A foaming agent injection control method based on melt pressure real-time feedforward compensation

Abstract

The application provides a foaming agent injection control method based on melt pressure real-time feedforward compensation, relates to the technical field of foaming agent injection process control, and comprises the following steps: receiving a target mass flow instruction, simultaneously collecting melt pressure values at a foaming agent injection point and foaming agent temperature values of the foaming agent in a gas injection pipeline section in real time at a preset frequency; calling an embedded thermodynamic state model, continuously calculating an instantaneous density value of the foaming agent under the current working condition according to the melt pressure values and the foaming agent temperature values collected in real time; obtaining a compensated volume flow set value which can offset the influence of the current melt pressure disturbance based on a target mass flow value corresponding to the target mass flow instruction and the instantaneous density value; and sending the volume flow set value to a flow control executor on the gas injection pipeline section so as to adjust the actual foaming agent volume flow injected into the polymer melt, and then keep the foaming agent mass injected into the polymer melt per unit time constant.

Description

Technical Field

[0001] This invention belongs to the field of foaming agent injection process control technology, specifically relating to a foaming agent injection control method based on real-time feedforward compensation of melt pressure. Background Technology

[0002] Extrusion foaming is a typical process for producing polystyrene foam boards. Inside the extruder barrel, the polymer melt is conveyed forward by the screw. A physical foaming agent (such as n-pentane, isopentane, or mixtures thereof) is injected into the melt through an injection port in the middle of the barrel via an injection line. After being sheared, mixed, and dissolved by the screw, the melt is extruded from the die and foamed under reduced pressure, ultimately forming a foam product with a uniform cell structure. Precise control of the foaming agent injection amount is crucial for ensuring product quality. Too much injection will result in excessively large cells and reduced product strength; too little injection will lead to insufficient foaming and excessively high density. Therefore, it is necessary to maintain a constant mass of foaming agent injected into the polymer melt per unit time.

[0003] In the prior art, for example, invention patent CN101200108A discloses a gaseous foaming agent flow control system. This system adopts a closed-loop control method, adjusting an electromagnetic proportional valve, a high-pressure servo valve, and an adjustable throttle valve to deliver the foaming agent according to the set foaming agent flow rate and temperature values, thereby accurately and uniformly introducing the required foaming agent flow rate into the polymer. The core of this solution lies in forming a feedback closed loop by detecting the temperature and pressure signals within the foaming agent pipeline to ensure the stability of the foaming agent volumetric flow rate.

[0004] However, physical blowing agents, such as pentane, are compressible fluids whose density changes with pressure. The melt pressure inside the extruder barrel is not constant; it fluctuates periodically and drifts slowly due to factors such as feed fluctuations, screw rotation, and changes in material viscosity. When the melt pressure changes, even if the flow valve on the blowing agent pipeline remains fixed, the instantaneous density of the blowing agent at the injection point will change due to the different melt back pressures it experiences. This results in fluctuations in the actual injected mass of blowing agent corresponding to the same volumetric flow rate. Summary of the Invention

[0005] In view of the above-mentioned defects or deficiencies in the prior art, a foaming agent injection control method based on real-time melt pressure feedforward compensation is provided, which is applied to a foaming extrusion system. The production line of the system includes a melt preheating device for providing polymer melt and an injection pipeline section for injecting physical foaming agent into the polymer melt, comprising the following steps: Receive the target mass flow rate command, and at the same time collect the melt pressure value at the foaming agent injection point and the foaming agent temperature value in the gas injection pipeline section in real time at a preset frequency; The built-in thermodynamic state model is invoked, and the instantaneous density value of the foaming agent under the current working condition is continuously calculated based on the real-time collected melt pressure value and foaming agent temperature value. Based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value, a compensated volumetric flow rate setting value that can offset the influence of the current melt pressure disturbance is obtained. The volumetric flow rate setpoint is sent to the flow control actuator on the gas injection pipeline section to adjust the actual volumetric flow rate of the foaming agent injected into the polymer melt, thereby keeping the mass of foaming agent injected into the polymer melt constant per unit time.

[0006] According to the technical solution provided in this application, the air injection pipeline section of the foaming extrusion system includes at least two foaming agent injection points distributed along the axial direction of the extruder screw; Sending the volumetric flow rate setpoint to the flow control actuator on the gas injection pipeline section to adjust the actual blowing agent volumetric flow rate injected into the polymer melt includes the following steps: Real-time acquisition of independent melt pressure values ​​at each foaming agent injection point; For each foaming agent injection point, the independent instantaneous density value of the foaming agent at each injection point is calculated based on the independent melt pressure value and the foaming agent temperature value at that injection point. Take the reciprocal of each independent instantaneous density value to obtain the reciprocal density value corresponding to that injection point; calculate the sum of the reciprocal density values ​​of all foaming agent injection points to obtain the total reciprocal value; For each foaming agent injection point, the reciprocal value of the density at that injection point is divided by the total reciprocal value, and the resulting ratio is used as the compensation allocation weight for that foaming agent injection point; wherein, the sum of the compensation allocation weights of all foaming agent injection points is always 1; Multiply the volumetric flow rate setpoint by the corresponding compensation allocation weight for each foaming agent injection point to obtain an independent volumetric flow rate setpoint for each foaming agent injection point. Each of the independent volumetric flow rate settings is sent to its corresponding flow control actuator installed on the gas injection pipeline section.

[0007] According to the technical solution provided in this application, before dividing the reciprocal value of the density at each foaming agent injection point by the total reciprocal value and using the resulting ratio as the compensation allocation weight for that foaming agent injection point, the method further includes the following steps: Retrieve the actual volumetric flow rate values ​​fed back by the flow control actuators at each foaming agent injection point in the previous control cycle; The independent volumetric flow rate set value generated for each foaming agent injection point in the previous control cycle is compared with the actual volumetric flow rate value retrieved at the corresponding injection point to calculate the flow tracking deviation of each foaming agent injection point in the previous control cycle. If the flow tracking deviation at any foaming agent injection point exceeds a preset deviation threshold and the number of consecutive cycles exceeds the preset diagnostic cycle number, then the foaming agent injection point is determined to be an abnormal injection point, and the remaining foaming agent injection points are normal injection points. The step of dividing the reciprocal of the density at each foaming agent injection point by the total reciprocal of the density, and using the resulting ratio as the compensation allocation weight for that foaming agent injection point, includes the following steps: For each normal injection point, the reciprocal value of the density at that injection point is divided by the total reciprocal value, and the resulting ratio is used as the compensation allocation weight for that foaming agent injection point.

[0008] According to the technical solution provided in this application, before calling the built-in thermodynamic state model and continuously calculating the instantaneous density value of the foaming agent under the current working condition based on the real-time collected melt pressure value and foaming agent temperature value, the following steps are also included: The fluctuation characteristics of the melt pressure value collected in real time are analyzed, and the dominant fluctuation period of the melt pressure value within a preset observation window is extracted. Obtain the hysteresis response time required for the delivery of foaming agent from its flow control actuator to the foaming agent injection point in the pre-calibrated gas injection pipeline section; If the dominant fluctuation period is greater than or equal to a preset multiple of the lag response time, the current operating condition is determined to be a slow-changing operating condition. The process of calling the built-in thermodynamic state model and continuously calculating the instantaneous density value of the foaming agent under the current operating conditions based on the real-time collected melt pressure value and foaming agent temperature value includes the following steps: If the current operating condition is determined to be a slow-changing condition, the built-in thermodynamic state model is invoked, and the instantaneous density value of the foaming agent under the current operating condition is continuously calculated based on the real-time collected melt pressure value and foaming agent temperature value.

[0009] According to the technical solution provided in this application, after obtaining the pre-calibrated hysteresis response time required for the delivery of foaming agent from its flow control actuator to the foaming agent injection point in the gas injection pipeline section, the method further includes the following steps: If the dominant fluctuation period is less than a preset multiple of the lag response time, the current operating condition is determined to be a rapidly changing operating condition. If the current operating condition is determined to be a rapidly changing operating condition, then retrieve the historical sequence of the melt pressure values ​​stored before the current moment within the most recent preset time period, as well as the instantaneous density values ​​that have been calculated and stored by the thermodynamic state model and correspond to each melt pressure value in the historical sequence after shifting forward by the hysteresis response time along the time axis. A response mapping relationship is constructed based on the historical sequence, which describes the correspondence between the melt pressure value and the instantaneous density value after the hysteresis response time; The melt pressure value and the foaming agent temperature value collected at the current moment are mapped according to the response mapping relationship to obtain the density prediction value, and the density prediction value is used as the instantaneous density value of the foaming agent under the current working condition.

[0010] According to the technical solution provided in this application, after receiving the target mass flow rate instruction, and before obtaining the compensated volumetric flow rate setpoint that can offset the influence of the current melt pressure disturbance based on the target mass flow rate value corresponding to the target mass flow rate instruction and the instantaneous density value, the method further includes the following steps: Call a pre-stored pressure-solubility relationship that describes the change in the solubility of the blowing agent as a function of the melt pressure under the current blowing agent and temperature conditions; Substituting the real-time collected melt pressure value into the pressure-solubility relationship, the maximum saturated mass fraction of foaming agent that can be dissolved per unit mass of polymer melt under the current melt pressure condition is obtained. Multiply the maximum saturated mass fraction by the polymer melt mass flow rate at the current yield to obtain the maximum dissolved mass flow rate of the blowing agent under the current melt pressure conditions; The process of obtaining a compensated volumetric flow rate setpoint that can offset the influence of current melt pressure disturbance based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value includes the following steps: If the target mass flow rate value is less than or equal to the maximum dissolved mass flow rate of the foaming agent, then based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value, a compensated volumetric flow rate setting value that can offset the influence of the current melt pressure disturbance is obtained.

[0011] According to the technical solution provided in this application, after obtaining the maximum dissolved mass flow rate of the foaming agent under the current melt pressure conditions, the method further includes the following steps: If the target mass flow rate is greater than the maximum dissolved mass flow rate of the foaming agent, then the volumetric flow rate setpoint is obtained based on the maximum dissolved mass flow rate of the foaming agent and the instantaneous density value.

