced packaging material. Specific adjustment rules are as follows:

[0275] For polyethylene film packaging materials with an elastic modulus of less than 500 MPa and a thickness of less than 0.1 mm, the compensation gain coefficient is... Take a value between 1.00 and 1.05;

[0276] For polyester film packaging materials with an elastic modulus between 500 MPa and 1500 MPa and a thickness between 0.1 mm and 0.3 mm, the compensation gain coefficient... Take a value between 0.95 and 1.00;

[0277] For paper-based packaging materials with an elastic modulus greater than 1500 MPa and a thickness greater than 0.3 mm, the compensation gain coefficient... Take a value between 0.90 and 0.95.

[0278] After changing the type of packaging material, the control system will estimate the parameter vector. Reset to initial value and the covariance matrix Reset to initial value This eliminates the influence of historical data from the previous type of packaging material on the current identification process, enabling the recursive least squares algorithm with a variable forgetting factor to quickly converge to new model parameters that adapt to the characteristics of the replaced packaging material within the initial few shearing cycles.

[0279] Effect Comparison

[0280] To verify the technical effectiveness of this embodiment, on the same vertical packaging machine roll film fixed-length feeding and shearing system, 5000 continuous shearing tests were conducted using the following three control methods, and the deviation range of the shearing length was statistically analyzed:

[0281] Comparative Example 1: The existing pulse counting semi-closed-loop control method is adopted. This method only accumulates the number of pulses through an incremental rotary encoder. When the feeding displacement corresponding to the accumulated pulse value reaches the preset basic feeding displacement of 201.0 mm, shearing is triggered without any error compensation.

[0282] Comparative Example 2: The existing closed-loop feedback correction control method is adopted. This method measures the actual shearing length after each shearing, multiplies the difference between the actual shearing length and the preset shearing length of 200.0 mm by the feedback gain of 0.8, and then adds it to the basic feeding displacement for the next shearing for compensation.

[0283] The method in this embodiment employs the online identification and compensation method for nonlinear error in the shear length of packaging materials described in this invention.

[0284] During the test, the ambient temperature was 23±2℃, the relative humidity was 55±5%, and the same batch of composite plastic film with a thickness of 0.08mm was used. The comparison results of the shear length deviation of the three methods are shown in Table 1.

[0285] Table 1 Comparison of shear length deviation among the three control methods

[0286] Comparative 1 pulse counting semi-closed-loop control +4.82 -3.95 +1.26 1.84 Comparative Example 2: Full Closed-Loop Feedback Correction Control +1.68 -1.52 +0.12 0.62 Method of this embodiment +0.28 -0.24 +0.02 0.11

[0287] As shown in Table 1, the pulse counting semi-closed-loop control method in Comparative Example 1, due to its failure to consider material tensile deformation, exhibits the largest shear length deviation, with a maximum positive deviation of +4.82 mm and a standard deviation of 1.84 mm. The full closed-loop feedback correction control method in Comparative Example 2 effectively reduces the deviation through feedback correction; however, due to feedback lag and limitations of the linear compensation model, the maximum positive deviation remains at +1.68 mm, with a standard deviation of 0.62 mm. The method in this embodiment, by identifying the nonlinear error model online and performing feedforward prediction compensation, controls the maximum positive deviation within +0.28 mm and reduces the standard deviation to 0.11 mm, achieving an accuracy improvement of approximately 55% compared to Comparative Example 2, fully demonstrating the technical effectiveness of this invention.

