Modular intelligent continuous regenerated fiber production line and process

Abstract

The invention relates to the field of regenerated fiber production equipment manufacturing and process integration, and discloses a modular intelligent continuous regenerated fiber production line which comprises a sorting and cleaning module, a melt extrusion module, an impurity filtering module, a granulation module, a decoloration module, a solid phase polycondensation tackifying module and a melt spinning module. The self-adaptive material distribution device is used for realizing material connection among the modules; the automatic control system is used for realizing collaborative operation of all the modules; wherein the solid phase polycondensation tackifying module is provided with an intelligent control unit for dynamically optimizing the operation of the solid phase polycondensation tackifying module. Compared with the prior art that each process is relatively independent and depends on manual scheduling or simple linkage, the scheme effectively overcomes the common problems of unsmooth material conveying, unbalanced matching between modules and insufficient automation degree in the traditional regeneration process, and remarkably improves the production continuity and the resource utilization rate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of regenerated fiber production equipment manufacturing and process integration, and particularly relates to a modular intelligent continuous regenerated fiber production line and process. BACKGROUND

[0002] The modular intelligent continuous regenerated fiber production line and process is an advanced manufacturing technology applied to the recycling and regeneration of waste polymer-containing materials such as waste textiles and plastic bottle pieces. The core goal is to convert waste raw materials with complex sources and different characteristics into regenerated fibers with specific performance indicators that can be used again in the textile or other industrial fields through a series of physical and chemical processes. This technical field is of great significance for promoting resource recycling, reducing environmental pollution, and promoting green and sustainable development.

[0003] However, in the prior art practice, the production process of regenerated fibers still faces many challenges. The traditional production line often relies on segmented material transportation and a relatively extensive coordination mechanism in the connection of each process unit, which leads to difficulty in accurately matching the running rhythm between different modules, easy formation of production bottlenecks, and the need to improve the overall automation and intelligence level, thereby affecting the continuity of production and the efficiency of material flow. In particular, in the key solid-phase polycondensation adhesion link, the control logic is mostly based on experience accumulation or simplified process models, lacking deep insight and accurate description of the complex reaction kinetics, mass transfer phenomena and crystallization behavior inside the polymer, which makes it difficult to achieve fine regulation of the final molecular structure and performance of the product, and the batch stability of the product quality is also restricted. SUMMARY

[0004] The purpose of the present application is to provide a modular intelligent continuous regenerated fiber production line and process, which solves the problems of insufficient coordination between process units, low material flow efficiency, and limited control precision of the solid-phase polycondensation core module in the prior art.

[0005] To achieve the above purpose, the present application is implemented by the following technical solutions: The modular intelligent continuous regenerated fiber production line comprises: a sorting and cleaning module, a melt extrusion module, a impurity filtering module, a granulation module, a decolorization module, a solid-phase polycondensation adhesion module, and a melt spinning module; a material self-adaptive distribution device for realizing the material connection between modules; an automatic control system for realizing the collaborative work of the modules; The solid-phase polycondensation adhesion module is configured with an intelligent control unit for dynamically optimizing its operation, and the intelligent control unit is based on the prediction and control of the physical and chemical model of the solid-phase polycondensation process.

[0006] The overall architecture of the production line and the core intelligent features. Its innovation is first reflected in the clear division of modularization and the introduction of material self-adaptive distribution device. This design ensures smooth and efficient connection of each processing stage from waste raw materials to regenerated fibers, breaking the limitations of low matching degree and easy bottleneck between traditional regeneration equipment. More core innovation lies in the clear configuration of an intelligent control unit based on a physicochemical model for the key solid-phase polycondensation module. This means that the control strategy no longer relies solely on simple feedback regulation, but can deeply understand and predict the complex reaction and transfer phenomena in the solid-phase polycondensation process, thereby achieving dynamic, mechanism-based optimal operation. This model-based prediction and control method is a fundamental innovation to realize the intelligentization of the regenerated fiber production process and improve product quality stability and production efficiency.