[0012] According to the technical solution provided in this application, the preset multiple is a dynamically adaptive multiple, and its determination process includes: The density-pressure relationship of the foaming agent at the foaming agent temperature value is obtained in real time, and the partial derivative of density with respect to pressure at the current operating point is determined accordingly. Using the melt pressure value sequence within the preset observation window, the pressure fluctuation amplitude is extracted, and combined with the density partial derivative with respect to pressure, the maximum relative change in foaming agent density caused by melt pressure fluctuation within the hysteresis response time is estimated. Obtain the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section, and calculate the minimum ratio of the dominant fluctuation period to the hysteresis response time required to keep the mass flow error caused by volumetric flow compensation within the preset accuracy range, in conjunction with the maximum relative change in the density of the foaming agent. The minimum ratio is assigned to the preset multiple in real time, and the current working condition is determined to be either a slow-changing working condition or a fast-changing working condition based on the dynamically updated preset multiple.

[0013] According to the technical solution provided in this application, obtaining the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section includes the following steps: During the continuous operation of the foaming extrusion system, the sequence of volumetric flow rate setpoints received by the flow control actuator and the sequence of injection pressure response measured by the dynamic pressure sensor installed on the injection pipeline section are continuously collected. Using the volumetric flow rate setpoint sequence as input and the gas injection pressure response sequence as output, a local dynamic model with the flow control actuator as the core and including the gas capacity characteristics of the downstream gas injection pipeline is identified online using a recursive least squares algorithm with a forgetting factor. Solve for the dominant pole of the local dynamic model, and determine the distance from the dominant pole to the origin as an eigenvalue characterizing the upper limit of the dynamic response rate of the flow control actuator.

[0014] According to the technical solution provided in this application, during the online identification of the local dynamic model, the thermodynamic state model is invoked. Based on the gas injection pressure response sequence and the real-time collected temperature value of the foaming agent, the collected pressure data is converted into equivalent pressure data based on a preset reference density. The equivalent pressure data is then used to replace the original pressure data in the identification operation of the recursive least squares algorithm with a forgetting factor, so as to eliminate the influence of time-varying model parameters introduced by the drift of foaming agent density with operating conditions on the identification results.

[0015] Compared with the prior art, the beneficial effects of this application are as follows: I. By directly collecting the melt pressure value at the foaming agent injection point as the basis for density calculation, accurate perception of the actual back pressure on the foaming agent is achieved. The foaming agent directly contacts the polymer melt at the injection point, and the back pressure it experiences is the melt pressure. Substituting this pressure value into the thermodynamic state model to calculate the instantaneous density value, it truly reflects the compression state of the foaming agent under the current injection conditions, avoiding the shortcomings of traditional methods that cannot accurately obtain the actual back pressure at the injection point due to measuring the internal pressure of the foaming agent pipeline.

[0016] Second, by dividing the target mass flow rate value by the instantaneous density value to obtain the compensated volumetric flow rate setpoint, proactive compensation for melt pressure disturbances is achieved. When the melt pressure increases, causing the foaming agent density to increase, the division operation automatically yields a decreased volumetric flow rate setpoint; when the melt pressure decreases, causing the foaming agent density to decrease, the division operation automatically yields an increased volumetric flow rate setpoint. This calculation is completed before the actual mass flow rate deviation occurs, fundamentally eliminating the response lag of feedback control's "deviation first, correction later" approach, thus maintaining a constant mass of foaming agent injected into the polymer melt per unit time.

[0017] Third, by continuously operating the thermodynamic state model online, density calculation and feedforward compensation are completed synchronously within a single control cycle. Based on the real-time collected melt pressure and foaming agent temperature values, the controller continuously outputs the instantaneous density value under the current operating conditions in a high-frequency cyclic calculation mode. There is no need to pre-calibrate empirical coefficients or add additional metering devices, resulting in a simple structure and fast response. Attached Figure Description

[0018] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 The flowchart illustrates the steps of the foaming agent injection control method based on real-time feedforward compensation of melt pressure provided in this application. Detailed Implementation

[0019] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] As mentioned in the background section, this application proposes a foaming agent injection control method based on real-time melt pressure feedforward compensation, applied to a foaming extrusion system. The system's production line includes a melt preheating device for providing polymer melt and an injection pipeline section for injecting a physical foaming agent into the polymer melt. Figure 1 As shown, it includes the following steps: S1. Receive the target mass flow rate command, and at the same time collect the melt pressure value at the foaming agent injection point and the foaming agent temperature value in the gas injection pipeline section in real time at a preset frequency. S2. Call the built-in thermodynamic state model and continuously calculate the instantaneous density value of the foaming agent under the current working condition based on the real-time collected melt pressure value and foaming agent temperature value. S3. Based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value, obtain the compensated volumetric flow rate setting value that can offset the influence of the current melt pressure disturbance. S4. The volumetric flow rate setpoint is sent to the flow control actuator on the gas injection pipeline section to adjust the actual volumetric flow rate of the foaming agent injected into the polymer melt, thereby keeping the mass of the foaming agent injected into the polymer melt constant per unit time.

[0022] It should be noted that the physical quantities such as pressure, temperature, density, and flow rate involved in this invention refer to numerical signals directly acquired by sensors at the corresponding measurement locations or processed by the controller. The acquisition, transmission, storage, and processing of these signals follow conventional signal processing standards in the industrial control field. The parameters mentioned in this invention, such as preset frequency, preset multiple, preset deviation threshold, preset diagnostic cycle number, and preset duration, refer to constant values ​​or configurable variables pre-set in the control system and stored in the controller's memory. Their specific values ​​can be calibrated and optimized during the system debugging phase based on factors such as production line specifications, foaming agent type, and process requirements.

[0023] In this invention, the foaming extrusion system refers to a continuous production equipment assembly that heats and melts polymer raw materials, injects a foaming agent, mixes them evenly, and then extrudes them to form foam products. It includes at least a melt preheating device, an extruder, a foaming agent injection pipeline section, a die, and a subsequent cooling and shaping device arranged sequentially along the material flow direction. The melt preheating device heats the solid polymer raw materials to a molten state and supplies them to the extruder. The extruder barrel is equipped with a screw driven by a drive mechanism, which conveys the polymer melt axially forward and builds pressure. The foaming agent injection pipeline section refers to a complete fluid transport path starting from the foaming agent storage tank or foaming agent supply source, passing through a flow control actuator and a conveying pipeline, and finally connecting to the injection port on the extruder barrel. This pipeline section is equipped with at least a flow control actuator for adjusting the volumetric flow rate of the foaming agent and a temperature sensor for measuring the temperature of the foaming agent.

[0024] In this embodiment of the invention, the physical blowing agent can be selected from n-pentane, isopentane, a mixture of n-pentane and isopentane, carbon dioxide, nitrogen, or other physical blowing agents commonly used in extrusion foaming processes. The polymer melt can be selected from polystyrene, polypropylene, polyethylene, polyethylene terephthalate, or other thermoplastic polymers suitable for extrusion foaming processes. The following examples use n-pentane as the physical blowing agent and polystyrene melt as the polymer melt for illustration, but the scope of protection of this invention is not limited thereto.

[0025] In this invention, the controller refers to an industrial control device with functions of data acquisition, numerical calculation, logical judgment, and command output, such as a programmable logic controller, embedded microcontroller, industrial control computer, or process control station of a distributed control system. The controller has a built-in memory for storing the calculation program of the thermodynamic state model, the target mass flow command, preset parameters, historical data sequences, and various intermediate variables involved in the control algorithm. The controller connects to the melt pressure sensor, the foaming agent temperature sensor, and the flow control actuator through analog input channels or a digital communication bus to realize signal acquisition and command issuance.

[0026] In this invention, the thermodynamic state model refers to a mathematical equation or its simplified form that can calculate the density value of a substance based on its temperature and pressure. In the embodiments of this invention, the thermodynamic state model adopts the Penn-Robinson equation. The Penn-Robinson equation is a cubic equation of state that describes the degree to which the intermolecular interaction forces of real fluids deviate from those of an ideal gas by introducing an eccentricity factor. It has high accuracy in predicting the density of nonpolar and weakly polar small molecule fluids over a wide range of pressures and temperatures. The standard form of the Penn-Robinson equation and the specific expressions of its parameters are well known to those skilled in the art and will not be elaborated here. When deploying the Penn-Robinson equation in a controller, the equation needs to be rewritten into an iterative solution format with density as the solution objective, and a convergence tolerance and a maximum number of iterations should be preset to ensure that each density calculation can converge within a single control cycle. In addition to the Penn-Robinson equation, thermodynamic state models can also be the Soavi-Redlich-Kuang equation, the Benedict-Weib-Rubin equation, or multi-parameter empirical state equations based on Helmholtz free energy. The specific selection can be flexibly determined according to the type of foaming agent and the operating conditions.

[0027] In this invention, the instantaneous density value refers to the foaming agent density calculated by the controller within a single control cycle using a thermodynamic state model based on the melt pressure and foaming agent temperature values ​​collected at the current moment. Since the melt pressure fluctuates in real time, the thermodynamic state model is re-called every control cycle; therefore, the instantaneous density value is also a dynamically updated numerical sequence over time. The instantaneous density value reflects the true density of the foaming agent at the injection point, under the thermodynamic state at the corresponding moment in the control cycle, and directly determines the number of foaming agent molecules that can be carried by the same volumetric flow rate. In this invention, the target mass flow rate value refers to the preset, desired mass of foaming agent injected into the polymer melt per unit time, typically measured in kilograms per hour or grams per second. This value is usually predetermined by the process formulation based on the target expansion ratio, extrusion yield, and foaming agent type of the final foamed product, and is either issued to the controller as an instruction or stored in the controller's formulation parameter table for later use. In this invention, the volumetric flow rate setpoint refers to the volumetric flow rate value that the flow control actuator in the foaming agent injection pipeline should achieve, generated by the controller after feedforward compensation calculation. Its unit is liters per hour or milliliters per second. Since the density of the foaming agent at the injection port varies with the melt pressure, the volumetric flow rate setpoint corresponding to the same target mass flow rate value is different under different pressure conditions.

[0028] This embodiment provides a foaming agent injection control method based on real-time melt pressure feedforward compensation, applied to a foaming extrusion system. The system production line includes a melt preheating device for providing polymer melt and an injection pipeline section for injecting physical foaming agent into the polymer melt.

