An adaptive control method and system in rubber eraser multicolor co-extrusion

Abstract

The present application relates to the technical field of plastic extrusion setting, and discloses a self-adaptive control method and system in multi-color co-extrusion of erasers. In order to solve the problems of tension fluctuation, pattern distortion and poor working condition adaptability caused by viscoelastic hysteresis in the process of multi-color co-extrusion of erasers, the present application takes a unified viscoelastic constitutive model as the common underlying framework of the identification link and the feedforward link, uses the recursive least squares method to identify the equivalent viscoelastic parameters of the eraser melt in real time, and directly calls the identified parameters to calculate the viscoelastic feedforward compensation amount of the traction speed, thereby eliminating the model fault and parameter conversion error between identification and feedforward from the root. The present application can effectively reduce the tension fluctuation under dynamic working conditions, inhibit the color stripe distortion and interface shift, improve the batch production consistency of products, reduce the cost of manual parameter adjustment, and adapt to the flexible production demand of multiple varieties.

Description

Technical Field

[0001] This invention relates to the field of plastic extrusion shaping technology, specifically to an adaptive control method and system for multi-color co-extrusion of erasers. Background Technology

[0002] Multi-color co-extrusion is the core molding process for the large-scale production of colored erasers. Through multi-channel melt laminar flow composite extrusion, it achieves continuous molding of multi-color stripes and functional layers, offering advantages such as high production efficiency, uniform coloring of the product body, and no splicing defects. In recent years, with the upgrading of stationery consumption, the market's requirements for the refinement of eraser appearance and the richness of patterns have continued to increase. The industry is accelerating its transformation from traditional PVC substrates to environmentally friendly TPE / TPR substrates, with the proportion of high-end differentiated products increasing year by year. Simultaneously, the production end is also evolving towards high-speed mass production, flexible production of multiple varieties in small batches, and intelligent manufacturing. The synchronous control precision of the extrusion-traction process has become the core key to determining the product's pattern quality, dimensional stability, and production yield.

[0003] Currently, the extrusion-traction control in the eraser manufacturing industry generally adopts a traditional architecture of "master-slave speed synchronization + fixed-parameter PID tension closed loop + manual sampling and parameter adjustment". Since eraser substrates are mostly viscoelastic polymers filled with a large amount of powder, they are in a high-temperature, high-elasticity state after extrusion, exhibiting significant creep and stress relaxation effects. Traditional passive feedback control has an inherent lag, easily causing tension overshoot and oscillations under dynamic conditions such as acceleration and deceleration, leading to a breathing effect with uneven width of colored stripes. Simultaneously, the control loops for main extrusion flow, secondary extrusion flow, and traction speed are intercoupled, and parameter adjustments are mutually constrained. Furthermore, slow time-varying disturbances such as raw material batch fluctuations, screw wear, and environmental temperature drift continuously degrade the control effect, making it difficult to maintain stable multi-color interface accuracy over the long term. This reliance on operator experience for parameter adjustment fails to meet the efficiency requirements of flexible production.

[0004] While some research and applications of adaptive control exist in the general polymer extrusion field, they are mostly designed for products such as pipes, films, and cables with low filler and low viscoelasticity. They fail to consider the specific working conditions of eraser materials, which exhibit high abrasiveness, strong viscoelasticity, and high interfacial precision requirements. Therefore, they cannot directly meet the mass production needs of the stationery manufacturing industry, which demands low cost, high uptime, and low maintenance capabilities. Currently, the eraser manufacturing field still lacks targeted, systematic adaptive control solutions, hindering further improvements in product quality and production efficiency. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides an adaptive control scheme for multi-color co-extrusion of erasers.

[0006] According to a first aspect of the present invention, an adaptive control method for multi-color co-extrusion of an eraser is proposed, comprising the following steps: S1: Real-time acquisition of operating data from the multi-color co-extrusion production line for erasers. The operating data should include at least the traction tension, extruder speed, and traction machine speed. S2: Calculate the nominal tensile strain of the profile based on the operating data; S3: Using a pre-defined unified viscoelastic constitutive model as the identification framework, and employing the recursive least squares method, the equivalent viscoelastic parameters of the rubber melt are identified in real time based on the nominal tensile strain and traction tension. S4: Based on the same unified viscoelastic constitutive model as the identification process, the equivalent viscoelastic parameters obtained in real time are directly called to calculate the viscoelastic feedforward compensation amount of the traction speed. S5: The viscoelastic feedforward compensation is superimposed on the traction control command and sent to the corresponding actuator to form a continuous closed-loop control.

[0007] According to some embodiments, in the method of the first aspect of the present invention, in step S3, the recursive least squares method adopts an adaptive forgetting factor mechanism, and the value of the forgetting factor is dynamically adjusted according to the current working condition.

[0008] According to some embodiments, in the method of the first aspect of the present invention, the adaptive forgetting factor mechanism specifically means: when the steady-state operating condition is identified, a higher steady-state forgetting factor is used, with a value range of 0.995 to 0.999; when the operating condition is identified as changing, a lower dynamic tracking forgetting factor is used, with a value range of 0.95 to 0.98; and the operating condition is identified by statistical hypothesis testing.

[0009] According to some embodiments, in the method of the first aspect of the present invention, under steady-state operating conditions, a micro-amplitude pseudo-random excitation signal is superimposed on the traction speed command to provide continuous excitation for the identification process of the recursive least squares method, and the tension fluctuation caused by the excitation signal is within the allowable range of product size tolerance.

[0010] According to some embodiments, in the method of the first aspect of the present invention, a multi-rate hierarchical scheduling mechanism is adopted: feedback control and feedforward compensation operate in a first control cycle, and parameter identification operates in a second identification cycle; the first control cycle is shorter than the second identification cycle.

[0011] According to some embodiments, the method of the first aspect of the present invention further includes a multivariable decoupling control step: Based on the real-time identified viscoelastic parameters, the steady-state gain of the system is derived. A decoupling network is then constructed to decouple the three inputs of the main extruder speed, auxiliary extruder speed, and traction machine speed from the three outputs of melt pressure, color layer interface position, and traction tension into independent single-input single-output control loops. The viscoelastic feedforward compensation and the feedback control quantities of each loop are processed by the decoupling network and then sent to the corresponding actuators.

[0012] According to some embodiments, in the method of the first aspect of the present invention, the decoupling network is constructed based on the relative gain matrix method, specifically as follows: The relative gain matrix G(0) is calculated based on the system steady-state gain obtained in real time, and then the relative gain matrix is ​​calculated using the following formula. ,in This represents element-wise multiplication; based on the relative gain matrix. The parameters of the decoupled network are updated online, so that the input and output of the coupled system form a one-to-one correspondence.

[0013] According to some embodiments, in the method of the first aspect of the present invention, after each update of the decoupling network parameters, the condition number of the decoupling matrix is ​​checked; if the condition number exceeds a preset safety threshold, the parameter update is rejected and the currently effective decoupling network parameters are used.

[0014] According to some embodiments, in the method of the first aspect of the present invention, the decoupled network update is operated in a third update cycle, which is longer than the second identification cycle.