[0007] Preferably, the physicochemical model contained in the intelligent control unit is a reaction kinetics network model refined based on quantum chemical calculation. The rate constant of elementary reaction j is calculated by transition state theory: Wherein: k TST,j represents the rate constant of elementary reaction j calculated based on transition state theory, whose unit depends on the reaction order, s -1 or L·mol -1 ·s -1 ; κ j represents the tunneling correction factor of elementary reaction j, which is usually close to 1 for reactions not involving light atom transfer; k B represents the Boltzmann constant, whose value is 1.380649×10 -23 J·K -1 ; T represents the absolute temperature, in K; h represents the Planck constant, whose value is 6.62607015×10 -34 J·s; represents the partition function of the transition state of elementary reaction j, which does not include the vibration contribution along the reaction coordinate; Q R,j represents the total partition function of the reactants of elementary reaction j; E a,j represents the activation energy of elementary reaction j, in J·mol -1 ; R represents the ideal gas constant, whose value is 8.314 J·mol -1 ·K -1 .

[0008] This step further defines the construction method of the reaction kinetics part in the physicochemical model. Its innovative mechanism lies in abandoning the practice of relying heavily on empirical parameter fitting in traditional macroscopic kinetic models, and instead starting from the micro level, using quantum chemical calculation methods to refine the key parameters that describe the chemical reaction rate, activation energy and pre-exponential factor (these parameters are obtained through a transition state theory expression containing temperature, partition function and basic physical constants). The reaction kinetics network model constructed in this way can more accurately reflect the true rates of various main reactions and side reactions in the solid-state polycondensation process, improving the prediction accuracy of the model for complex reaction systems. This method of parameterization of macroscopic process models guided by first-principles calculations provides a more reliable and accurate "brain" for the intelligent control unit, and is a key innovation point for improving model prediction accuracy and control optimization effect.

[0009] Preferably, the physicochemical model included in the intelligent control unit further comprises a coupled mass transfer-crystallization model, which uses the free volume theory to describe the diffusion coefficient of small molecule byproducts in the polymer amorphous phase: Wherein: A D,sm represents the pre-exponential factor of small molecule sm diffusion, with unit of m 2 ·s -1 ; B D,sm is a dimensionless parameter related to the minimum local free volume required for the transition of small molecule sm; v f represents the average fractional free volume of the polymer, which is a dimensionless parameter; v f (T) = v f,g + α f,v (T-T g ), where v f,g is the fractional free volume of the polymer at the glass transition temperature T g , α f,v is the thermal expansion coefficient of the free volume fraction (K -1 ), and T g (K) itself is also a function of molecular weight and crystallinity.

[0010] Another important component of the physicochemical model is the coupled description of the mass transfer and crystallization processes in the solid phase. The rate of solid-phase polycondensation reaction is not only controlled by the chemical reaction itself, but also strongly depends on the removal efficiency of small molecule by-products from the inside of the polymer particles (mass transfer) and the change in the crystallization state of the polymer itself. The innovative mechanism of the present invention is that by introducing a diffusion model based on free volume theory, it can more accurately describe the ease with which small molecules migrate in the polymer matrix (this is closely related to the free volume of the polymer, that is, the gap between molecules); at the same time, combined with the crystallization kinetics model, it dynamically tracks the changes in polymer crystallinity during the reaction and its impact on mass transfer and reaction. Integrating the three mutually coupled key physicochemical processes of chemical reaction, mass transfer and crystallization into a unified model enables the intelligent control unit to understand and predict the SSP process more comprehensively, which is another important innovation for achieving fine control of the final performance of the product (viscosity, molecular weight distribution and thermal stability).

[0011] Preferably, the intelligent control unit adopts a stochastic model predictive control (SMPC) strategy, the objective function of which includes optimization items for the intrinsic viscosity IV, molecular weight distribution MWD and color index of the regenerated fiber, and takes into account the raw material characteristics d rw random fluctuations.

[0012] The core control algorithm adopted by the intelligent control unit - stochastic model predictive control (SMPC) - is clarified. A major challenge facing the production of regenerated fibers is the wide range of raw material sources and large fluctuations in properties. Traditional deterministic control strategies are difficult to adapt to this uncertainty. The innovative mechanism of the present invention is that the SMPC strategy can explicitly incorporate the random fluctuations in raw material properties into the optimization decision-making process. It no longer pursues a single, optimal solution under ideal conditions, but takes the expected performance of key product indicators (intrinsic viscosity IV, molecular weight distribution MWD and color) or the probability of meeting quality requirements as the goal, taking into account uncertainty. This forward-looking optimization control method that takes randomness into account significantly enhances the robustness and adaptability of the production line to raw material fluctuations, and is a key technological innovation for achieving stable production of high-quality regenerated fibers.