[0029] The method includes the following steps.

[0030] Step 1: The controller receives the target mass flow rate command from the host computer or formula management system, and at the same time, collects the melt pressure value at the foaming agent injection point and the foaming agent temperature value in the gas injection pipeline section in real time at a preset frequency.

[0031] The controller receives the target mass flow rate command via either a digital communication bus or by reading the target mass flow rate value from a preset formula parameter table in its internal memory. The target mass flow rate value characterizes the desired mass of blowing agent injected into the polymer melt per unit time. The preset frequency refers to the rate at which the controller executes the data acquisition and calculation cycle for this step; its value needs to comprehensively consider the main frequency components of melt pressure fluctuations and the computational load the controller can withstand. In this embodiment, the preset frequency is set between 20 Hz and 100 Hz, meaning a complete feedforward compensation calculation is performed every 10 to 50 milliseconds.

[0032] Real-time acquisition of melt pressure is achieved through a high-temperature melt pressure sensor installed at the foaming agent injection port on the extruder barrel. The sensor's pressure-sensing diaphragm is in direct contact with the polymer melt, and its output signal is converted into a standard analog signal or digital bus signal via a signal conditioning circuit before being input to the controller. Real-time acquisition of foaming agent temperature is achieved through a temperature sensor installed on the injection pipeline near the injection point. The temperature sensor can be a thermocouple or a resistance temperature detector (RTD), with its probe inserted into the foaming agent fluid or installed on the outer wall of the pipeline, supplemented by a temperature field compensation algorithm to accurately reflect the actual temperature of the fluid. It should be noted that since the foaming agent is in direct contact with the polymer melt at the injection point, the back pressure it experiences is the pressure of the polymer melt at that point. Therefore, by measuring the melt pressure value, the true pressure conditions experienced by the foaming agent at the injection point are obtained.

[0033] Step 2: The controller calls the built-in thermodynamic state model and continuously calculates the instantaneous density of the foaming agent under the current operating conditions based on the real-time collected melt pressure and foaming agent temperature values.

[0034] In each control cycle, the controller takes the melt pressure and blowing agent temperature values ​​collected in step one as inputs and substitutes them into a preset thermodynamic state model. The thermodynamic state model exists in the controller's memory as a subroutine or function module. Internally, it first converts the input pressure and temperature values ​​into the unit system required for model calculation, then executes an iterative solution process, and finally outputs the density value of the blowing agent under that operating condition. Since the melt pressure value is a physical quantity that changes dynamically over time, the thermodynamic state model receives newly collected pressure values ​​in each cycle. Therefore, the output instantaneous density value is also a continuously updated numerical stream, tracking in real time the density change of the blowing agent at the injection point caused by melt pressure fluctuations.

[0035] Step 3: Based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value calculated in Step 2, the controller obtains a compensated volumetric flow rate setpoint that can offset the influence of the current melt pressure disturbance.

[0036] In this embodiment, the specific calculation method for obtaining the volumetric flow rate setpoint based on the target mass flow rate value and the instantaneous density value is a division operation, that is, dividing the target mass flow rate value by the instantaneous density value, and the quotient obtained is the volumetric flow rate setpoint. The physical basis of this division operation lies in the law of conservation of mass: mass flow rate equals volumetric flow rate multiplied by density. Therefore, given the target mass flow rate and the current density, the volumetric flow rate to be controlled must be equal to the mass flow rate divided by the density.

[0037] When the melt pressure increases due to feeding fluctuations or screw speed changes, the foaming agent is compressed more at the injection point, resulting in a higher instantaneous density. The division operation automatically yields a smaller volumetric flow rate setpoint than the original value, causing the flow control actuator to close the valve opening to maintain a constant mass of foaming agent passing through the injection point per unit time. Conversely, when the melt pressure decreases, causing the instantaneous density of the foaming agent to decrease, the division operation automatically yields an increased volumetric flow rate setpoint, and the flow control actuator correspondingly opens the valve. Throughout this process, the target mass flow rate itself remains unchanged; what changes is the volumetric flow rate required to achieve that target mass under varying density conditions. This division operation can be completed within a single control cycle, and its result is directly used as the volumetric flow rate setpoint output for that cycle, achieving proactive compensation for melt pressure disturbances. The advance compensation referred to here means that the compensation action is completed before the foaming agent mass flow rate deviation actually occurs, based solely on the density change trend indicated by the melt pressure change, thus offsetting the impact of the disturbance at the source.

[0038] Step 4: Send the volumetric flow rate setpoint obtained in Step 3 to the flow control actuator on the gas injection pipeline section to adjust the actual volumetric flow rate of the foaming agent injected into the polymer melt, thereby keeping the mass of foaming agent injected into the polymer melt constant per unit time.

[0039] The controller sends the volumetric flow rate setpoint to the flow control actuator via an analog output channel or digital communication bus. Upon receiving the setpoint, the flow control actuator adjusts the valve opening using a built-in proportional-integral-derivative controller or servo drive mechanism, ensuring that the actual volumetric flow rate of the foaming agent flowing through the pipeline quickly tracks the setpoint. Since the volumetric flow rate setpoint calculated in step three has already compensated for the impact of melt pressure fluctuations on the foaming agent density, the mass of foaming agent carried by the volumetric flow rate delivered by the flow control actuator according to this setpoint is exactly equal to the target injection amount in the process formulation, thus maintaining a constant mass of foaming agent injected into the polymer melt per unit time.

[0040] This embodiment overcomes the limitations of traditional solutions that rely solely on internal pressure measurements within the blowing agent pipeline and cannot detect polymer-side pressure fluctuations by directly incorporating the melt pressure at the injection point into the calculation and feedforward compensation chain for blowing agent density. The melt pressure, as a disturbance source, is directly measured and participates in the compensation calculation. There is a one-to-one correspondence between the compensation logic and the physical causes of the disturbance. The compensation action is completed before the actual mass flow deviation occurs, eliminating the need to wait for downstream concentration detection feedback. This rapid response fundamentally solves the technical problem of uneven blowing agent injection caused by melt pressure fluctuations.

[0041] In a preferred embodiment, the air injection section of the foaming extrusion system includes at least two foaming agent injection points distributed along the axial direction of the extruder screw; Sending the volumetric flow rate setpoint to the flow control actuator on the gas injection pipeline section to adjust the actual blowing agent volumetric flow rate injected into the polymer melt includes the following steps: Real-time acquisition of independent melt pressure values ​​at each foaming agent injection point; For each foaming agent injection point, the independent instantaneous density value of the foaming agent at each injection point is calculated based on the independent melt pressure value and the foaming agent temperature value at that injection point. Take the reciprocal of each independent instantaneous density value to obtain the reciprocal density value corresponding to that injection point; calculate the sum of the reciprocal density values ​​of all foaming agent injection points to obtain the total reciprocal value; For each foaming agent injection point, the reciprocal value of the density at that injection point is divided by the total reciprocal value, and the resulting ratio is used as the compensation allocation weight for that foaming agent injection point; wherein, the sum of the compensation allocation weights of all foaming agent injection points is always 1; Multiply the volumetric flow rate setpoint by the corresponding compensation allocation weight for each foaming agent injection point to obtain an independent volumetric flow rate setpoint for each foaming agent injection point. Each of the independent volumetric flow rate settings is sent to its corresponding flow control actuator installed on the gas injection pipeline section.

[0042] Specifically, this embodiment further defines the air injection pipeline section of the foaming extrusion system as including at least two foaming agent injection points distributed along the axial direction of the extruder screw. In industrial practice, for extruders with high yield or large length-to-diameter ratio, arranging multiple foaming agent injection ports along the barrel axial direction helps the foaming agent to be more uniformly dispersed in the melt. However, this also brings new problems, such as different melt pressures at each injection point due to their different axial positions, leading to an imbalance in the injection volume at each point. This embodiment is proposed to solve this problem. In this embodiment, multiple foaming agent injection points are arranged sequentially along the extruder barrel axial direction. Each injection point is connected to the main pipe or distributor of the air injection pipeline section through an independent branch pipe, and each branch pipe is equipped with a separate flow control actuator. Because the axial positions of each injection point are different, the melt delivery distance between each point and the extruder die head is different. Therefore, the melt pressure values ​​at each point are independent and significantly different.

[0043] In this embodiment, the step of sending the volumetric flow rate setpoint to the flow control actuator on the gas injection pipeline to adjust the actual foaming agent volumetric flow rate of the injected polymer melt specifically includes the following process.

[0044] First, the independent melt pressure value at each foaming agent injection point is acquired in real time. A melt pressure sensor is installed at each injection point, and the output signal of each sensor is independently connected to the corresponding input channel of the controller. The controller synchronously or sequentially reads the pressure values ​​of all injection points in each control cycle, forming a vector of independent melt pressure values.

[0045] Secondly, for each foaming agent injection point, based on the independent melt pressure and foaming agent temperature at that point, the thermodynamic state model is invoked to independently calculate the independent instantaneous density value of the foaming agent at each injection point. Since the melt pressure values ​​at each injection point are different, the independent instantaneous density values ​​at each point are also different from each other. The density value is larger at the high-pressure injection point closer to the die head, and smaller at the low-pressure injection point farther from the die head.

[0046] Then, the reciprocal of each independent instantaneous density value is taken to obtain the reciprocal density value corresponding to that injection point. The reciprocal density value represents the volume occupied by a unit mass of foaming agent under the current pressure conditions, that is, the specific volume of the foaming agent at that injection point. The larger the reciprocal of the density, the larger the specific volume of the foaming agent at that point, the smaller the mass of foaming agent that can be transported with the same volumetric flow rate, or in other words, the larger the volumetric flow rate required to transport a unit mass of foaming agent.

[0047] Next, the sum of the reciprocals of the densities at all foaming agent injection points is calculated to obtain the total reciprocal value. This total reciprocal value represents the sum of the specific volumes at all injection points under the current operating conditions. This total reciprocal value serves as a normalization benchmark and will be used in subsequent weight allocation calculations.