[0015] According to a second aspect of the present invention, an adaptive control system for multi-color co-extrusion of erasers is provided, comprising: The data acquisition module is used to collect real-time operating data of the multi-color co-extrusion production line for erasers. The operating data includes at least traction tension, extruder speed, and traction machine speed. The perception and identification module is used to calculate the nominal tensile strain of the profile based on the running data, and uses the recursive least squares method to identify the equivalent viscoelastic parameters of the rubber melt in real time, based on the preset unified viscoelastic constitutive model. The feedforward decision module is used to directly call the equivalent viscoelastic parameters obtained in real time based on the same unified viscoelastic constitutive model as the identification process to calculate the viscoelastic feedforward compensation amount of the traction speed. The execution control module is used to superimpose the viscoelastic feedforward compensation amount onto the traction control command and send it to the corresponding actuator to form a continuous closed-loop control.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. The feedforward compensation amount is matched with the actual material properties in real time, eliminating control deviations caused by model discontinuities at the fundamental level: In existing technologies, the identification and feedforward stages use different constitutive models. The parameters output from the identification cannot be directly used for feedforward calculations and require mathematical approximation transformation. This transformation process itself introduces errors, leading to a mismatch between the feedforward compensation and the actual material properties. This invention uses a unified viscoelastic constitutive model as the identification framework and the basis for feedforward calculations. This allows the equivalent viscoelastic parameters identified in real-time by RLS to be directly used for calculating the feedforward compensation without any model parameter transformation. Therefore, the feedforward compensation always precisely matches the actual viscoelastic properties of the rubber melt at the current moment, eliminating compensation deviations caused by model discontinuities.

[0017] 2. Balancing steady-state noise immunity with dynamic tracking speed, ensuring stable convergence of RLS recognition across all operating conditions: Existing RLS algorithms use a fixed forgetting factor. In slow-time-varying industrial scenarios like eraser extrusion, characterized by long-term steady-state operation and occasional abrupt changes in operating conditions, a fixed forgetting factor cannot satisfy both requirements. If it is too small, parameters oscillate during steady-state operation; if it is too large, tracking lags during dynamic operation. This invention adaptively adjusts the forgetting factor according to the operating conditions: a high value is used during steady-state operation to effectively filter out measurement noise and ensure the statistical stability of parameter estimation; a low value is switched when operating conditions change to quickly track changes in material parameters. Simultaneously, a micro-amplitude PRBS excitation signal is actively injected during steady-state operation to provide continuous identification conditions for RLS and prevent parameter drift caused by long-term lack of excitation. Therefore, RLS identification maintains stable convergence under all operating conditions, providing reliable material state information for feedforward control and decoupled control.

[0018] 3. Multi-loop coupling interference is effectively isolated, eliminating linkage misalignment problems: Existing fixed decoupling matrices fail due to screw wear and material batch variations, causing mutual interference between multiple loops and preventing engineers from independently optimizing them. This invention, based on real-time system state identification using RLS, employs a relative gain matrix method to update the decoupling network online. It decouples the three inputs—main extrusion speed, auxiliary extrusion flow rate, and traction speed—from the three outputs—melt pressure, interface position, and traction tension—into independent single loops, ensuring that each control channel does not interfere with the others. This allows engineers to independently tune and optimize each loop, eliminating the problem of linkage misalignment.

[0019] 4. Each functional module operates at its own pace, with reasonable allocation of computing power and coordinated system response. Existing control architectures place all modules in the same runtime cycle, causing fast modules to be forced to adapt to the pace of slow modules, resulting in delayed responses; or slow modules to excessively consume computing resources, leading to inefficiency. In this invention, feedback control / feedforward compensation uses a three-level time scale for separate operation: short cycle for feedback, medium cycle for parameter identification, and long cycle for decoupling network updates. This allows each module to work at its optimal pace, ensuring the real-time performance of the fast loop while avoiding unnecessary repetitive calculations by slow modules, resulting in a coordinated and efficient overall system response. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating an embodiment 1000 of an adaptive control method for multi-color co-extrusion of an eraser according to the present invention. Figure 2 This is a flowchart illustrating an embodiment 2000 of an adaptive control method for multi-color co-extrusion of an eraser according to the present invention. Figure 3 This is a schematic diagram of an embodiment 3000 of an adaptive control system in multi-color co-extrusion of an eraser according to the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Figure 1 This is a schematic flowchart of an embodiment 1000 of an adaptive control method for multi-color co-extrusion of an eraser according to the present invention. Figure 1 As shown, Example 1000 includes steps S1-S5.

[0023] In step S1, real-time operational data of the multi-color co-extrusion production line for erasers is collected. This data includes at least traction tension, extruder speed, and traction machine speed. Step S1 deploys multiple types of sensors on the multi-color co-extrusion production line to construct a synchronous data acquisition network covering multiple physical quantities such as tension, speed, temperature, and pressure. This provides a complete, synchronous, and reliable data foundation for subsequent strain calculations, parameter identification, and control decisions. Unlike existing technologies that use sensor data only for monitoring displays or over-limit alarms, the data collected in this step is directly used as input variables for recursive least squares online identification.

[0024] In some specific embodiments, step S1 involves deploying multiple types of sensors on the multi-color co-extrusion production line for erasers, including: The tension sensor, employing either a strain gauge or piezoelectric type, is installed on the tension measuring roller preceding the traction roller, with its force axis strictly aligned with the traction direction of the profile. When the profile passes over the measuring roller with a certain tension, the sensor outputs a voltage or current signal proportional to the tension magnitude. Typical outputs are 0~10V voltage or 4~20mA current, which, after calibration, are converted into a tension value in Newtons (N).

[0025] The extruder speed and traction roller speed are acquired using incremental encoders. The encoders are installed at the ends of each screw drive shaft and traction roller drive shaft, outputting a specific number of pulse signals per revolution. The speed value, expressed in revolutions per minute (RPM), can be calculated by counting these pulses.

[0026] Optionally, in some specific embodiments, the running data in step S1 of this aspect includes: Melt pressure A melt pressure sensor installed at the die inlet monitors the melt pressure in front of the die in real time, in MPa. This data has two uses: first, it is used for online correction of the gear pump volumetric efficiency in step S2. The higher the melt pressure, the greater the pressure difference on both sides of the internal gap of the gear pump, the greater the backflow, and the lower the volumetric efficiency; second, it serves as the measured feedback value of the melt pressure loop in multivariable decoupling control.

[0027] melt temperature Temperature data is collected by thermocouples located at various sections of the barrel and the die head, with units expressed in °C. Temperature directly affects the viscosity of the rubber melt: as temperature increases, molecular chain movement intensifies, viscosity decreases, and fluidity increases; as temperature decreases, viscosity increases, and fluidity decreases. Temperature data is input into the calculation of the feedforward compensation, allowing the feedforward compensation to automatically adjust with temperature changes.

[0028] Color layer interface position The data is acquired through an online visual inspection system. An industrial camera is installed between the die outlet and the cooling water tank to acquire real-time images of the profile cross-section or surface. Image processing algorithms are used to identify the boundary lines between different color layers, expressed in pixel coordinates or actual dimensions. This data is the measured feedback value of the interface position loop in multivariable decoupling control.