[0013] Preferably, the optimization problem of the SMPC strategy is expressed as: in: In the prediction domain N pH The control input sequence to be optimized is u c This may include temperature setpoints for each section of the reactor and inert gas flow rates; represents the random disturbance d on the raw material characteristics rw The mathematical expectation of the distribution of the raw material characteristics d rwThe initial intrinsic viscosity IV0, end group concentration [-COOH]0, [-OH]0, moisture content w of the incoming material can be included c , impurity species and content I c ; N pH is the length of the prediction horizon; is the stage cost function at step j within the prediction horizon, which quantifies the combined cost of the current state and control input , said state may include intrinsic viscosity IV, number average molecular weight M n , weight average molecular weight M w , polydispersity index PDI(M w / M n ), color parameters, and temperature profile, small molecule byproduct concentration profile within the reactor; is the terminal cost function at the end of the prediction horizon.

[0014] The specific mathematical form of the SMPC strategy is defined. Its innovative mechanism is reflected in the setting of the optimization objective and constraint conditions. The objective function guides the control decision by minimizing the expected value of the cumulative operating cost (stage cost) and the deviation of the final product state (terminal cost) within a certain period of time, ensuring the economy and effectiveness of the control. More importantly, the concept of "chance constraint" is introduced, which does not require the intrinsic viscosity to strictly reach the target under any circumstances, but requires the probability of the intrinsic viscosity meeting the requirements to reach an acceptable level considering the uncertainty. This probability-based constraint handling method makes the control strategy more flexible and practical in dealing with random disturbances, effectively balances the reliability of product quality and the economy of production process, and is one of the core innovations of the successful application of SMPC strategy in complex industrial processes. The intelligent control unit adopts a physical information neural network (PINN) as a surrogate model of the physicochemical model, and the loss function L PINN of the PINN contains a residual term L PDE based on the control equation of the physicochemical model.

[0015] The technical means used to solve the problem that the calculation amount of a complex physical and chemical model is too large and it is difficult to meet the real-time requirements of SMPC online optimization. The innovation mechanism lies in introducing a physical information neural network (PINN) as a proxy model of a high-fidelity physical and chemical model. The PINN is special in that its training process not only depends on data, but more importantly, the physical law (reflected in the control equation of the physical and chemical model) is introduced as a constraint (realized through a residual term in the loss function) into the optimization process of the neural network. This enables the PINN to greatly reduce the computational cost of model evaluation while ensuring high prediction accuracy. Using the PINN to replace the complex mechanism model for online calculation of SMPC greatly improves the response speed and practicality of the intelligent control system, and is a key innovation to realize the landing application of advanced control strategies in complex industrial scenarios.

[0016] Preferably, the intelligent control unit further comprises a raw material property online estimation module, which estimates the raw material property based on online sensor data y sens and updates the posterior probability distribution P rw (d rw |y rw ) of the key properties d sens of the raw material through Bayesian inference.

[0017] Since the properties of the regenerated raw material are difficult to completely predict, the innovation mechanism of the present application lies in establishing a raw material property online estimation module. The module uses the data collected by the online sensor (near-infrared spectrometer) deployed on the production line in real time, and dynamically updates the knowledge (i.e. posterior probability distribution) of the key properties (initial viscosity, component content) of the current batch of raw material through Bayesian inference statistical methods. This online and adaptive estimation capability enables the intelligent control system to timely grasp the actual situation of the raw material, rather than relying solely on historical statistics or offline detection, thereby providing more accurate input information for the SMPC strategy and further improving the precision of control and the ability to respond to disturbances, which is an important link to realize truly intelligent production.

[0018] Preferably, the automatic control system further performs geometric nonlinear control theory analysis based on a nonlinear system model of the solid-phase polycondensation thickening module to optimize sensor layout or evaluate system controllability and observability, and the nonlinear system model is represented as: y nl =h nl (x nl ); where x nl is a state vector, u nl,i is a control input, f nl (x nl ) is a drift vector field, and gnl,i (x nl ) is a control vector field, y nl is a measurement output, h nl (x nl ) is an output function.