[0048] Next, for each foaming agent injection point, the reciprocal of the density at that point is divided by the total reciprocal of the density, and the resulting ratio is used as the compensation allocation weight for that injection point. This division operation is the density reciprocal normalization process, which results in each injection point receiving a weight coefficient between 0 and 1, with the sum of the compensation allocation weights for all injection points always being 1. The physical meaning of using the density reciprocal as the basis for the allocation weight is that injection points with larger density reciprocal values ​​indicate larger specific volumes of foaming agent and a larger volumetric flow rate required to transport a unit mass of foaming agent; therefore, they should receive a larger volumetric share when allocating the total flow rate. Injection points with smaller density reciprocal values ​​have smaller specific volumes, and their volumetric share is correspondingly reduced. In this way, although the volumetric flow rate settings allocated to each injection point are different, the mass of foaming agent transported by each point tends to be balanced.

[0049] Then, the previously calculated total volumetric flow rate setpoint is multiplied by the corresponding compensation allocation weight for each foaming agent injection point to obtain the independent volumetric flow rate setpoint for each foaming agent injection point. Since the sum of all weights is always 1, the sum of each independent volumetric flow rate setpoint equals the total volumetric flow rate setpoint, ensuring that the total injection volume remains constant.

[0050] Finally, the independent volumetric flow rate setpoints are sent to their respective flow control actuators installed on the gas injection pipeline section, and each actuator independently performs flow adjustment, thereby completing the injection of foaming agent at each injection point according to the differentiated volumetric flow rate.

[0051] The technical effect of this embodiment is that, under the premise of keeping the total injection mass of multiple injection points constant, the algorithm of density reciprocal normalization for weight allocation makes the mass of foaming agent delivered to each injection point similar to each other, overcoming the defect that the actual injection amount at each point is significantly different due to the axial melt pressure gradient, improving the uniformity of the axial distribution of foaming agent in the polymer melt, and ultimately improving the uniformity of the cell structure of foam products along the length direction.

[0052] In a preferred embodiment, before dividing the reciprocal of the density at each foaming agent injection point by the total reciprocal and using the resulting ratio as the compensation allocation weight for that foaming agent injection point, the method further includes the following step: Retrieve the actual volumetric flow rate values ​​fed back by the flow control actuators at each foaming agent injection point in the previous control cycle; The independent volumetric flow rate set value generated for each foaming agent injection point in the previous control cycle is compared with the actual volumetric flow rate value retrieved at the corresponding injection point to calculate the flow tracking deviation of each foaming agent injection point in the previous control cycle. If the flow tracking deviation at any foaming agent injection point exceeds a preset deviation threshold and the number of consecutive cycles exceeds the preset diagnostic cycle number, then the foaming agent injection point is determined to be an abnormal injection point, and the remaining foaming agent injection points are normal injection points. The step of dividing the reciprocal of the density at each foaming agent injection point by the total reciprocal of the density, and using the resulting ratio as the compensation allocation weight for that foaming agent injection point, includes the following steps: For each normal injection point, the reciprocal of the density at that injection point is divided by the total reciprocal, and the resulting ratio is used as the compensation allocation weight for that foaming agent injection point.

[0053] Specifically, in a multi-point injection system, the pipelines and valves at each injection point may experience scaling, blockage, mechanical wear, or electrical faults during long-term operation, causing the actual flow rate at a particular injection point to fail to effectively track its independent volumetric flow rate setpoint. If this abnormal point is not addressed, it essentially becomes an uncontrollable injection point, continuously injecting inaccurate foaming agent dosage into the melt, disrupting the local foaming agent concentration distribution, and consequently affecting product quality. This embodiment aims to automatically identify and isolate such abnormal injection points, enabling the system to maintain normal collaborative operation of other injection points even in degraded mode. Before calculating the compensation allocation weight for each foaming agent injection point, this embodiment adds the following diagnostic and processing steps.

[0054] The first step involves retrieving the actual volumetric flow rate values ​​fed back by the flow control actuators at each foaming agent injection point in the previous control cycle. After receiving and executing the volumetric flow rate setpoint, the flow control actuators feed back the actual measured volumetric flow rate values ​​to the controller via their integrated sensors or downstream independent flow meters. The controller stores this feedback value in its memory. Before entering the weight calculation for the current cycle, the controller retrieves the actual volumetric flow rate values ​​for each injection point stored in the memory from the previous cycle.

[0055] The second step involves comparing the independent volumetric flow rate setpoint generated for each foaming agent injection point in the previous control cycle with the actual volumetric flow rate value retrieved at the corresponding injection point, thus calculating the flow rate tracking deviation for each foaming agent injection point in the previous control cycle. The comparison can be made by subtracting the actual value from the setpoint and taking the absolute value, or by using a percentage of the relative deviation. This deviation value characterizes the accuracy with which the injection point executed the set flow rate command in the previous cycle.

[0056] The third step is to perform anomaly diagnosis and determination. When the flow tracking deviation at any foaming agent injection point exceeds a preset deviation threshold, and the number of consecutive cycles exceeding this threshold reaches a preset diagnostic cycle number, the controller determines that the foaming agent injection point is an abnormal injection point, while the remaining foaming agent injection points are determined to be normal injection points. The preset deviation threshold is set comprehensively based on the accuracy level of the flow control actuator and the allowable flow error range of the process. The preset diagnostic cycle number is set based on the typical time scale of melt pressure fluctuations and the need to avoid accidental glitch triggering false alarms; for example, it can be set to 5 to 20 consecutive control cycles. Setting the condition of exceeding the specified number of consecutive cycles is to avoid false diagnosis caused by instantaneous sensor noise or brief external disturbances, thereby ensuring that the system has sufficient confidence when making isolation decisions.

[0057] The fourth step involves recalculating the weights of normal injection points. For each normal injection point, the inverse of its density is divided by the sum of the inverse densities of all normal injection points; the resulting ratio is used as the compensation allocation weight for that injection point. Injection points deemed abnormal are completely excluded in this weight allocation process; their compensation allocation weight is set to zero, and the flow control actuators on the corresponding pipelines are either closed or maintained at a minimum safe opening, stopping the foaming agent injection at that point. This operation is equivalent to the system automatically removing an uncontrollable injection point from the control architecture and redistributing its original allocation share among the remaining normal injection points according to their inverse density ratio. Because the allocation weights among the normal injection points are renormalized, their sum remains constant at 1, thus maintaining the total injected mass flow rate. In actual physical processes, after the injection stops at the abnormal injection point, the local concentration of foaming agent near that point will decrease. However, since the remaining normal injection points continue to inject foaming agent along the screw axis in a mass-balanced manner, and under the continuous shearing and conveying action of the screw, the foaming agent in the melt will tend to be uniformly distributed again within a certain axial distance. The impact of local concentration deviation on the final product is significantly reduced.

[0058] The technical advantage of this embodiment is that, through the periodic diagnosis and automatic isolation mechanism based on the historical tracking deviation of the previous cycle, the system can autonomously identify the source of the fault and cut it off from the control link when a slow or sudden fault occurs at the injection point. The remaining normal injection points automatically complete the flow allocation reconstruction. The entire diagnosis and reconstruction process does not require manual intervention and does not interrupt production, thereby significantly improving the reliability and fault tolerance of the multi-point injection system under long-term continuous operation conditions.

[0059] In a preferred embodiment, before calling the built-in thermodynamic state model to continuously calculate the instantaneous density value of the foaming agent under the current operating conditions based on the real-time collected melt pressure value and foaming agent temperature value, the following steps are further included: The fluctuation characteristics of the melt pressure value collected in real time are analyzed, and the dominant fluctuation period of the melt pressure value within a preset observation window is extracted. Obtain the hysteresis response time required for the delivery of foaming agent from its flow control actuator to the foaming agent injection point in the pre-calibrated gas injection pipeline section; If the dominant fluctuation period is greater than or equal to a preset multiple of the lag response time, the current operating condition is determined to be a slow-changing operating condition. The process of calling the built-in thermodynamic state model and continuously calculating the instantaneous density value of the foaming agent under the current operating conditions based on the real-time collected melt pressure value and foaming agent temperature value includes the following steps: If the current operating condition is determined to be a slow-changing condition, the built-in thermodynamic state model is invoked, and the instantaneous density value of the foaming agent under the current operating condition is continuously calculated based on the real-time collected melt pressure value and foaming agent temperature value.

[0060] It's important to note that the feedforward compensation logic described earlier implicitly assumes that the time required for the foaming agent to flow from the flow control actuator to the injection point in the injection line is negligible; that is, the effect of the valve action is instantaneous at the injection point. However, in practical engineering, the flow control actuator is typically installed far from the extruder barrel (to avoid the influence of high temperatures on the actuator), the injection line is of a certain length, and the foaming agent is transported in the line at a limited flow rate. Therefore, there is a non-negligible transport time between the valve outlet and the injection point. We define this transport time as the hysteresis response time, which physically means: after the flow control actuator changes the valve opening, how long does it take for the foaming agent fluid to transmit the corresponding flow rate change to the injection point? The hysteresis response time can be pre-calibrated and stored in the controller during the system commissioning phase through step response testing. The specific calibration method is as follows: The controller sends a small step change in the volumetric flow rate setpoint to the flow control actuator, while continuously recording the pressure sensor signal at the injection point. The time when the pressure signal first appears at the trend inflection point associated with this step change is taken as the response time. The time difference between this response time and the time when the step command is issued is the hysteresis response time. The test can be repeated multiple times and the average value is taken to improve the calibration accuracy.

[0061] After clarifying the concept of hysteresis response time, the fluctuation characteristics of melt pressure values ​​are further analyzed. The fluctuation of melt pressure values ​​is not a single-frequency sine wave, but a composite signal superimposed with multiple time-scale components: pressure changes caused by feed fluctuations and material viscosity drift are usually relatively slow, with fluctuation periods ranging from several seconds to tens of seconds; while the periodic pulsations caused by screw rotation have a higher frequency, with fluctuation periods related to screw speed, typically ranging from tens of milliseconds to hundreds of milliseconds. This embodiment uses fluctuation characteristic analysis to extract the dominant fluctuation period of melt pressure values ​​within a preset observation window. The preset observation window refers to the time length covered by the most recent continuous sequence of melt pressure values ​​stored in the controller's memory, for example, data from the most recent 5 to 30 seconds. Fluctuation characteristic analysis can be implemented using the zero-crossing detection method or the autocorrelation function method: the zero-crossing detection method estimates the dominant period by finding the number of times the pressure signal crosses its sliding average value; the autocorrelation function method calculates the autocorrelation coefficient of the pressure sequence at different hysteresis times, and uses the hysteresis time corresponding to the first maximum value of the autocorrelation coefficient as the dominant fluctuation period. The controller performs a fluctuation characteristic analysis once in each control cycle or every few control cycles to update the estimate of the dominant fluctuation cycle.