[0029] In step S2, the nominal tensile strain of the profile is calculated based on the operational data. Step S2 utilizes the velocity data acquired in step S1 and reconstructs the nominal tensile strain in real time using an indirect measurement method that combines velocity difference integration and online correction of volumetric efficiency. Since melt strain cannot be directly measured by sensors on industrial production lines—meaning strain sensors cannot be directly mounted on the high-temperature melt—yet strain is a core state variable in the viscoelastic constitutive equation, the RLS algorithm would lack crucial input without strain data, rendering the entire identification framework inoperable. Step S2 indirectly reconstructs strain using measurable velocity quantities, providing a calculable input variable for RLS identification.

[0030] In some specific embodiments, in step S2, the tensile strain ε of the rubber melt during the extrusion-traction process is defined as the relative change in length of the profile in the traction direction. In continuous extrusion production, the melt exits from the die head at a speed... Extruded, and then pulled by traction rollers at a speed Pulling forward. If When the profile is stretched, the strain is positive, i.e., tensile strain; if When profiles are stacked, the strain is negative, i.e., compressive strain; if the two are equal, the strain is zero. The nominal tensile strain ε is calculated using the difference between the traction speed and the extrusion speed:

[0031] In some specific embodiments, traction speed Traffic speed of traction machine and traction roller radius The calculation yielded: .in The unit is RPM. The unit is meters (m). The principle of this formula is: for every revolution of the traction roller, the profile is pulled forward a distance equal to the circumference of the traction roller, which is 2π. Rotation per minute The total distance traveled in a circle is divided by 60 to convert it to the distance traveled per second (m / s).

[0032] In some specific embodiments, the extrusion line speed The calculation involves the flow rate relationship of the gear pump. The linear velocity of the melt at the die outlet is equal to the volumetric flow rate per unit time through the cross-sectional area of ​​the die divided by the cross-sectional area: Where Q is the melt volumetric flow rate (m³ / s) supplied to the die head via the gear pump. Let be the cross-sectional area (m²) of the die exit.

[0033] In some specific embodiments, the volumetric flow rate Q is determined by the actual discharge volume of the gear pump. Theoretically, the gear pump should discharge a certain volume of melt per revolution. That is, the theoretical displacement multiplied by the drive speed of the gear pump. The theoretical volumetric flow rate is obtained. However, due to the internal gaps in the gear pump, the melt flows back from the high-pressure side to the low-pressure side under pressure, causing internal leakage. Therefore, the actual discharge rate is less than the theoretical discharge rate. The ratio of the actual discharge rate to the theoretical discharge rate is defined as the volumetric efficiency. It is dimensionless and ranges from 0 to 1. Therefore .

[0034] Based on the above relationships, the complete formula for calculating extrusion speed is: If the extruder spindle drives the gear pump via a gearbox at a transmission ratio i, then .

[0035] Optionally, in some specific embodiments, the volumetric efficiency in step S2 is... It is not a fixed value, but a dynamic quantity that varies with operating conditions. Its variation stems from the following physical mechanism: During operation, the melt, driven by pressure, flows back from the high-pressure side to the low-pressure side through the gap between the gears and the pump casing, resulting in internal leakage. The magnitude of the internal leakage depends on: the gap size, which gradually increases with wear and tear on the gear pump and screw, exhibiting a slow time-varying process over thousands of hours; the melt pressure, where higher melt pressure in front of the die and greater pressure difference across the gear pump lead to more severe internal leakage; and the melt viscosity, which decreases with increasing temperature, increasing fluidity and thus internal leakage.

[0036] Therefore, in actual calculations, Online corrections are required based on real-time monitoring of melt pressure and temperature. The correction method is as follows: .in, This is the reference volumetric efficiency of the gear pump under nominal operating conditions, and is the factory calibration value. This is a pressure correction factor that decreases monotonically as pressure increases, with a typical value of 0.90~1.00; This is a temperature correction factor that decreases monotonically as temperature increases, with typical values ​​ranging from 0.92 to 1.00.

[0037] The correction factor was obtained through offline calibration of the gear pump. Under laboratory conditions, the ratio of actual flow rate to theoretical flow rate was measured under different pressure and temperature combinations, and pressure-efficiency curves and temperature-efficiency curves were plotted and stored as a correction factor table in the industrial control computer. During online operation, the correction factor was adjusted based on real-time data collected. and By looking up the table and interpolating, the correction factor under the current operating condition can be obtained.

[0038] In step S3, using a preset unified viscoelastic constitutive model as the identification framework, the equivalent viscoelastic parameters of the rubber melt are identified in real time based on the nominal tensile strain and traction tension using the recursive least squares method.

[0039] In this invention, the inventive concept of step S3 includes three levels: First, at the model level, the same viscoelastic constitutive model as the subsequent feedforward control step S4 is used as the identification framework, so that the parameters output by identification can be directly used for the calculation of feedforward compensation without any transformation, eliminating the parameter gap caused by the use of the Kelvin-Voigt model for identification and the use of the generalized Maxwell model for feedforward in the traditional scheme; Second, at the algorithm level, the working condition is automatically identified through CUSUM statistical hypothesis testing, so that the forgetting factor can adaptively switch between steady-state high value and dynamic low value, solving the contradiction that the fixed forgetting factor cannot take into account both steady-state noise resistance and dynamic tracking speed in industrial scenarios with slow time-varying and sporadic changes; Third, at the engineering level, by actively injecting PRBS micro-amplitude excitation within the tolerance range, the engineering implementation problem of parameter drift caused by the lack of continuous excitation during long-term steady-state operation of RLS is solved.

[0040] In some specific embodiments, step S3 uses a fractional-order viscoelastic model as a unified identification-feedforward framework, whose constitutive equation is: Where: τ is the traction tension, ε is the nominal tensile strain, E is the equivalent elastic modulus, η is the equivalent viscosity coefficient, and α is the fractional order. This represents a fractional differential operator.

[0041] The physical meaning of the parameters in this model is clear: E represents the instantaneous elastic response of the material, which is proportional to the strain; η represents the viscous dissipation characteristics of the material, which is proportional to the fractional derivative of the strain; α determines the intermediate state of the material between pure elasticity and pure viscosity. The closer α is to 0, the closer the material behavior is to that of an elastic body; the closer α is to 1, the closer the material behavior is to that of a Newtonian fluid.

[0042] The reason this invention chooses a fractional-order model instead of an integer-order model is that the integer-order Kelvin-Voigt model (α=1) assumes that the viscous response of the material is linear, i.e., stress is proportional to the first power of the strain rate. However, the relaxation behavior of rubber melt over a wide frequency range is not an exponential decay over a single time scale, but rather exhibits a power-law decay characteristic over multiple time scales, showing a higher elastic modulus at high-speed stretching and a lower modulus at low-speed stretching. The fractional-order model uses an additional parameter α to characterize this cross-time-scale response characteristic, and only three parameters are needed to accurately describe the viscoelastic relaxation behavior of rubber melt over a wide frequency range. This fewer parameter count makes it suitable for real-time identification.

[0043] The three identified parameters are directly used in the calculation of the feedforward compensation in step S4. Since the identification and feedforward use the exact same mathematical expression, namely the same fractional-order viscoelastic constitutive equation, the identified E, η, and α can be directly substituted into the feedforward equation without any parameter transformation or approximation.