[0019] Theoretical basis for system-level design optimization of key modules (especially SSP module) is proposed. The solid state polymerization process has significant nonlinear characteristics. The innovation mechanism of the present invention is that the nonlinear system model (consisting of a set of state equations and output equations) describing the dynamic behavior of the SSP module is analyzed in depth by applying geometric nonlinear control theory. Through this analysis, the controllability (i.e. whether the system can be driven to the desired state through control input) and observability (i.e. whether the internal state of the system can be accurately estimated through sensor output) of the system state under the existing sensor and actuator configuration can be theoretically evaluated. The analysis results can be used to guide the optimal layout of sensors (placed at the most sensitive position to the system state) or to evaluate the necessity of increasing / adjusting actuators, thereby fundamentally improving the performance potential of the control system and the effectiveness of information acquisition. This deep system theory-based analysis and design is an innovative guarantee to ensure that the intelligent control strategy can fully exert its effectiveness.

[0020] A process based on the above production line, the process comprising the following steps: Sorting and cleaning the waste fiber raw material, melting and extruding, filtering impurities, granulating, and decolorizing to obtain regenerated polymer chips; Inputting the regenerated polymer chips into the solid state polymerization and tackification module for tackification reaction; Melting and spinning the tackified polymer to obtain regenerated fibers; Among them, during the viscosity-increasing reaction process of the solid-phase polycondensation viscosity-increasing module, the intelligent control unit is based on the real-time estimation of the random fluctuations in the characteristics of the regenerated polymer chips, and the random model predictive control SMPC strategy is used to dynamically regulate the reaction temperature, reaction time and inert gas flow rate to synergistically optimize the intrinsic viscosity, molecular weight distribution and color of the resulting polymer. The random fluctuations in the characteristics of the feed chips are perceived and quantified in real time through the online estimation module; then, the SMPC strategy in the intelligent control unit receives this real-time estimation information and uses its internal prediction model (accelerated by PINN) to dynamically and proactively optimize the settings of key process parameters such as reaction temperature, reaction time, and inert gas flow rate; the ultimate goal is to synergistically maintain multiple key quality indicators of the final product, such as the intrinsic viscosity, molecular weight distribution and color, within the target range and optimize them as much as possible while responding to fluctuations in raw materials. This closed-loop, multivariable, model-based, and real-time information-based intelligent optimization control process is optimal for achieving high-quality, stable production of regenerated fibers. The SMPC strategy, when dynamically regulating reaction parameters, further considers entropy generation constraints derived from nonequilibrium thermodynamic analysis. These entropy generation constraints are used to limit the maximum temperature gradient within the reactor or the heating or cooling rate of the material.

[0021] The optimization connotation of the SMPC strategy has been further deepened at the process level. Its innovative mechanism lies in introducing the principle of non-equilibrium thermodynamics (NET) into the optimization control of the SSP process. By analyzing the entropy (a physical quantity that measures the disorder and energy dissipation of the system) generated by the irreversible processes of heat transfer, mass transfer, and chemical reactions inside the SSP reactor, the key factors affecting the efficiency and stability of the system can be identified. In addition to considering product quality and production efficiency in the optimization objectives, the SMPC strategy also introduces constraints based on entropy generation analysis to limit the maximum allowable temperature gradient in the reactor or the rate of material heating and cooling. The purpose of this is to guide the SSP process to operate under conditions that are closer to thermodynamic reversibility, thereby reducing ineffective energy dissipation, improving energy utilization efficiency, and improving equipment stability and product uniformity by avoiding excessive thermal shock. This is an innovative embodiment of optimizing the production process at a higher level, taking into account economic benefits, product quality, and green sustainability. In summary, the present invention includes at least one of the following beneficial technical effects: 1. This invention achieves highly integrated and intelligently coordinated recycled fiber production processes through the construction of modular production units, supplemented by adaptive material distribution and automated control systems. This design imbues the production line with unprecedented fluidity and overall operational efficiency. Compared to existing technologies where each process is relatively independent and relies on manual scheduling or simple linkage, this solution effectively overcomes the common problems of poor material transportation, unbalanced matching between modules, and insufficient automation in traditional recycling processes, significantly improving production continuity and resource utilization.