[0062] After obtaining the dominant fluctuation period and the lag response time, the controller compares the two. This embodiment sets a preset multiple to measure the sufficiency of the dominant fluctuation period relative to the lag response time. The value of the preset multiple needs to ensure that, when the condition is determined to be slow-changing, the change in melt pressure within a complete delivery lag time window is sufficiently small, so that the density value calculated based on the pressure value collected in the previous cycle can still represent the true density at the injection point in the current cycle. The preset multiple is typically a value between 3 and 10, and the specific value can be determined according to the actual fluctuation characteristics of the production line and the allowable control precision.

[0063] When the dominant fluctuation period is greater than or equal to a preset multiple of the hysteresis response time, it means that the melt pressure fluctuation is slow enough that the pressure value changes negligibly within a hysteresis response time. At this point, the current operating condition is determined to be a slow-varying condition. Under slow-varying conditions, the controller does not need to perform additional predictive processing on the pressure signal. It directly calls the thermodynamic state model and, based on the real-time collected melt pressure and foaming agent temperature values, calculates the instantaneous density value of the foaming agent under the current operating condition, and then proceeds to the subsequent steps of generating and sending the volumetric flow rate setpoint.

[0064] The technical advantage of this embodiment lies in introducing the hysteresis response time, a physical quantity characterizing the dynamic properties of pipeline transmission, and quantitatively comparing it with the dominant fluctuation period of melt pressure, thus constructing a working condition discrimination criterion with clear physical basis. Under slowly varying working conditions that meet the discrimination criteria, the instantaneous density calculation method is directly adopted, ensuring the response speed and computational simplicity of feedforward compensation.

[0065] In a preferred embodiment, after obtaining the pre-calibrated hysteresis response time required for the delivery of the foaming agent from its flow control actuator to the foaming agent injection point in the gas injection pipeline section, the method further includes the following step: If the dominant fluctuation period is less than a preset multiple of the lag response time, the current operating condition is determined to be a rapidly changing operating condition. If the current operating condition is determined to be a rapidly changing operating condition, then retrieve the historical sequence of the melt pressure values ​​stored before the current moment within the most recent preset time period, as well as the instantaneous density values ​​that have been calculated and stored by the thermodynamic state model and correspond to each melt pressure value in the historical sequence after shifting forward by the hysteresis response time along the time axis. A response mapping relationship is constructed based on the historical sequence, which describes the correspondence between the melt pressure value and the instantaneous density value after the hysteresis response time; The melt pressure value and the foaming agent temperature value collected at the current moment are mapped according to the response mapping relationship to obtain the density prediction value, and the density prediction value is used as the instantaneous density value of the foaming agent under the current working condition.

[0066] Specifically, when the current operating condition is determined to be a rapidly changing condition, it means that the melt pressure fluctuates rapidly, and within a lag response time, the melt pressure value has already undergone a non-negligible change. If the instantaneous density value is still calculated directly using the melt pressure value collected at the current moment through a thermodynamic state model, this density value reflects the state of the foaming agent at the injection point at the current moment. However, when the portion of foaming agent delivered by the flow control actuator, adjusted according to this density value, actually arrives at the injection point, the melt pressure at the injection point is no longer the pressure value used in the density calculation. In other words, the calculated density value and the actual pressure experienced by the foaming agent at the injection point are not time-corresponding, resulting in a misalignment of the compensating phase, which in severe cases exacerbates the fluctuation of the injection volume.

[0067] To address the phase misalignment problem under this rapidly changing operating condition, this embodiment employs the following steps.

[0068] The first step is for the controller to retrieve the historical sequence of melt pressure values ​​stored before the current moment within the most recent preset time period, as well as the instantaneous density values ​​that have been calculated and stored by the thermodynamic state model after shifting each melt pressure value along the time axis by the lag response time.

[0069] The preset duration refers to the forward tracing time for retaining historical data in the controller's memory. This duration should cover at least several dominant fluctuation cycles to ensure sufficient data samples for constructing mapping relationships; for example, it can be 5 to 10 times the dominant fluctuation cycle. Each melt pressure value stored in the historical sequence has a timestamp, and the controller has also calculated and stored the corresponding instantaneous density value in each historical control cycle using the thermodynamic state model. When a mapping relationship needs to be constructed, the controller performs a time registration operation on the historical sequence: for each melt pressure value in the historical sequence, starting from the timestamp corresponding to that pressure value, it moves forward along the time axis by the length of a lag response time. At this moved timestamp position, it finds the instantaneous density value in the stored instantaneous density value sequence that is closest to that timestamp, and pairs these two values ​​together. The physical meaning of this pairing operation is that, in historical data, the melt pressure value at time t determines the foaming agent density value after adding the hysteresis response time to time t. Therefore, using the pressure value at time t to match the density value after adding the hysteresis response time to time t is a true record of the transmission hysteresis effect in historical data.

[0070] The second step involves constructing a response mapping relationship based on several pairs of pressure and density values ​​that have been time-registered in the historical sequence. This response mapping relationship describes the correspondence between the melt pressure value and the instantaneous density value after a lag response time. The specific method for constructing the mapping relationship can be piecewise linear interpolation: the pressure values ​​of the historical paired data are arranged in ascending order to form several pressure intervals. Within each interval, the pressure value and density value have an approximately linear relationship, thus forming a broken-line mapping curve. Alternatively, a polynomial fitting method can be used, with pressure as the independent variable and density as the dependent variable, to fit a low-order polynomial as the mapping relationship. The mapping relationship can be dynamically updated in each control cycle based on the latest historical sequence, or it can be updated every few control cycles to save computation.

[0071] The third step involves mapping the currently collected melt pressure and foaming agent temperature values ​​according to the constructed response mapping relationship to obtain the density prediction value. Specifically, the currently collected melt pressure value is substituted into the mapping relationship, and the mapping relationship outputs the corresponding density value. Since the mapping relationship is constructed based on the pairing between pressure values ​​and density values ​​after a lag time in historical data, this mapped output value is essentially a prediction of the density change trend caused by the current pressure value after a lag response time, that is, a prediction of "what the density will be at the injection point when the foaming agent flowing out after the valve adjustment reaches the injection point". This density prediction value is the instantaneous density value used in the current control cycle under rapidly changing conditions.

[0072] After obtaining the density prediction value, the controller uses it as the instantaneous density value and enters the process of calculating the target mass flow rate value and the instantaneous density value to obtain the volumetric flow rate setpoint.

[0073] The technical advantage of this embodiment is that, under rapidly changing operating conditions, the real-time pressure value with the risk of phase lag is no longer used directly for density calculation. Instead, the pressure-density lag pairing relationship accumulated in historical operating data is used to construct a mapping relationship for prediction. Thus, while keeping the feedforward compensation framework unchanged, the phase misalignment of density calculation caused by the transmission lag of the gas injection pipeline is effectively compensated, and the accuracy and reliability of feedforward compensation under rapidly fluctuating melt pressure conditions are significantly improved.

[0074] In a preferred embodiment, after receiving the target mass flow rate instruction, and before obtaining the compensated volumetric flow rate setpoint that can offset the influence of the current melt pressure disturbance based on the target mass flow rate value corresponding to the target mass flow rate instruction and the instantaneous density value, the method further includes the following steps: Call a pre-stored pressure-solubility relationship that describes the change in the solubility of the blowing agent as a function of the melt pressure under the current blowing agent and temperature conditions; Substituting the real-time collected melt pressure value into the pressure-solubility relationship, the maximum saturated mass fraction of foaming agent that can be dissolved per unit mass of polymer melt under the current melt pressure condition is obtained. Multiply the maximum saturated mass fraction by the polymer melt mass flow rate at the current yield to obtain the maximum dissolved mass flow rate of the blowing agent under the current melt pressure conditions; The process of obtaining a compensated volumetric flow rate setpoint that can offset the influence of current melt pressure disturbance based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value includes the following steps: If the target mass flow rate value is less than or equal to the maximum dissolved mass flow rate of the foaming agent, then based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value, a compensated volumetric flow rate setting value that can offset the influence of the current melt pressure disturbance is obtained.

[0075] Specifically, in the extrusion foaming process, the foaming agent needs to be absorbed and dissolved by the polymer melt at the injection port. According to Henry's Law, under certain temperature conditions, the saturated solubility of a gas or volatile liquid in a liquid is directly proportional to the partial pressure of that gas or volatile liquid at the liquid surface. For the combination of polymer melt and physical foaming agent, the higher the melt pressure, the greater the saturated solubility of the foaming agent in the melt, and the higher the upper limit of the mass fraction of foaming agent that the melt can dissolve. In actual production lines, the target mass flow rate is usually calculated by the process formulation based on the desired foaming ratio of the product, assuming that the injected foaming agent can be completely dissolved and uniformly dispersed by the melt. However, if the operating window is low due to low melt pressure, the foaming agent's solubility in the melt decreases, and the originally set target mass flow rate may exceed the upper limit of the foaming agent that the current melt can dissolve. In this case, the excess foaming agent cannot be dissolved and may accumulate in a free state in certain areas of the screw, forming unstable cavitation, interfering with downstream concentration detection, and causing abnormal cell structure during subsequent extrusion molding.

[0076] To address the aforementioned issues, this embodiment adds the following solubility constraint judgment step after receiving the target mass flow rate instruction and before obtaining the volumetric flow rate setting value based on the target mass flow rate value and the instantaneous density value.

[0077] First, the controller invokes a pre-stored pressure-solubility relationship. This relationship is a curve or lookup table describing the maximum saturated mass fraction of blowing agent that can be dissolved per unit mass of polymer melt as a function of melt pressure, under the current blowing agent type and polymer melt temperature. This relationship can be pre-obtained through offline laboratory testing: under different constant temperatures and pressures, after the polymer melt and blowing agent are fully contacted and equilibrated, the mass fraction of blowing agent dissolved in the melt is measured, and a family of curves is plotted with pressure on the horizontal axis and saturated mass fraction on the vertical axis. This family of curves is stored in the controller's memory in the form of a data table or interpolation function for online recall.