[0044] In some specific embodiments, recursive least squares (RLS) is used in step S3. Optionally, the core idea of ​​the RLS algorithm is: at each time step, based on the current new data, the parameter estimates from the previous time step are corrected so that the corrected parameters can better fit all historical data, where the weight of recent data is greater than that of distant data. Specifically: The fractional-order viscoelastic constitutive equation is transformed into a linear regression form in the discrete-time domain. The fractional derivative is calculated using the α estimate from the previous time step, resulting in an approximate linear regression form:

[0045] Where k is the discrete-time index. The current tension observation value, data vector The components are as follows: , which corresponds to the regression value of the elastic modulus E; , which is the regression value corresponding to the viscosity coefficient η; The regression value of α is obtained by calculating the sensitivity of fractional derivatives to α.

[0046] The identification framework will be presented in a unified form: .in This is the parameter vector to be identified. In each identification cycle, RLS performs the following three recursive calculations sequentially: The first step is to calculate the gain vector: .

[0047] The gain vector K determines the proportion of the current identification error used to correct the parameter estimates. λ in the denominator is the forgetting factor. This is a quadratic form of the data vector and covariance matrix, measuring the information content of the current data. The physical meaning of this formula is: the greater the information content of the current data, the smaller the magnitude of the gain vector, because the parameters have already been well estimated and do not require significant correction; conversely, the more new information the current data carries, the larger the gain vector, and the greater the magnitude of parameter correction.

[0048] The second step is to update the parameter estimates: .

[0049] Where τ(k) is the measured tension, and φᵀ(k)·θ(k−1) is the model-predicted tension based on the parameters of the previous moment. The difference between the two is the prediction error. The physical meaning of this formula is: if the model prediction is consistent with the actual measurement, the parameters remain unchanged; if there is a prediction error, the parameters are corrected in the direction of decreasing error, and the correction magnitude is controlled by the gain vector.

[0050] The third step is to update the covariance matrix: .

[0051] The covariance matrix P reflects the uncertainty of parameter estimation. The physical meaning of this formula is that the information content of the P matrix decreases after each parameter update. Dividing by the forgetting factor λ moderately expands the P matrix, preserving its responsiveness to new data.

[0052] Optionally, the recursive least squares method employs an adaptive forgetting factor mechanism, whereby the value of the forgetting factor is dynamically adjusted based on the current operating condition. Specifically, the adaptive forgetting factor mechanism works as follows: when a steady-state operating condition is identified, a higher steady-state forgetting factor is used, ranging from 0.995 to 0.999; when a changing operating condition is identified, a lower dynamic tracking forgetting factor is used, ranging from 0.95 to 0.98; and the operating condition is identified through statistical hypothesis testing.

[0053] The forgetting factor λ determines the rate at which the weights of historical data decay in parameter estimation. In recursive least squares, the weight of the data from the i-th sampling period at time k is... In other words, the further away from the current time, the smaller the weight of the data, and the decay rate is exponential. The closer λ is to 1, the greater the weight of the old data is retained, and the smoother the parameter estimation; the smaller λ is, the faster the old data is forgotten, and the stronger the dominance of the new data.

[0054] Under steady-state operating conditions, the forgetting factor is set to 0.995~0.999. This range is chosen based on the time-scale characteristics of disturbances in the rubber extrusion process. Raw material batch variations, screw wear, and ambient temperature drift are all slow time-varying disturbances on the order of hours or even days.

[0055] When the forgetting factor λ = 0.995, the weight of the data before the 100th sampling period is: This means that about 60% of the information is still retained; the weight of data from before the 200th sampling period is... If the identification period is 1 second, then data from the past 100 seconds has a higher weight, and parameter estimation is mainly based on statistical averaging of data from the most recent 2 minutes, effectively filtering out high-frequency measurement noise below the second level. The typical timescale for raw material batch changes is on the order of hours, and a batch of raw materials can be produced continuously for several hours to tens of hours, much longer than the 2-minute time window. Therefore, parameter estimation can track the slow changes between batches.

[0056] When the forgetting factor λ = 0.999, the weight of the data before the 1000th sampling period is: ≈0.368. If the identification period is 1 second, the parameter estimation is statistically smoothed based on data from the past 1000 seconds, resulting in stronger filtering of measurement noise and more stable parameter estimation. For slow-changing processes like equipment wear on a daily scale, the amount of equipment wear is extremely small within a 17-minute statistical window, thus the parameter estimation can provide a highly stable benchmark value.

[0057] The core function of the high-value forgetting factor is to smooth out high-frequency measurement noise above tens of hertz, so that the parameter estimation mainly reflects the real changes in material properties rather than the random fluctuations of measurement noise.

[0058] Under changing operating conditions, the forgetting factor switches to 0.95~0.98. When the system detects a sudden change in operating conditions, such as the production line speed switching from low speed to high speed, or a change in raw material batches causing changes in material rheological properties, the original parameter estimates no longer match the new operating conditions. Parameter tracking needs to be completed within a short time to converge to the new steady-state value.

[0059] When the forgetting factor λ = 0.95, the weight of the data before the 20th sampling period is: That is, only about 36% of the information is retained; the weight of data before the 50th sampling period is... Less than 10% are retained. If the identification period is 1 second, the data within the past 20 seconds has the main weight, the old data is quickly forgotten, and the new data dominates the identification results, so that the parameter estimation converges to the parameter value under the new working condition within tens of seconds.

[0060] When the forgetting factor λ = 0.98, the weight of the data before the 50th sampling period is: This is equivalent to 20 periods when λ=0.95; the data weights before the 100th sampling period are... The parameter tracking speed is slightly slower than λ=0.95, but the suppression of measurement noise is slightly better.

[0061] The low value range of 0.95 to 0.98 reflects the following trade-offs: if λ is below 0.95, the tracking speed is faster, but it is too sensitive to measurement noise at individual data points, and parameter estimation may oscillate violently under new operating conditions and be difficult to converge; if λ is above 0.98, the tracking speed is too slow, and the system is still dominated by old data for tens of seconds after the operating conditions change, resulting in untimely parameter convergence and the feedforward compensation not matching the actual material state for a long time. The value range of 0.95 to 0.98 achieves a reasonable balance between tracking speed and noise resistance.

[0062] In some specific embodiments, the identification of the operating condition is achieved through cumulative sum CUSUM statistical hypothesis testing. This method calculates the cumulative sum statistic S(k) of the system output residual e(k) in real time, where the residual is the difference between the measured tension τ(k) and the model predicted tension φᵀ(k)·θ(k−1).

[0063] When the system is in steady state, the residual e(k) fluctuates randomly around the zero mean, and its probability distribution approximates a normal distribution with a mean of zero. (Cumulative sum statistic) It hovers slightly around zero and does not deviate significantly.

[0064] When operating conditions change, such as a change in speed command causing a trend deviation in tension, or a change in material batches causing a sudden change in constitutive parameters, the residuals no longer fluctuate randomly around the zero mean, but instead continuously skew towards the positive or negative direction. The cumulative sum statistic S(k) subsequently increases or decreases continuously, gradually deviating from the preset statistical threshold. Once S(k) exceeds the upper or lower threshold range, it is determined that the system operating conditions have changed, triggering the forgetting factor to switch from a high value to a low value.

[0065] The advantage of the CUSUM method over simple single-point threshold judgment is that single-point threshold judgment is prone to false triggering due to occasional spikes in measurement noise, while CUSUM accumulates residual information from multiple sampling points, is not sensitive to occasional spikes, and is only triggered when there is a systematic and continuous deviation, thus having higher reliability and anti-interference ability.