[0022] 2. Targeting the core process of solid-state polycondensation and thickening, the present invention innovatively introduces an intelligent control unit based on deep physical and chemical mechanisms. This unit incorporates a reaction kinetics network and coupled mass transfer-crystallization model refined through quantum chemistry. This advance enables a new level of precision in the understanding and regulation of complex SSP processes, enabling a more accurate understanding of the evolution of polymer microstructures. Compared to existing technologies that rely heavily on empirical parameters or simplified models for control, the present invention fundamentally enhances the ability to predict and precisely control the SSP reaction process, thereby effectively ensuring the stability and optimization of the inherent quality of regenerated fiber products.

[0023] 3. The present invention uses a stochastic model predictive control (SMPC) strategy and combines it with online estimation technology of raw material characteristics, so that the production line can actively adapt to the inherent uncertainty of recycled raw materials. The intelligent control core can sense and quantify the fluctuations of feed characteristics in real time and adjust process parameters proactively. Compared with the existing technology, which often shows adjustment lag and difficulty in maintaining stable production when facing raw material differences, the solution provided by the present invention significantly enhances the robustness of the entire production system to raw material changes, ensuring the consistency of product performance and the smooth operation of the production process under complex raw material conditions.

[0024] 4. The present invention not only realizes the intelligent optimization of single-point modules, but also accelerates control decisions through full-line automated collaboration and the application of advanced agent models (physical information neural network PINN), and introduces system-level analysis theory (geometric nonlinear control theory) to guide the optimal configuration of key components, and even incorporates entropy generation constraints based on non-equilibrium thermodynamics at the process level. This multi-dimensional, systematic intelligent design has brought about improvements in the overall performance and resource efficiency of the production line. Compared with the existing technology, which often lacks a global optimization perspective, slow control response, or system design relies on trial and error, the present invention effectively solves the problems of low energy efficiency, weak system adaptability, and lack of precise theoretical guidance for operation and maintenance decisions through the integration of scientific top-level design and advanced algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a schematic diagram of the production line architecture of the present invention; Figure 2It is a schematic diagram of the process flow of the present invention. DETAILED DESCRIPTION

[0026] The following is combined with Figure 1 -Attached Figure 2 , the present invention is described in further detail.

[0027] The present invention provides a modular intelligent continuous regenerated fiber production line, such as Figure 1 and Figure 2 As shown, the production line includes: S1. Overall construction of production line and intelligent material flow: In this embodiment, the physical architecture of this modular, intelligent, continuous recycled fiber production line has been meticulously designed, with its core focus on achieving continuous, automated processing from waste raw materials to primary recycled chips. The front end of the line primarily comprises a series of process modules operating in tandem, with the waste fiber raw materials first being directed to the sorting and cleaning module.

[0028] Generally, the sorting and cleaning module includes a near-infrared spectroscopy sorting device for identifying fibers of different materials, a high-pressure water washing device for removing surface stains, and a crushing device for preliminary shredding to facilitate subsequent processing.

[0029] In some embodiments, the sorting and cleaning module may also be integrated with a color sorting unit to pre-sort the raw materials according to the color requirements of the final recycled fiber product.

[0030] In this embodiment, the purity and uniformity of the material after being processed by the sorting and cleaning module are preliminarily guaranteed, and then the material enters the melt extrusion module through the conveying device.

[0031] Specifically, the melt extrusion module utilizes a twin-screw or single-screw extruder with precise temperature control in stages to ensure the material is fully plasticized and melted under appropriate shear and temperature conditions. The extruder's screw configuration and aspect ratio are optimized based on the rheological properties of the recycled polymer being processed.

[0032] The molten polymer is then fed into a filter module. This module is typically equipped with automatic backwashing or a replaceable multi-layer filter screen to effectively remove tiny solid impurities and unmelted particles remaining in the melt, preventing these impurities from affecting subsequent pelletization and the quality of the final fiber. The filter accuracy can be adjusted to 50 microns or higher, depending on product requirements.

[0033] In this embodiment, the clean melt that has undergone fine filtration is then introduced into a granulation module and converted into recycled polymer chips with regular shape and uniform size.