[0078] Secondly, the controller substitutes the real-time collected melt pressure value into the pressure-solubility relationship to obtain the maximum saturated mass fraction of blowing agent that can be dissolved per unit mass of polymer melt under the current melt pressure condition. If the real-time collected melt pressure value falls between two discrete pressure points in the data table, the controller obtains the corresponding saturated mass fraction value through linear interpolation or taking the value from the nearest neighbor point.

[0079] The controller then multiplies the obtained maximum saturation mass fraction by the polymer melt mass flow rate at the current yield to obtain the maximum dissolved mass flow rate of the blowing agent under the current melt pressure conditions. The polymer melt mass flow rate at the current yield is a known parameter of the extruder operation, which can be calculated from parameters such as feed rate, screw speed, and die cross-sectional area, or issued to the controller by the host computer based on the production plan. The physical meaning of the maximum dissolved mass flow rate of the blowing agent is: the maximum mass of blowing agent that can be dissolved per second by the polymer melt flowing through the injection point at the current melt pressure and yield; any injection exceeding this limit will not be effectively absorbed by the melt.

[0080] Next, the controller compares the received target mass flow rate value with the calculated maximum dissolving mass flow rate of the blowing agent. If the target mass flow rate value is less than or equal to the maximum dissolving mass flow rate of the blowing agent, it indicates that the current required injection amount is within the melting capacity range of the melt, and the injected blowing agent can be fully dissolved without any over-injection problem. In this case, the controller directly uses the original logic to obtain the compensated volumetric flow rate setpoint based on the target mass flow rate value and the instantaneous density value.

[0081] The technical advantage of this embodiment lies in embedding a safety constraint judgment step based on the physical upper limit of the foaming agent's solubility into the feedforward compensation calculation chain. This ensures that the target injection amount undergoes physical feasibility verification before entering the feedforward calculation. When the melt pressure is too low or the dissolving capacity is insufficient, this judgment step can trigger a corresponding target value correction operation (as follows). When the melt pressure is normal and the dissolving capacity is sufficient, the system operates normally at the original target mass flow rate value without introducing any additional computational overhead. This mechanism effectively avoids the process risks of free foaming agent accumulation and abnormal cell structure caused by the formula setting value exceeding the current melt dissolving capacity.

[0082] Furthermore, after obtaining the maximum dissolved mass flow rate of the foaming agent under the current melt pressure conditions, the method further includes the following steps: If the target mass flow rate is greater than the maximum dissolved mass flow rate of the foaming agent, then the volumetric flow rate setpoint is obtained based on the maximum dissolved mass flow rate of the foaming agent and the instantaneous density value.

[0083] Specifically, after obtaining the maximum dissolving mass flow rate of the blowing agent, if a comparison reveals that the target mass flow rate is greater than the maximum dissolving mass flow rate, it indicates that the blowing agent injection amount required by the current process formulation has exceeded the physical upper limit of the blowing agent that the polymer melt can dissolve under the current melt pressure conditions. If feedforward compensation and injection continue according to the original target mass flow rate value, the portion of the blowing agent exceeding the dissolving capacity will not be effectively dissolved and may accumulate freely in the melt. At this point, the controller needs to automatically adjust the injection amount target.

[0084] The specific correction method is as follows: the controller abandons the target mass flow rate value originally given by the process formula in the current control cycle, and instead uses the maximum dissolved mass flow rate of the foaming agent as the alternative target mass flow rate value. Subsequently, the controller performs a calculation (in this embodiment, a division operation) between this alternative target value and the calculated instantaneous density value to obtain the corresponding volumetric flow rate setpoint. This volumetric flow rate setpoint represents the volumetric flow rate calculated under the current melt pressure conditions, with the upper limit of the mass of foaming agent that the melt can dissolve as the target. After the flow control actuator executes according to this setpoint, the mass of foaming agent injected per unit time is approximately equal to the absorption limit that the current melt can dissolve, which neither exceeds the dissolving capacity nor deviates too much from the process target.

[0085] It should be noted that this correction is only a temporary adjustment for the current control cycle. As the extruder's operating status evolves, if the melt pressure rises back to the normal range in subsequent control cycles, causing the maximum dissolved mass flow rate of the foaming agent to again exceed or equal the original target mass flow rate value, the system will automatically revert to the normal operating branch before the correction was triggered and continue to perform feedforward compensation according to the original target mass flow rate value. This periodic dynamic judgment and automatic recovery mechanism ensures the system's adaptability to melt pressure fluctuations.

[0086] The technical advantage of this embodiment is that when a momentary condition occurs where the melt pressure is too low, resulting in insufficient dissolving capacity, the system automatically and temporarily limits the injection target value to within the current melt's dissolving saturation limit. This prevents a chain reaction of problems such as free cavitation, downstream detection interference, and abnormal bubble formation caused by forcibly injecting the set amount of the formula. Once the pressure returns to normal, the system seamlessly returns to the original target mass flow rate for control. The entire correction and recovery process is completed automatically by the controller without manual intervention, thus balancing process safety, control accuracy, and operational automation.

[0087] In a preferred embodiment, the preset multiple is a dynamically adaptive multiple, and its determination process includes: The density-pressure relationship of the foaming agent at the foaming agent temperature value is obtained in real time, and the partial derivative of density with respect to pressure at the current operating point is determined accordingly. Using the melt pressure value sequence within the preset observation window, the pressure fluctuation amplitude is extracted, and combined with the density partial derivative with respect to pressure, the maximum relative change in foaming agent density caused by melt pressure fluctuation within the hysteresis response time is estimated. Obtain the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section, and calculate the minimum ratio of the dominant fluctuation period to the hysteresis response time required to keep the mass flow error caused by volumetric flow compensation within the preset accuracy range, in conjunction with the maximum relative change in the density of the foaming agent. The minimum ratio is assigned to the preset multiple in real time, and the current working condition is determined to be either a slow-changing working condition or a fast-changing working condition based on the dynamically updated preset multiple.

[0088] It should be noted that the preset multiplier determines the boundary by which the controller classifies the current operating condition as a slow-changing or fast-changing condition. The preset multiplier can be a fixed value. However, in the long-term operation of an actual foaming extrusion production line, process parameters such as foaming agent temperature, extrusion yield, screw speed, and melt viscosity are not strictly constant. They will slowly drift due to factors such as product specification changes, ambient temperature variations, or equipment aging. These parameter changes will affect the rationality of the fast / slow judgment criteria in multiple ways. Changes in foaming agent temperature will alter the density-pressure relationship curve of the foaming agent, causing the same amplitude of melt pressure fluctuation to result in different foaming agent density fluctuation amplitudes under different temperature conditions. The fluctuation amplitude of the melt pressure itself also varies significantly at different yield rates; the pressure fluctuation amplitude is usually larger at high yield rates and relatively stable at low yield rates. Furthermore, the dynamic response characteristics of the flow control actuator—especially the time required from receiving a change in the setpoint to actually completing the valve action—will gradually change with valve wear, air source pressure fluctuations, or hydraulic system aging. If the fixed preset multiple calibrated during the system debugging phase is consistently used, the originally safe multiple may become insufficient when the above-mentioned operating conditions deviate significantly. This could cause situations that should be classified as rapidly changing operating conditions to be misclassified as slowly changing operating conditions, leading to a decrease in the accuracy of simple feedforward compensation due to phase misalignment. Conversely, situations that could be classified as slowly changing operating conditions might be conservatively classified as rapidly changing operating conditions, causing the system to unnecessarily employ more complex prediction mapping algorithms and increasing computational overhead. To address the criterion mismatch problem caused by the fixed preset multiple drifting due to operating conditions, the preset multiple is further limited to a dynamic adaptive multiple, the determination process of which includes the following steps.

[0089] The first step is to acquire the density-pressure relationship of the blowing agent at the current blowing agent temperature in real time, and determine the density partial derivative with respect to pressure at the current operating point. The density-pressure relationship can be generated by the thermodynamic state model built into the controller. Specifically, after acquiring the current blowing agent temperature, the controller, under the condition of a fixed temperature, repeatedly calls the thermodynamic state model to calculate the corresponding density value within a preset neighborhood of the measured melt pressure value, using small pressure steps, thus obtaining a local curve showing the density change with pressure under isothermal conditions. Subsequently, the controller calculates the slope of the tangent to this local curve at the measured pressure point; this slope value is the density partial derivative with respect to pressure. The partial derivative characterizes the sensitivity of the blowing agent density to pressure changes at the current temperature: a larger partial derivative means that a pressure fluctuation of the same magnitude will cause a larger density fluctuation, requiring higher accuracy in the feedforward compensation response to the pressure signal; a smaller partial derivative indicates lower density sensitivity to pressure fluctuations. Since the density-pressure relationship changes with temperature, the partial derivative of density with respect to pressure is also a quantity that is dynamically updated according to the operating conditions.

[0090] The second step involves extracting the pressure fluctuation amplitude using the melt pressure value sequence within a preset observation window. This amplitude, combined with the density partial derivative with respect to pressure, is used to estimate the maximum relative change in blowing agent density caused by melt pressure fluctuations within the hysteresis response time. The pressure fluctuation amplitude is extracted by taking the difference between the maximum and minimum melt pressure values ​​within the preset observation window, or the root mean square deviation of the pressure values ​​around their moving average, as a measure of the current pressure fluctuation amplitude. After obtaining the pressure fluctuation amplitude, it is multiplied by the density partial derivative with respect to pressure obtained in the first step. The resulting product is an estimate of the possible change in blowing agent density caused by pressure fluctuations within the hysteresis response time under the current operating conditions. If the relative density change is required, this density change is divided by the nominal density value at the current operating point (i.e., the density value calculated by the thermodynamic state model at the current pressure and temperature values) to obtain the dimensionless maximum relative density change.