[0066] When the residual regression is within the threshold range and remains stable for a period of time, that is, when the cumulative sum and statistics fall back to within the threshold, the system is judged to have returned to steady state. The forgetting factor gradually recovers to a high value, and a first-order low-pass filter is used for transition to avoid switching shock.

[0067] In some specific embodiments, in step S3, under steady-state operating conditions, a micro-amplitude pseudo-random excitation signal is superimposed on the traction speed command to provide continuous excitation for the identification process of the recursive least squares method, and the tension fluctuation caused by the excitation signal is within the allowable range of product size tolerance.

[0068] The mathematical convergence of the RLS algorithm is based on the premise that the system has continuous excitation, that is, the input data vector φ(k) must contain a sufficiently rich number of frequency components to keep the covariance matrix P(k) positive definite. If the production line operates in a constant-speed steady state for a long time, with no significant fluctuations in traction speed and tension, the components in the data vector φ(k) lack change, the eigenvalues ​​of the covariance matrix will gradually approach zero, and the parameter estimation will lose its convergence direction.

[0069] To ensure continuous excitation, in step S3, this scheme superimposes a micro-amplitude pseudo-random binary sequence (PRBS) signal as an active excitation source onto the traction speed command under steady-state operating conditions. PRBS is a signal that pseudo-randomly transitions between two levels. Its characteristics are: the signal level switches only between two states, making it easy to generate and implement; its spectrum is approximately uniformly distributed over a wide frequency band; it is a deterministic sequence rather than random noise, making it easy to distinguish from measurement noise; and it can simultaneously excite multiple frequency components, ensuring that each component of the data vector φ(k) produces sufficient change.

[0070] When the PRBS signal is superimposed on the traction speed command, it will generate a small response fluctuation in the tension measurement value after being transmitted through the speed-tension dynamic system. The amplitude of this fluctuation is proportional to the amplitude of the PRBS signal. Let the PRBS amplitude be Δv, and the DC gain of the speed-tension system be G(0), then the tension response amplitude is approximately G(0)×Δv. This invention configures the amplitude Δv of the PRBS signal so that the peak value of the tension response does not exceed the tension fluctuation range allowed by the product dimensional tolerance. A typical design is that the tension fluctuation does not exceed ±2% of the rated tension. This constraint ensures that the active excitation will not cause the cross-sectional dimensions of the product profile to exceed the specifications, and no defective products will be produced.

[0071] In step S4, based on the same unified viscoelastic constitutive model as in the identification step, the equivalent viscoelastic parameters obtained in real-time identification are directly called to calculate the viscoelastic feedforward compensation amount of the traction speed. In some specific embodiments, step S4 is based on the same unified viscoelastic constitutive model as in step S3, and the equivalent viscoelastic parameters (E, η, α) identified in real-time in step S3 are directly called to calculate the viscoelastic feedforward compensation amount of the traction speed.

[0072] In some specific embodiments, since steps S3 and S4 use the exact same fractional-order viscoelastic constitutive mode, the parameter vector identified in step S3 is... This parameter can be directly passed to the feedforward controller in step S4. The significance of this parameter passing path lies in the fact that, in traditional schemes, the identification stage uses the Kelvin-Voigt model to output E and η, while the feedforward stage uses the generalized Maxwell model, which requires... and From E and η, we can derive... and In cases involving ill-conditioned mathematical transformations, minute identification errors can be amplified to an extreme degree; however, in this scheme, the identification output is directly equal to the feedforward input, and the parameters have the same physical meaning, requiring no transformation.

[0073] In some specific embodiments, the core idea of ​​feedforward control in step S4 is: when a change in the traction speed command is detected, the tension fluctuation trend caused by the speed change is calculated in advance, and a reverse compensation amount is applied at the same time as the speed command is issued, so that the actual tension is kept as close as possible to the set value. From the perspective of control theory, the feedforward compensation amount... The calculation is essentially the inverse problem of the viscoelastic constitutive equation. Given the expected tension change target... Using the current material parameters (E, η, α), the compensation amount that needs to be superimposed on the speed command is calculated.

[0074] Based on the fractional-order viscoelastic constitutive equation, the general form of the feedforward compensation can be expressed as: .in The rate of change of the speed command (m / s²) The current melt temperature is given. The specific form of the function f is derived from the inverse solution of the constitutive equation, reflecting the effect of the material parameters (E, η, α) on the rate of change of velocity. and temperature A comprehensive response.

[0075] In the discrete time domain, the current feedforward compensation amount When superimposed on the velocity command, the resulting additional strain rate is proportional to the velocity command rate. This can be achieved by adjusting... The magnitude of the feedforward compensation can control the fluctuation range of tension during speed changes. The feedforward compensation is not calculated and added in every control cycle. During steady-state operation, the speed command remains unchanged, and the theoretical value of the feedforward compensation is zero, requiring no calculation. The feedforward controller only initiates calculation and adds the compensation to the control command when the rate of change of the speed command exceeds a preset trigger threshold. This triggering mechanism effectively reduces the consumption of computational resources.

[0076] In step S5, the viscoelastic feedforward compensation is superimposed on the traction control command and sent to the corresponding actuator to form continuous closed-loop control. In some specific embodiments, step S5 superimposes the viscoelastic feedforward compensation calculated in step S4 onto the traction control command and sends it to the corresponding actuator to form continuous closed-loop control. That is, in each control cycle, the sensor collects the actual tension value, compares it with the set value to form a feedback control quantity, and then superimposes it with the feedforward compensation quantity before outputting it to the actuator.

[0077] Within each control cycle, the system performs the following operations: acquires the actual traction tension τ(k) at the current moment via step S1; calculates the tension setpoint. Deviation from the measured value τ(k) The PID feedback controller calculates the feedback control quantity based on the deviation e(k). Step S4: Calculate the feedforward compensation amount. ; to feedback control quantity With feedforward compensation By superimposing the data, the final control command is obtained. The control command is sent to the servo driver of the traction motor, and the driver adjusts the speed of the traction roller according to the command.

[0078] Optionally, the present invention employs a multi-rate hierarchical scheduling mechanism: feedback control and feedforward compensation operate in the first control cycle, and parameter identification operates in the second identification cycle; the first control cycle is shorter than the second identification cycle.

[0079] Feedback control and feedforward compensation require rapid responses to transient changes in tension and sudden changes in speed commands, thus operating at the highest frequency. Optionally, the first control cycle is 50~200ms, matching the inertial response time constant of the tension system, which is typically in the range of hundreds of milliseconds to seconds, ensuring the real-time performance of the fast loop.

[0080] Parameter identification runs in the second identification cycle, with selectable values ​​ranging from 500ms to 2s. The reason for a longer identification cycle than the control cycle is that the changes in material parameters (E, η, α) are slow time-varying, with raw material batch changes occurring on an hourly basis and equipment wear on a daily basis, eliminating the need for parameter updates in every control cycle; a longer identification cycle allows for the accumulation of more data samples, improving the statistical reliability of parameter estimation; and separating the identification task from the control task in time avoids the impact of identification calculations on the real-time performance of control.