[0288] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0289] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for online identification and compensation of nonlinear error in the shear length of packaging materials, characterized in that, Includes the following steps: Step 1: In the packaging material fixed-length shearing system, material tension data is collected by tension sensor, feeding displacement data is collected by rotary encoder, actual shearing length data is collected by laser rangefinder, and ambient temperature and relative humidity data are collected by temperature and humidity sensor. Step 2: Based on the viscoelastic mechanical properties of the packaging material under tension, construct a nonlinear error dynamic model to describe the nonlinear relationship between shear length error and material tension and feeding displacement. The nonlinear error dynamic model includes a first-order, second-order, and third-order term of the average material tension, as well as a first-order term of total feeding displacement, a first-order term of ambient temperature, and a first-order term of ambient relative humidity. Step 3: After each shearing is completed, the length error observation value is calculated based on the difference between the actual shearing length and the preset shearing length. The model parameters of the nonlinear error dynamic model are identified and updated online using a recursive least squares algorithm with a variable forgetting factor. The variable forgetting factor is dynamically adjusted according to the magnitude of the one-step prediction error. Step 4: Using the updated model parameters and the currently collected material tension data, ambient temperature data, and ambient relative humidity data, predict the length error of the next shearing cycle, and calculate the feedforward compensation amount of the feeding displacement based on the predicted length error; Step 5: Construct a disturbance observer for the feeding servo system, estimate the equivalent load disturbance torque referred to the motor shaft online, calculate the feeding displacement error caused by the servo dynamic error based on the equivalent load disturbance torque, and invert the feeding displacement error as the additional compensation amount for the servo dynamic error. Step 6: Add the feedforward compensation amount of the feeding displacement to the additional compensation amount of the servo dynamic error to obtain the total feeding compensation amount. Add the total feeding compensation amount to the feeding displacement setting value of the next shearing cycle. The control system uses the corrected feeding displacement setting value as the target value of feeding control. When the cumulative value of the feeding displacement encoder reaches the corrected feeding displacement setting value, a shearing command is issued.

2. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 1, characterized in that, In step 1: The tension sensor is installed on the feeding path in the tension adjustment area between the unwinding mechanism and the feeding mechanism. The tension sensor outputs an analog voltage signal from 0V to 10V. The analog voltage signal is converted into a digital tension value by an analog-to-digital converter, and the digital tension value is denoted as [value missing]. The unit is Newton, and the sampling frequency of the digital tension value is set to 1000Hz. Indicates the first Each sampling time; The rotary encoder is an incremental rotary encoder, which is mounted on the drive motor shaft of the feeding mechanism. The incremental rotary encoder outputs A-phase pulse signals and B-phase pulse signals. The control system performs a 4x frequency multiplication on the A-phase and B-phase pulse signals to obtain the encoder pulse count value. Multiplying the encoder pulse count value by the conversion factor between the nominal circumference of the feeding roller and the reduction ratio yields the feeding displacement data, which is denoted as […]. The unit is millimeters; The laser rangefinder is installed at the exit of the shearing mechanism. After each shearing action, the laser rangefinder measures the actual length of the cut material. The actual shear length measured after the first shearing is denoted as . The unit is millimeters; The temperature and humidity sensor is a digital temperature and humidity sensor, which is installed on the feeding path and located between the tension sensor and the feeding mechanism. The digital temperature and humidity sensor measures the ambient temperature and relative humidity of the packaging material's surrounding environment in real time. The ambient temperature at each sampling time is recorded as . The unit is Celsius, the first The relative humidity of the environment at each sampling time is recorded as follows: Expressed as a percentage; The material tension data, the feeding displacement data, the actual shearing length data, the ambient temperature data, and the ambient relative humidity data are stored in the data buffer of the control system according to a unified timestamp.

3. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 2, characterized in that, The process of constructing the nonlinear error dynamic model in step 2 includes: Establish actual shear length With preset cutting length Length error Relationship: Establish length error The compositional relationship: In the formula, This represents the nonlinear error component caused by material tension, expressed in millimeters. This represents the inherent error component of the system, expressed in millimeters. Nonlinear error components caused by material tension Described using a cubic polynomial structure: In the formula, For the first The average value of material tension over one shear cycle, in Newtons; The coefficient of the first term is expressed in millimeters per Newton. The coefficient of the quadratic term is expressed in millimeters per square Newton. is the coefficient of the cubic term, with units of millimeters per cubic Newton; No. The average material tension over one shear cycle Calculated from all material tension samples during this shear cycle: In the formula, For the first The starting sampling number of each shearing cycle For the first The end sampling sequence number of each shearing cycle For the first Number of sampling points within a shearing cycle; System inherent error components The following structure is used for description: In the formula, For the first Total feed displacement within a shearing cycle, in millimeters; The displacement error coefficient is dimensionless. This is the temperature effect coefficient, expressed in millimeters per degree Celsius. This is the humidity influence coefficient, expressed as a percentage per millimeter. Nonlinear error components caused by material tension With the inherent error components of the system Adding them together yields the complete expression for the nonlinear error dynamic model: Define parameter vector and regression vector They are respectively: The nonlinear error dynamic model is then expressed in linear regression form:

4. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 3, characterized in that, The specific process of using the recursive least squares algorithm with a variable forgetting factor to identify and update the model parameters of the nonlinear error dynamic model online in step 3 includes: Each time the first The actual shear length was measured after the second shearing. Then, calculate the first... Observed value of length error during secondary shearing : Construct the first The regression vector of the second shearing , of which Total feeding displacement within one shearing cycle The ambient temperature is calculated from the encoder pulse count value. Take the first The average value of all ambient temperature samples within each shear cycle, and the ambient relative humidity. Take the first The average value of all environmental relative humidity samples within each shearing cycle; Calculate the gain matrix according to the following recursive update formula. Parameter estimation vector Covariance Matrix : In the formula, The variable forgetting factor is defined by the following dynamic adjustment formula: In the formula, The lower limit of the forgetting factor is set at 0.95; This is the prediction error for one step. The error variance reference value is set to 1.0; covariance matrix The initial value is set to ,in It is a 6th-order identity matrix; the initial values ​​of the parameter estimation vector are set to... .

5. The method for online identification and compensation of nonlinear error in the shearing length of packaging materials according to claim 4, characterized in that, The specific process of predicting the length error of the next shearing cycle and calculating the feedforward compensation amount of the feeding displacement using the updated model parameters in step 4 includes: After completing the first The parameter estimation vector is obtained by shearing and updating once. Then, collect the current time, i.e., the [number]th [time]. Material tension at the beginning of each shear cycle Collect the ambient temperature at the current moment. and ambient relative humidity , obtain the The preset total feed displacement for each shearing cycle ; Construct the first The predicted regression vector of the second shearing Because of the The second cut is not yet complete. The average material tension over one shear cycle Using the material tension at the current moment As an approximation: Using the latest parameter estimation vector Predicting the first Length error of the second cut : Based on the predicted length error Calculate the feedforward compensation amount for the feed displacement : In the formula, For compensation gain coefficient, compensation gain coefficient The value ranges from 0.85 to 1.

15.

6. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 5, characterized in that, The specific process of constructing the disturbance observer of the feeding servo system and estimating the equivalent load disturbance torque online in step 5 includes: Establish a simplified first-order dynamic model of the feeding servo system: In the formula, Feeding speed, in millimeters per second; The coefficient of viscous friction is expressed in Newton-millimeter-second (N·m·s). The equivalent moment of inertia is expressed in kilograms per square millimeter. This is the torque constant, expressed in Newton-millimeter per ampere. This refers to quadrature-axis current, measured in amperes. The equivalent load disturbance torque referred to the motor shaft is expressed in Newton-millimeter (N·mm). The state equation for the perturbation observer is designed as follows: In the formula, This is an estimated feed rate, in millimeters per second. This is an estimate of the equivalent load disturbance torque, in Newton-millimeter units. The actual feeding speed is obtained by differential calculation of the feedback signal from the incremental rotary encoder, in millimeters per second. The gain coefficient of the first observer. The gain coefficient of the second observer; First observer gain coefficient Second observer gain coefficient Tuning was performed according to the observer pole placement method, configuring the two closed-loop poles of the perturbation observer as follows: and .

7. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 6, characterized in that, The specific process of calculating the feeding displacement error caused by the servo dynamic error based on the equivalent load disturbance torque in step 5, and then inverting the feeding displacement error as the additional compensation amount for the servo dynamic error, includes: In the Within each shear cycle, the estimated value of the equivalent load disturbance torque The feed displacement error caused by the load disturbance is calculated by accumulating the errors. : In the formula, For the first The start time of each shearing cycle For the first The end time of each shearing cycle, The control cycle of the control system, in milliseconds; Feed displacement error caused by load disturbance Take the opposite number as the additional compensation amount for servo dynamic error. :

8. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 7, characterized in that, The specific process of adding the feedforward compensation amount of the feeding displacement to the additional compensation amount of the servo dynamic error in step 6 to obtain the total feeding compensation amount, and then adding the total feeding compensation amount to the feeding displacement setting value of the next shearing cycle, includes: Calculate the first Total compensation for each shearing operation : Calculate the corrected feed displacement setpoint : In the formula, Based on preset shearing length Conversion of basic feeding displacement, basic feeding displacement Based on the preset cutting length Multiply by the feed roller circumference compensation coefficient to obtain; The control system in the In each shearing cycle, the corrected feed displacement setting value is used. As the target value for feeding control, the cumulative value of the feeding displacement fed back by the incremental rotary encoder is compared in real time with the corrected feeding displacement setpoint. When the cumulative value of the feeding displacement reaches the corrected feeding displacement set value... At that time, the control system sends a shearing command to the shearing mechanism, driving the shearing mechanism to complete the first shearing step. The next cutting action.

9. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 8, characterized in that, The method for online identification and compensation of nonlinear error in the shear length of packaging materials also includes the following steps: Step 7: After completing the first step After the first shearing, the laser range sensor measures the first... Actual shear length of the second ,Will Updated to Then return to step 3, use the new actual shear length data to recursively update the model parameters of the nonlinear error dynamic model, and then continue to execute steps 4 to 6 to predict the next step. The length error of each shearing is calculated and the compensation amount of the feeding displacement is calculated. This process is repeated to achieve continuous online identification and successive feedforward prediction compensation of nonlinear errors during continuous fixed-length shearing of packaging materials. During the cyclic execution process, the control system synchronously segments and stores the material tension data, feeding displacement data, ambient temperature data, and ambient relative humidity data from step 1 according to the shearing cycle. The data segment of each shearing cycle is identified by the timestamp of the first sampling time within that shearing cycle. When executing step 3, the data segment corresponding to the shearing cycle is extracted from the data buffer to calculate the average material tension, total feeding displacement, average ambient temperature, and average ambient relative humidity.

10. The method for online identification and compensation of nonlinear error in the shear length of packaging materials according to claim 5, characterized in that, When the type of packaging material changes, the compensation gain coefficient Adjustments should be made based on the elastic modulus and thickness of the replaced packaging material; For polyethylene film packaging materials with an elastic modulus of less than 500 MPa and a thickness of less than 0.1 mm, the compensation gain coefficient is... Take a value between 1.00 and 1.05; For polyester film packaging materials with an elastic modulus between 500 MPa and 1500 MPa and a thickness between 0.1 mm and 0.3 mm, the compensation gain coefficient... Take a value between 0.95 and 1.00; For paper-based packaging materials with an elastic modulus greater than 1500 MPa and a thickness greater than 0.3 mm, the compensation gain coefficient... Take a value between 0.90 and 0.95; After changing the type of packaging material, the control system will estimate the parameter vector. Reset to initial value and the covariance matrix Reset to initial value This eliminates the influence of historical data from the previous type of packaging material on the current identification process, enabling the recursive least squares algorithm with a variable forgetting factor to quickly converge to new model parameters that adapt to the characteristics of the replaced packaging material within the initial few shearing cycles.

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