[0091] The third step involves obtaining the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section. Combined with the maximum relative change in foaming agent density, the minimum ratio of the dominant fluctuation period to the hysteresis response time required to keep the mass flow error caused by volumetric flow compensation within the preset accuracy range is calculated. The upper limit of the dynamic response rate of the flow control actuator characterizes the shortest time required for the actuator to adjust the actual flow rate to within the allowable error band near the new setpoint after receiving a command to change the volumetric flow setpoint. This upper limit can be obtained by consulting the technical specifications in the actuator's product manual or through online identification methods. When the upper limit is expressed as a time constant, its reciprocal is a measure of the response rate. After obtaining the upper limit of the response rate, the controller performs the following calculations: the maximum relative change in foaming agent density represents the magnitude of density change that a disturbance may cause within the hysteresis response time window; the upper limit of the response rate represents the speed at which the actuator compensates for this change by adjusting the flow rate. To ensure that the mass flow error caused by volumetric flow compensation remains within a preset accuracy range, the dominant fluctuation period must be long enough to prevent pressure changes from causing density errors exceeding the accuracy tolerance within a transmission lag time, while also allowing sufficient time for the actuator to complete flow adjustment. The controller incorporates the maximum permissible error value within the preset accuracy range, the maximum relative change in density, the upper limit of the response rate, and the lag response time into an analytical formula describing the relationship between mass flow error and control parameters, and then calculates the minimum ratio of the required dominant fluctuation period to the lag response time.

[0092] The fourth step involves assigning the minimum ratio calculated above to a preset multiple in real time, and using this dynamically updated preset multiple to determine whether the current operating condition is a slow-changing or fast-changing condition. The updated preset multiple replaces the fixed preset multiple in Example 4, and is refreshed every control cycle or every few control cycles as the operating condition changes, ensuring that the fast / slow criterion always matches the current actual process conditions.

[0093] In a preferred embodiment, obtaining the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section includes the following steps: During the continuous operation of the foaming extrusion system, the sequence of volumetric flow rate setpoints received by the flow control actuator and the sequence of injection pressure response measured by the dynamic pressure sensor installed on the injection pipeline section are continuously collected. Using the volumetric flow rate setpoint sequence as input and the gas injection pressure response sequence as output, a local dynamic model with the flow control actuator as the core and including the gas capacity characteristics of the downstream gas injection pipeline is identified online using a recursive least squares algorithm with a forgetting factor. Solve for the dominant pole of the local dynamic model, and determine the distance from the dominant pole to the origin as an eigenvalue characterizing the upper limit of the dynamic response rate of the flow control actuator.

[0094] It should be noted that relying solely on the nominal value provided in the product manual to obtain the upper limit of the dynamic response rate of a flow control actuator may present two practical problems. First, the data in the product manual is usually obtained under standard test conditions, which may not be entirely consistent with the actual installation environment in terms of pipe length, number of bends, valve type, and foaming agent properties, resulting in a discrepancy between the nominal and actual values. Second, even if an accurate response rate value is calibrated during the initial installation and commissioning phase, factors such as mechanical wear of the valve core, aging of seals, and pressure fluctuations in the pneumatic or hydraulic drive system will cause the actual response rate of the actuator to gradually decrease over time. If a fixed upper limit value is consistently used in the dynamic calculation of preset multiples, the accuracy of the calculation results will decay over time. Therefore, this embodiment employs an online identification method to continuously obtain the upper limit of the dynamic response rate of the flow control actuator, specifically including the following steps.

[0095] The first step involves continuously acquiring the volumetric flow rate setpoint sequence received by the flow control actuator and the injection pressure response sequence measured by a dynamic pressure sensor installed on the injection line during continuous operation of the foaming extrusion system. The volumetric flow rate setpoint sequence is the command value issued by the controller to the flow control actuator in each control cycle, and the controller itself naturally maintains a complete record of this sequence. The injection pressure response sequence is acquired by a dynamic pressure sensor installed at an appropriate location downstream of the flow control actuator on the injection line. This dynamic pressure sensor differs from the sensor used to measure the melt pressure at the foaming agent injection point; it is installed inside the foaming agent line rather than on the extruder barrel and is used to sense pressure changes in the foaming agent fluid within the line. The dynamic pressure sensor needs to have a sufficiently fast response speed, and its frequency response range should cover the typical operating frequency band of the flow control actuator, for example, not less than 100 Hz. The sensor continuously acquires the foaming agent line pressure at a sampling rate equal to or higher than the preset frequency, forming a pressure response sequence time-aligned with the volumetric flow rate setpoint sequence.

[0096] The second step involves using the volumetric flow rate setpoint sequence as input and the injection pressure response sequence as output, and employing a recursive least squares algorithm with a forgetting factor to identify an online local dynamic model centered on the flow control actuator and incorporating the gas capacity characteristics of the downstream injection pipeline. This local dynamic model can take the form of a first-order inertial element with pure time delay or a second-order underdamped system. The first-order inertial element with pure time delay model includes three parameters to be identified: steady-state gain, time constant, and pure time delay. The second-order model includes four parameters to be identified: steady-state gain, natural frequency, damping ratio, and pure time delay. The order and structure of the model can be pre-selected during the system design phase based on the actuator type and pipeline specifications, and then fixedly written into the controller program. This embodiment preferentially uses the first-order inertial element with pure time delay model because it has fewer parameters, faster identification convergence, and meets the objectives of this step.

[0097] The recursive least squares algorithm with a forgetting factor is an online parameter estimation method. It uses the criterion of minimizing the weighted sum of squares of the errors between the model's predicted output and the actual acquired output, recursively updating the model parameters based on new input and output data in each sampling period. The forgetting factor is a constant between 0.9 and 1, which assigns exponentially decaying weights to historical data, ensuring that recently acquired data contributes more to parameter estimation than older data, thus enabling the model parameters to track the slow time-varying characteristics of the actuator response. The specific value of the forgetting factor needs to be balanced between tracking speed and estimation stationarity; this embodiment uses a value between 0.95 and 0.99. Before executing the recursive least squares algorithm, the volumetric flow rate setpoint sequence and the injection pressure response sequence need to be preprocessed, including removing outliers, subtracting the mean to eliminate steady-state bias, and setting the initial values ​​and covariance matrix of the parameter estimates according to the standard procedures for system identification. These preprocessing operations are routine in online identification practices in industrial control and will not be detailed here.

[0098] The third step is to solve for the dominant pole of the obtained local dynamic model and determine the distance from the dominant pole to the origin as the characteristic value characterizing the upper limit of the dynamic response rate of the flow control actuator. For a first-order inertial plus pure time-delay model, the inertial part after the time delay is a first-order rational transfer function, and its pole is a negative real number. The distance from this pole to the origin is the reciprocal of its absolute value, which is equal to the reciprocal of the inertial time constant. The larger this distance value, the faster the system response. For a second-order model, there is a pair of conjugate complex poles or two real poles, of which the pole closer to the origin is the dominant pole. The distance from the dominant pole to the origin determines the decay rate of the system's free response, which also characterizes the upper limit of the actuator's response speed. After each model parameter update, the controller recalculates the position of the dominant pole and its distance to the origin, and uses this distance value as the characteristic value of the required upper limit of the dynamic response rate.

[0099] In a preferred embodiment, during the online identification of the local dynamic model, the thermodynamic state model is invoked, and the collected pressure data is converted into equivalent pressure data based on a preset reference density according to the gas injection pressure response sequence and the real-time collected foaming agent temperature value. The equivalent pressure data is then used to replace the original pressure data in the identification operation of the recursive least squares algorithm with a forgetting factor, so as to eliminate the influence of time-varying model parameters introduced by the foaming agent density drift with the operating conditions on the identification results.

[0100] It should be noted that the recursive least squares identification using the volumetric flow rate setpoint sequence and the injection pressure response sequence implicitly assumes that the system's dynamic characteristics are constant or only slowly time-varying. However, the injection pressure response sequence is affected not only by changes in the flow control actuator opening but also by changes in the density of the foaming agent fluid itself. Specifically, the foaming agent density changes with temperature and local pipeline pressure, and this density change affects the equivalent gas capacity of the pipeline—that is, the amount of change in the mass of foaming agent that the pipeline can accommodate under a unit pressure change. When the foaming agent density drifts significantly, for example, due to a large adjustment in the extrusion yield causing a continuous rise in the foaming agent temperature or a step shift in pipeline pressure due to process adjustments, the equivalent gas capacity of the pipeline also changes accordingly. This change is not physically a change in the dynamic characteristics of the actuator itself, but in the previous identification framework, since the input and output data were collected with the volumetric flow rate setpoint as input and pressure as output, the change in pipeline gas capacity caused by density drift was mistakenly interpreted as a change in model parameters, leading to fluctuations in the identified local dynamic model parameters. Such parameter fluctuations contradict the purpose of calculating the upper limit of the dynamic response rate. Previous embodiments required a value that accurately reflects the actuator's own response speed, rather than a mixed change incorporating the effects of foaming agent density drift. To address this issue, this embodiment introduces density compensation preprocessing in the identification calculation, as detailed below.

[0101] During the identification process, the controller calls the thermodynamic state model and converts the collected pressure data into equivalent pressure data based on a preset reference density, according to the pressure values ​​corresponding to each sampling point in the gas injection pressure response sequence and the real-time collected foaming agent temperature values.

[0102] The specific execution method of this conversion operation is as follows: The preset reference density is the foaming agent density value corresponding to a certain calibration condition, calibration temperature, and calibration pressure during the system debugging phase, and is stored as a constant in the controller. For each sampling point in the injection pressure response sequence, the controller obtains the foaming agent temperature value and the actual measured pressure value corresponding to that sampling point, and calls the thermodynamic state model to calculate the true density value under the actual temperature and pressure values; then, it calculates the ratio of the true density value to the preset reference density, uses this ratio as a correction factor, and multiplies the actual measured pressure value by this correction factor to obtain the equivalent pressure data. The physical meaning of the equivalent pressure data is: if the density of the foaming agent at the current moment is equal to the preset reference density, then at the current temperature value and the current actuator opening, the required pipeline pressure value to achieve the same change effect in the mass of foaming agent in the pipeline as the actual one is the equivalent pressure value. By mapping the true pressure data to the equivalent pressure data under the reference density condition, the modulation effect of foaming agent density drift on the pipeline pressure response is removed from the data.