[0081] In industrial control computer or PLC programming, multi-rate scheduling is implemented by setting multiple timer interrupts. The timer interrupt corresponding to the first control cycle has the highest priority, ensuring that feedback control and feedforward compensation execute on time under any circumstances, guaranteeing real-time control. The timer interrupt corresponding to the second identification cycle has a lower priority and executes during the idle intervals of control interrupts, without preempting the response time of control interrupts. Under multi-rate scheduling, each functional module runs independently according to its own cycle, exchanging data through shared memory. The parameter identification module writes the latest identification results to the shared memory area every 500ms to 2s, and the feedforward control module reads the latest parameter values ​​from the shared memory in each control cycle for feedforward calculation. This data exchange method is asynchronous: the feedforward control module may use the same set of parameter values ​​for multiple consecutive cycles until the identification module writes new values.

[0082] According to such Figure 1 The embodiment shown in this invention uses a unified constitutive model to connect the identification and compensation stages, ensuring that the material parameters upon which the feedforward control is based are always consistent with the true viscoelastic state of the melt, thereby achieving active suppression. Based on this principle, the system can predict the tension fluctuation trend caused by speed changes in advance based on the real-time parameters identified online and apply compensation synchronously, effectively reducing tension overshoot and oscillations in the dynamic process. Simultaneously, because identification, compensation, and closed-loop control operate collaboratively within a unified framework, the system has autonomous adaptability to slow time-varying disturbances such as raw material batch differences, temperature drift, and equipment wear. Ultimately, at the overall control level, it achieves effective reduction of tension fluctuations, shortening of waste length in the variable speed section, and stable consistency of the cross-sectional dimensions and interface positions of multi-color co-extruded products.

[0083] Figure 2 This is a schematic flowchart of an embodiment 2000 of an adaptive control method for multi-color co-extrusion of an eraser according to the present invention. Figure 2As shown, Embodiment 2000 includes steps S201-S205, and also includes a multivariable decoupling control step SA. Steps S201-S205 and... Figure 1 Steps S1-S5 in Example 1000 are the same and will not be repeated here. The multivariable decoupling control step SA specifically includes steps SA1 and SA2.

[0084] In some specific embodiments, step SA in this invention decouples the coupling relationships between the three inputs—main extruder speed, auxiliary extruder speed, and traction machine speed—and the three outputs—melt pressure, color layer interface position, and traction tension—online. This transforms the originally interconnected multivariate system into multiple independent single-variable systems, meaning each input only affects its corresponding output. This eliminates the multivariate coupling interference problems in existing technologies, such as losing dimensions after adjusting tension or deviating the interface after adjusting dimensions. Unlike existing methods that use fixed decoupling matrices or neural network black-box decoupling, the decoupling network in this scheme is based on real-time system state updates obtained through RLS identification, ensuring that the decoupling effect does not deteriorate with screw wear or material batch changes. Simultaneously, condition number verification ensures that the decoupling matrix is ​​always non-singular, balancing adaptability and system stability.

[0085] In step SA1, the steady-state gain of the system is derived based on the real-time identified viscoelastic parameters. A decoupling network is then constructed to decouple the three inputs of the main extruder speed, auxiliary extruder speed, and traction machine speed from the three outputs of melt pressure, color layer interface position, and traction tension into independent single-input single-output control loops.

[0086] In the multi-color co-extrusion process of an eraser, the input vector of the controlled system These represent the main extruder speed, auxiliary extruder speed, and traction machine speed, respectively. Output vector These represent melt pressure, color layer interface position, and traction tension, respectively. There is a complex cross-coupling relationship between the system inputs and outputs: adjusting the main extruder speed u1 not only affects the melt pressure y1, but also influences the traction tension y3 and color layer interface position y2 by changing the total output; adjusting the traction machine speed u3 not only affects the traction tension y3, but also influences the color layer interface position y2 by changing the tensile state of the profile. This coupling relationship makes independent tuning of a single loop impossible, and decoupling is necessary to isolate each channel.

[0087] The steady-state gain matrix G(0) of the system is a 3×3 matrix whose elements G(0) represents the steady-state gain of the j-th input to the i-th output, i.e., the limit of the ratio of the output change to the input change when the input change approaches zero. In existing technologies, G(0) is usually determined through offline step response experiments and remains fixed after measurement. However, during the rubber extrusion process, the actual steady-state gain of the system changes with screw wear and material batch variations, and a fixed gain matrix cannot adapt to these changes.

[0088] In this invention, G(0) is derived online based on the viscoelastic parameters obtained by real-time identification using RLS, combined with system structural parameters. Specifically, the system structural parameters include the displacement characteristics of the gear pump, the flow channel geometry parameters of the die, the radius of the traction roller, and the transmission ratio. These parameters are determined during production line installation and commissioning and are stored in the parameter table of the control system. The equivalent viscoelastic parameters E, η, and α identified by RLS in real-time reflect the current rheological properties of the material. After combining the two, the steady-state gain values ​​of each input channel to the output channel under the current operating conditions can be calculated through the physical model of the extrusion process, thereby forming a real-time 3×3 steady-state gain matrix G(0). Optionally, the physical model includes the pressure drop equation of the melt in the flow channel, the tensile deformation equation of the profile under traction, and the conservation equation of the interface position as a function of the flow rate of each stream. The elements in G(0) are continuously updated during production line operation as the RLS identification results are updated, ensuring that the decoupling design is always based on the current real system characteristics, rather than the fixed offline model at the factory.

[0089] Optionally, the decoupling network is constructed based on the relative gain matrix method, specifically: the relative gain matrix G(0) is calculated based on the real-time identified steady-state gain of the system, and the relative gain matrix is ​​calculated according to the following formula. ,in This represents element-wise multiplication; based on the relative gain matrix. The parameters of the decoupled network are updated online, so that the input and output of the coupled system form a one-to-one correspondence.

[0090] The RGA method is a widely used coupling analysis tool in the design of multivariable control systems. Its core idea is to determine whether an input-output pairing is suitable to form an independent control channel by comparing the ratio of the gain of a certain input to a certain output under the two conditions of open loops and closed loops.

[0091] Optionally, each element of the RGA matrix Λ It has a clear physical meaning: A value close to 1 indicates that the coupling between the j-th input and the i-th output is very weak, making them suitable for pairing to form independent control loops. A value close to 0 indicates strong coupling, making direct pairing unsuitable. A negative value indicates that the gain direction of the input-output pair may reverse when other loops are closed, and the control may be unstable.

[0092] Based on the analysis results of the RGA matrix Λ, this invention designs a decoupling network D(s) such that the product of the system transfer function matrix G(s) and the decoupling network D(s) G(s)·D(s) is approximately a diagonal matrix in steady state, that is, a one-to-one correspondence is formed between the input and the output.

[0093] Optionally, the decoupling network D(s) is constructed as follows: based on the input-output pairing scheme determined by the RGA matrix Λ, the pairing corresponding to the element closest to 1 in each row and column of Λ is selected, and a static decoupling matrix D0 is designed so that G(0)·D0 is a diagonal matrix. Specifically, D0 is the inverse matrix of G(0)⁻¹ multiplied by a diagonal scaling matrix, so that the diagonal elements of G(0)·D0 are normalized to 1. For dynamic decoupling, a dynamic compensation stage needs to be added to the static decoupling matrix to eliminate transient coupling caused by differences in the dynamic response speeds of each channel. In a typical implementation of this invention, the requirements for decoupling accuracy in the eraser extrusion process can be met by using static decoupling as the main method supplemented by first-order inertial compensation.

[0094] In some specific embodiments, the decoupling network parameters are updated in a third cycle, which is longer than the second identification cycle. Optionally, the third update cycle is 5 to 10 seconds. The reason why the decoupling network update cycle is longer than the identification cycle is that the change in the system transfer function G(s) is essentially the result of changes in material parameters and the accumulation of equipment wear, and its rate of change is slower than the change in the material parameters themselves. After the RLS identifies the new equivalent viscoelastic parameters, the system needs to accumulate enough data samples to stably estimate the new steady-state gain matrix G(0), and then calculate the RGA matrix based on the new G(0) and update the decoupling network parameters.

[0095] In each third update cycle, the system performs the following operations: reads the latest equivalent viscoelastic parameters E, η, and α from the RLS identification module; recalculates the steady-state gain matrix G(0) under the current operating condition in combination with the system structural parameters; calculates the RGA matrix Λ to determine the current optimal input-output pairing scheme; and updates the parameters of the decoupling network D(s) based on the RGA analysis results.

[0096] Optionally, after each update of the decoupling network parameters, the condition number of the decoupling matrix is ​​checked; if the condition number exceeds a preset safety threshold, the parameter update is rejected and the currently effective decoupling network parameters are used.

[0097] The online update of the decoupling network is not unconstrained. After each update of the decoupling network parameters, the system verifies the condition number of the decoupling matrix. The condition number is defined as the ratio of the maximum singular value to the minimum singular value of the matrix. The larger the condition number, the closer the matrix is ​​to singularity, and the more sensitive the calculation of its inverse matrix is ​​to errors.

[0098] For the decoupling matrix D, if the condition number cond(D) is too large, it indicates that the decoupling matrix is ​​close to singular, and the decoupling network itself will become an unstable link. Even small calculation errors or measurement noise may cause drastic fluctuations in the decoupled control quantity. In this invention, a safety threshold is preset, and the condition number is calculated after each update of the decoupling network; if the condition number exceeds the safety threshold, the parameter update is rejected, the currently effective decoupling network parameters are used, and a warning message is issued to prompt the operator to check the system status.

[0099] The difference between this condition number verification mechanism and existing technologies lies in the fact that existing decoupling schemes often do not perform stability checks when updating the decoupling matrix, which poses a risk of system instability due to sudden parameter changes. This invention, through condition number constraints, ensures absolute system stability while pursuing adaptive capability. When the identification result does not meet the well-state conditions of the decoupling matrix, it is preferable to temporarily refrain from decoupling in order to guarantee the stability of the closed-loop system.

[0100] In step SA2, the viscoelastic feedforward compensation and the feedback control quantities of each loop are processed by the decoupling network and then sent to the corresponding actuators.

[0101] In some specific embodiments, in the decoupled multivariable control system, the control command consists of two parts: one part is the viscoelastic feedforward compensation amount calculated in step S204, which is directly superimposed on the command of the corresponding channel; the other part is the feedback control amount calculated by each single-loop controller based on the deviation between the set value and the measured value. These two parts of the control amount are first summed in each channel to form the total control command for each channel, and then processed by the decoupling network D(s) before being sent to the corresponding actuator.

[0102] The decoupling network processes the overall control command as follows: In each control cycle, the overall control command from the three channels forms a vector. The decoupling network D performs a linear transformation on this vector to obtain the actual executor instruction vector. The commands are then distributed to the main extruder driver, auxiliary extruder driver, and traction machine driver, respectively. This ensures that the control intentions of each channel are isolated from each other at the execution level and do not interfere with each other.

[0103] According to such Figure 2The embodiment shown in this invention eliminates the mutual interference caused by multivariate coupling between the main extrusion speed, auxiliary extrusion flow rate, and traction speed through online adaptive decoupling based on the RGA method, allowing the three previously mutually constrained control loops to operate independently. Adjusting the melt pressure no longer causes interface position shifts, and adjusting the traction tension no longer induces cross-sectional dimension fluctuations. Compared to existing solutions where the fixed decoupling matrix gradually fails due to screw wear and material changes, this solution continuously updates the decoupling network based on real-time RLS identification results, and ensures that the update process always occurs within stable boundaries through condition number verification. This allows the system to maintain effective isolation and coordinated operation of each loop under all operating conditions, providing a reliable guarantee for the interface accuracy and dimensional consistency of multi-color co-extrusion products.

[0104] Figure 3 This is a schematic diagram of an embodiment 3000 of an adaptive control system in multi-color co-extrusion of an eraser according to the present invention. Figure 3 As shown, embodiment 3000 includes a data acquisition module 301, a perception and identification module 302, a feedforward decision module 303, and an execution control module 304.

[0105] The data acquisition module 301 is used to collect real-time operating data of the multi-color co-extrusion production line for erasers. The operating data includes at least the traction tension, extruder speed, and traction machine speed.

[0106] In some specific embodiments, the data acquisition module 301 is connected to various types of sensor signals arranged on the production line, including tension sensors, encoders, melt pressure sensors, and thermocouples. The tension sensor is installed at the tension measuring roller before the traction roller and outputs an analog signal proportional to the traction tension; the encoder is installed at the ends of the extruder screw drive shaft and the traction roller drive shaft, respectively, and outputs pulse signals; the melt pressure sensor is installed on the melt flow channel wall at the die inlet and outputs melt pressure signals; the thermocouples are arranged on each heating section of the barrel and the die body and output temperature signals.

[0107] Optionally, the data acquisition module 301 acquires the output signals of each sensor at a sampling frequency of 1kHz~2kHz, performs analog-to-digital conversion on the analog signals, performs pulse counting and speed conversion on the pulse signals, converts all data into physical quantity values ​​expressed in engineering units, and stores them in a circular buffer in time series form. The traction tension, extruder speed, and traction machine speed acquired by the data acquisition module 301 are transmitted to the sensing and identification module 302 as basic operating data; the acquired melt pressure and melt temperature are also transmitted to the sensing and identification module 302 as optional operating data for volumetric efficiency correction in strain calculation; the acquired color layer interface position is transmitted to the execution control module 304 as optional operating data for feedback of decoupling control.

[0108] The perception and identification module 302 is used to calculate the nominal tensile strain of the profile based on the running data, and to identify the equivalent viscoelastic parameters of the rubber melt in real time using the recursive least squares method with the framework of the preset unified viscoelastic constitutive model.

[0109] The sensing and identification module 302 first calculates the traction linear speed based on the traction machine speed and traction roller radius; it then calculates the extrusion linear speed by converting the extruder speed to the gear pump speed and adjusting the volumetric efficiency online based on melt pressure and temperature; finally, it calculates the nominal tensile strain using the speed difference. Subsequently, the sensing and identification module 302 uses a fractional-order viscoelastic model as the identification framework, constructing data pairs from the measured traction tension and the calculated strain, and performs parameter identification using a recursive least squares method with an adaptive forgetting factor, outputting the current equivalent viscoelastic parameter vector in each identification cycle.