[0103] Then, the equivalent pressure data replaces the original pressure data and participates in the identification operation of the recursive least squares algorithm with a forgetting factor. At this time, the input of the identification algorithm is still the volumetric flow rate setpoint sequence, and the output is replaced by the equivalent pressure sequence. Since the equivalent pressure sequence has eliminated the influence of density drift, the identified local dynamic model parameters will mainly reflect the mechanical dynamic characteristics of the flow control actuator and the pipeline gas capacity characteristics based on the reference density, eliminating spurious time variations introduced by density changes.

[0104] The technical advantage of this embodiment lies in that, by performing density compensation preprocessing on the pressure data involved in the identification, the external factor of foaming agent density drift with operating conditions is decoupled from the pipeline dynamic response data. This ensures that the upper limit of the dynamic response rate of the flow control actuator extracted by online identification only reflects the actuator's true response capability. This preprocessing step enables the online identification mechanism to maintain the stability and accuracy of the identification results across a wide operating range of the foaming extrusion system, thereby further improving the reliability of the dynamic adaptive preset multiple calculation.

[0105] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A foaming agent injection control method based on real-time melt pressure feedforward compensation, applied to a foaming extrusion system, the system production line including a melt preheating device for providing polymer melt and an injection pipeline section for injecting physical foaming agent into the polymer melt, characterized in that, Includes the following steps: Receive the target mass flow rate command, and at the same time collect the melt pressure value at the foaming agent injection point and the foaming agent temperature value in the gas injection pipeline section in real time at a preset frequency; The built-in thermodynamic state model is invoked, and the instantaneous density value of the foaming agent under the current working condition is continuously calculated based on the real-time collected melt pressure value and foaming agent temperature value. Based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value, a compensated volumetric flow rate setting value that can offset the influence of the current melt pressure disturbance is obtained. The volumetric flow rate setpoint is sent to the flow control actuator on the gas injection pipeline section to adjust the actual volumetric flow rate of the foaming agent injected into the polymer melt, thereby keeping the mass of the foaming agent injected into the polymer melt constant per unit time. The air injection pipeline section of the foaming extrusion system includes at least two foaming agent injection points distributed along the axial direction of the extruder screw; Sending the volumetric flow rate setpoint to the flow control actuator on the gas injection pipeline section to adjust the actual blowing agent volumetric flow rate injected into the polymer melt includes the following steps: Real-time acquisition of independent melt pressure values ​​at each foaming agent injection point; For each foaming agent injection point, the independent instantaneous density value of the foaming agent at each injection point is calculated based on the independent melt pressure value and the foaming agent temperature value at that injection point. Take the reciprocal of each independent instantaneous density value to obtain the reciprocal density value corresponding to that injection point; calculate the sum of the reciprocal density values ​​of all foaming agent injection points to obtain the total reciprocal value; For each foaming agent injection point, the reciprocal value of the density at that injection point is divided by the total reciprocal value, and the resulting ratio is used as the compensation allocation weight for that foaming agent injection point; wherein, the sum of the compensation allocation weights of all foaming agent injection points is always 1; Multiply the volumetric flow rate setpoint by the corresponding compensation allocation weight for each foaming agent injection point to obtain an independent volumetric flow rate setpoint for each foaming agent injection point. Each of the independent volumetric flow rate settings is sent to its corresponding flow control actuator installed on the gas injection pipeline section.

2. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 1, characterized in that, Before dividing the reciprocal of the density at each foaming agent injection point by the total reciprocal and using the resulting ratio as the compensation allocation weight for that foaming agent injection point, the method further includes the following steps: Retrieve the actual volumetric flow rate values ​​fed back by the flow control actuators at each foaming agent injection point in the previous control cycle; The independent volumetric flow rate set value generated for each foaming agent injection point in the previous control cycle is compared with the actual volumetric flow rate value retrieved at the corresponding injection point to calculate the flow tracking deviation of each foaming agent injection point in the previous control cycle. If the flow tracking deviation at any foaming agent injection point exceeds a preset deviation threshold and the number of consecutive cycles exceeds the preset diagnostic cycle number, then the foaming agent injection point is determined to be an abnormal injection point, and the remaining foaming agent injection points are normal injection points. The step of dividing the reciprocal of the density at each foaming agent injection point by the total reciprocal of the density, and using the resulting ratio as the compensation allocation weight for that foaming agent injection point, includes the following steps: For each normal injection point, the reciprocal of the density at that injection point is divided by the total reciprocal, and the resulting ratio is used as the compensation allocation weight for that foaming agent injection point.

3. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 1, characterized in that, Before calling the built-in thermodynamic state model to continuously calculate the instantaneous density value of the foaming agent under the current operating conditions based on the real-time collected melt pressure value and foaming agent temperature value, the following steps are also included: The fluctuation characteristics of the melt pressure value collected in real time are analyzed, and the dominant fluctuation period of the melt pressure value within a preset observation window is extracted. Obtain the hysteresis response time required for the delivery of foaming agent from its flow control actuator to the foaming agent injection point in the pre-calibrated gas injection pipeline section; If the dominant fluctuation period is greater than or equal to a preset multiple of the lag response time, the current operating condition is determined to be a slow-changing operating condition. The process of calling the built-in thermodynamic state model and continuously calculating the instantaneous density value of the foaming agent under the current operating conditions based on the real-time collected melt pressure value and foaming agent temperature value includes the following steps: If the current operating condition is determined to be a slow-changing condition, the built-in thermodynamic state model is invoked, and the instantaneous density value of the foaming agent under the current operating condition is continuously calculated based on the real-time collected melt pressure value and foaming agent temperature value.

4. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 3, characterized in that, After obtaining the pre-calibrated hysteresis response time required for the delivery of foaming agent from its flow control actuator to the foaming agent injection point in the gas injection pipeline section, the method further includes the following steps: If the dominant fluctuation period is less than a preset multiple of the lag response time, the current operating condition is determined to be a rapidly changing operating condition. If the current operating condition is determined to be a rapidly changing operating condition, then retrieve the historical sequence of the melt pressure values ​​stored before the current moment within the most recent preset time period, as well as the instantaneous density values ​​that have been calculated and stored by the thermodynamic state model and correspond to each melt pressure value in the historical sequence after shifting forward by the hysteresis response time along the time axis. A response mapping relationship is constructed based on the historical sequence, which describes the correspondence between the melt pressure value and the instantaneous density value after the hysteresis response time; The melt pressure value and the foaming agent temperature value collected at the current moment are mapped according to the response mapping relationship to obtain the density prediction value, and the density prediction value is used as the instantaneous density value of the foaming agent under the current working condition.

5. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 1, characterized in that, After receiving the target mass flow rate instruction, and before obtaining the compensated volumetric flow rate setpoint that can offset the influence of the current melt pressure disturbance based on the target mass flow rate value corresponding to the target mass flow rate instruction and the instantaneous density value, the method further includes the following steps: Call a pre-stored pressure-solubility relationship that describes the change in the solubility of the blowing agent as a function of the melt pressure under the current blowing agent and temperature conditions; Substituting the real-time collected melt pressure value into the pressure-solubility relationship, the maximum saturated mass fraction of foaming agent that can be dissolved per unit mass of polymer melt under the current melt pressure condition is obtained. Multiply the maximum saturated mass fraction by the polymer melt mass flow rate at the current yield to obtain the maximum dissolved mass flow rate of the blowing agent under the current melt pressure conditions; The process of obtaining a compensated volumetric flow rate setpoint that can offset the influence of current melt pressure disturbance based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value includes the following steps: If the target mass flow rate value is less than or equal to the maximum dissolved mass flow rate of the foaming agent, then based on the target mass flow rate value corresponding to the target mass flow rate command and the instantaneous density value, a compensated volumetric flow rate setting value that can offset the influence of the current melt pressure disturbance is obtained.

6. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 5, characterized in that, After obtaining the maximum dissolved mass flow rate of the foaming agent under the current melt pressure conditions, the method further includes the following steps: If the target mass flow rate is greater than the maximum dissolved mass flow rate of the foaming agent, then the volumetric flow rate setpoint is obtained based on the maximum dissolved mass flow rate of the foaming agent and the instantaneous density value.

7. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 3, characterized in that, The preset multiple is a dynamic adaptive multiple, and its determination process includes: The density-pressure relationship of the foaming agent at the foaming agent temperature value is obtained in real time, and the partial derivative of density with respect to pressure at the current operating point is determined accordingly. Using the melt pressure value sequence within the preset observation window, the pressure fluctuation amplitude is extracted, and combined with the density partial derivative with respect to pressure, the maximum relative change in foaming agent density caused by melt pressure fluctuation within the hysteresis response time is estimated. Obtain the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section, and calculate the minimum ratio of the dominant fluctuation period to the hysteresis response time required to keep the mass flow error caused by volumetric flow compensation within the preset accuracy range, in conjunction with the maximum relative change in the density of the foaming agent. The minimum ratio is assigned to the preset multiple in real time, and the current working condition is determined to be either a slow-changing working condition or a fast-changing working condition based on the dynamically updated preset multiple.

8. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 7, characterized in that, The process of obtaining the upper limit of the dynamic response rate of the flow control actuator on the gas injection pipeline section includes the following steps: During the continuous operation of the foaming extrusion system, the sequence of volumetric flow rate setpoints received by the flow control actuator and the sequence of injection pressure response measured by the dynamic pressure sensor installed on the injection pipeline section are continuously collected. Using the volumetric flow rate setpoint sequence as input and the gas injection pressure response sequence as output, a local dynamic model with the flow control actuator as the core and including the gas capacity characteristics of the downstream gas injection pipeline is identified online using a recursive least squares algorithm with a forgetting factor. Solve for the dominant pole of the local dynamic model, and determine the distance from the dominant pole to the origin as an eigenvalue characterizing the upper limit of the dynamic response rate of the flow control actuator.

9. The foaming agent injection control method based on real-time melt pressure feedforward compensation according to claim 8, characterized in that, During the online identification of the local dynamic model, the thermodynamic state model is invoked. Based on the gas injection pressure response sequence and the real-time collected foaming agent temperature value, the collected pressure data is converted into equivalent pressure data with a preset reference density as the benchmark. The equivalent pressure data is then used to replace the original pressure data in the identification calculation of the recursive least squares algorithm with a forgetting factor, so as to eliminate the influence of the time-varying model parameters introduced by the foaming agent density drift with the operating conditions on the identification results.

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