[0110] The perception and identification module 302 also monitors the operating condition in real time through CUSUM statistical hypothesis testing and adjusts the forgetting factor accordingly. Specifically, it is set to 0.995~0.999 in steady state and switches to 0.95~0.98 when the operating condition changes; during steady-state operation, a micro-amplitude PRBS signal is superimposed on the traction speed command as a continuous excitation. The perception and identification module 302 transmits the identified equivalent viscoelastic parameters to the feedforward decision module 303 and transmits the system state information to the execution control module 304.

[0111] The feedforward decision module 303 is used to directly call the equivalent viscoelastic parameters obtained in real time based on the same unified viscoelastic constitutive model as the identification process to calculate the viscoelastic feedforward compensation amount of the traction speed.

[0112] The feedforward decision module 303 receives the latest identified equivalent viscoelastic parameter vector from the perception and identification module 302. Since the identification framework of the perception and identification module 302 and the feedforward decision module 303 adopt the same fractional-order viscoelastic constitutive model, the feedforward decision module 303 can directly substitute the received E, η, and α into the feedforward control law without any model parameter transformation or approximation.

[0113] Optionally, the feedforward decision module 303 checks the rate of change of the speed command in each first control cycle. When the rate of change of the speed command exceeds a preset trigger threshold, it calculates the viscoelastic feedforward compensation amount of the traction speed based on the inverse solution of the constitutive equation, and transmits the calculated feedforward compensation amount to the execution control module 304. During steady-state operation, the feedforward compensation amount is set to zero, and calculation is not initiated.

[0114] The execution control module 304 is used to superimpose the viscoelastic feedforward compensation amount onto the traction control command and send it to the corresponding actuator to form a continuous closed-loop control.

[0115] The execution control module 304 receives feedforward compensation from the feedforward decision module 303 and system status information from the perception and identification module 302. Optionally, the execution control module 304 also receives measured values ​​of the color layer interface position from the data acquisition module 301. In each first control cycle, the execution control module 304 first calculates the feedback control quantity of each loop, and calculates the feedback control quantity by executing a PID control algorithm based on the deviation between the set value and the measured value of each output variable; then, it superimposes the feedforward compensation quantity and the feedback control quantity to obtain the total control command for each channel; the execution control module 304 sends the total control command to the corresponding actuator, driving each actuator to act according to the command, forming a continuous closed-loop control of "measurement → comparison → calculation → output → re-measurement".

[0116] Furthermore, the execution control module 304 also constructs and updates the decoupling network online based on the relative gain matrix method. This decouples the coupling system of three inputs (main extruder speed, auxiliary extruder speed, and traction machine speed) and three outputs (melt pressure, color layer interface position, and traction tension) into independent single-input single-output control loops. After each update of the decoupling network parameters, the condition number of the decoupling matrix is ​​checked. If the condition number exceeds a preset safety threshold, the update is rejected. The decoupling network updates run in the third update cycle, which is longer than the second identification cycle of the sensing and identification module 302. When the execution control module 304 detects abnormal sensor signals, identification parameters exceeding the physically reasonable range, or decoupling network updates being rejected multiple times, it downgrades the control mode to traditional PID control through a non-disruptive switching method to maintain continuous operation of the production line.

[0117] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0118] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An adaptive control method for multi-color co-extrusion of erasers, characterized in that, Includes the following steps: S1: Real-time acquisition of operating data from the multi-color co-extrusion production line for erasers, including at least traction tension, extruder speed, and traction machine speed; S2: Calculate the nominal tensile strain of the profile based on the aforementioned operating data; S3: Using a pre-defined unified viscoelastic constitutive model as the identification framework, and employing the recursive least squares method, the equivalent viscoelastic parameters of the rubber melt are identified in real time based on the nominal tensile strain and traction tension. S4: Based on the same unified viscoelastic constitutive model as the identification step, the equivalent viscoelastic parameters obtained in real time are directly called to calculate the viscoelastic feedforward compensation amount of the traction speed. S5: The viscoelastic feedforward compensation is superimposed on the traction control command and sent to the corresponding actuator to form a continuous closed-loop control.

2. The method according to claim 1, characterized in that, In step S3, the recursive least squares method adopts an adaptive forgetting factor mechanism, and the value of the forgetting factor is dynamically adjusted according to the current working condition.

3. The method according to claim 2, characterized in that, The adaptive forgetting factor mechanism is as follows: when the operating condition is identified as steady state, a higher steady state forgetting factor is used, with a value range of 0.995 to 0.999; when the operating condition is identified as changing, a lower dynamic tracking forgetting factor is used, with a value range of 0.95 to 0.98; the operating condition is identified through CUSUM statistical hypothesis testing.

4. The method according to claim 3, characterized in that, Under steady-state operating conditions, a micro-amplitude pseudo-random excitation signal is superimposed on the traction speed command to provide continuous excitation for the identification process of the recursive least squares method, and the tension fluctuation caused by the excitation signal is within the allowable range of product size tolerance, and the peak value of the tension response does not exceed ±2% of the rated tension.

5. The method according to claim 1, characterized in that, A multi-rate hierarchical scheduling mechanism is adopted: feedback control and feedforward compensation operate in the first control cycle, and parameter identification operates in the second identification cycle; the first control cycle is shorter than the second identification cycle.

6. The method according to claim 5, characterized in that, The method further includes a multivariable decoupling control step: Based on the real-time identified viscoelastic parameters, the steady-state gain of the system is derived. A decoupling network is then constructed to decouple the three inputs of the main extruder speed, auxiliary extruder speed, and traction machine speed from the three outputs of melt pressure, color layer interface position, and traction tension into independent single-input single-output control loops. The viscoelastic feedforward compensation and the feedback control quantities of each loop are processed by the decoupling network and then sent to the corresponding actuators.

7. The method according to claim 6, characterized in that, The decoupling network is constructed based on the relative gain matrix method, specifically as follows: The relative gain matrix G(0) is calculated based on the system steady-state gain obtained in real time, and then the relative gain matrix is ​​calculated using the following formula. ,in This represents element-wise multiplication; based on the relative gain matrix... The parameters of the decoupling network are updated online, so that the input and output of the coupled system form a one-to-one correspondence.

8. The method according to claim 7, characterized in that, After each update of the decoupling network parameters, the condition number of the decoupling matrix is ​​checked; if the condition number exceeds a preset safety threshold, the parameter update is rejected and the currently effective decoupling network parameters are used.

9. The method according to claim 6, characterized in that, The decoupled network update operates in a third update cycle, which is longer than the second identification cycle.

10. An adaptive control system for multi-color co-extrusion of erasers, characterized in that, include: The data acquisition module is used to collect real-time operating data of the multi-color co-extrusion production line for erasers. The operating data includes at least traction tension, extruder speed, and traction machine speed. The perception and identification module is used to calculate the nominal tensile strain of the profile based on the running data, and uses the recursive least squares method to identify the equivalent viscoelastic parameters of the rubber melt in real time, based on the preset unified viscoelastic constitutive model. The feedforward decision module is used to directly call the equivalent viscoelastic parameters obtained in real time based on the same unified viscoelastic constitutive model as the identification process to calculate the viscoelastic feedforward compensation amount of the traction speed. The execution control module is used to superimpose the viscoelastic feedforward compensation amount onto the traction control command and send it to the corresponding actuator to form a continuous closed-loop control.

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