[0034] Alternatively, the pelletizing module can utilize an underwater pelletizing system or a strand pelletizing system. Underwater pelletizing is particularly suitable for polymers with high viscosity or strict requirements on pellet shape, resulting in highly round pellets. The pellets are rapidly cooled and solidified in a cooling medium (usually water), followed by centrifugal dehydration and vibration screening to obtain qualified pellets.

[0035] If further color improvement is required for these initially formed recycled polymer chips, they are transported to the decolorization module. The decolorization module can use chemical decolorizers or physical adsorption methods to reduce the yellowness index of the chips and improve their appearance quality.

[0036] In this embodiment, the material transportation and distribution between the above modules are completed by a set of material adaptive distribution devices and an automatic control system in collaboration, which is the key to achieving continuous and stable operation of the production line.

[0037] The adaptive material distribution device includes material level sensors (ultrasonic level meters or radar level meters) installed at the inlet and outlet silos of each module, flow sensors (mass flow meters or belt scales) installed on the conveying pipeline or conveyor belt, and corresponding actuators (screw feeders with variable frequency speed regulation, pneumatic valves, conveyor belt motors).

[0038] The automatic control system collects the signals of these sensors in real time, and the real-time material level L of the silo i i (t) and the instantaneous flow rate F of the material between module i and module i+1 i,i+1 (t).

[0039] In one possible implementation, the automation control system is based on the preset processing capabilities of each module. and target buffer level Each actuator is dynamically adjusted through a certain control algorithm.

[0040] The discharge rate R of module i out,i (t) is controlled by the inlet silo level L of the next module i+1 i+1 (t) and the processing capacity of the module, its adjustment logic can be simplified as follows: like Then increase R out,i (t), where is the low material level threshold; like Then reduce R out,i (t), where is the high material level threshold.

[0041] More complex control uses a proportional-integral-derivative (PID) controller, which controls the output u i (t) Discharging device acting on regulating module i: in, is the material level deviation, K p,i , K i,i , K d,i These are the proportional, integral, and differential gains of the discharge control loop of module i. These parameters are adjusted based on the dynamic characteristics of the specific modules.

[0042] In some embodiments, the automated control system also includes fault warning and handling capabilities. If the feed flow rate of a module consistently falls below its minimum processing requirement, or if the material level in a silo remains abnormal, the system will issue an alarm and automatically adjust the operating parameters of upstream modules or activate an alternative transport path to ensure overall production continuity.

[0043] This intelligent material flow management ensures efficient coordination and a smooth transition from waste raw materials to qualified recycled polymer chips in the front-end processing, effectively avoiding production bottlenecks or interruptions caused by material mismatch. It also provides stable and homogeneous raw materials for the more complex solid-phase polycondensation viscosity-increasing module, a crucial prerequisite for achieving high-performance operation of the entire production line.

[0044] The front end of the production line constructed in this way not only improves the level of automation in material handling, but also creates favorable conditions for the refined control of subsequent processes and the overall improvement of product quality.

[0045] S2. In-depth mechanism modeling of solid-state polycondensation viscosity-enhancing module: In this example, in order to accurately describe the intrinsic nature of the chemical reaction during solid-state polycondensation (SSP), advanced quantum chemical calculation methods were used to refine the kinetic parameters of key elementary reactions.

[0046] In general, a specific density functional theory (DFT) functional, M06-2X or ωB97X-D, is selected in combination with an appropriately sized basis set, 6-311++G(d,p), to calculate the main chain growth reactions (esterification and transesterification of carboxyl and hydroxyl groups), the main degradation reactions (thermal degradation and hydrolysis), and some key side reactions (reaction pathways leading to yellowing, catalyst-related side reactions, and deactivation mechanisms) in the SSP process of recycled polyester (polyethylene terephthalate (PET)).

[0047] Specifically, the activation energy E of each elementary reaction j is calculated by locating the optimal geometric configurations of reactants, transition states, and products, and performing frequency calculations to confirm the transition state (which should have only one imaginary frequency) and obtain zero-point vibrational energy (ZPE) correction. a,j and pre-exponential factors.

[0048] In one possible implementation, the pre-exponential factor can be further calculated using transition state theory (TST) to obtain the rate constant k TST,j : in: k TST,j It represents the rate constant of elementary reaction j calculated based on transition state theory. Its unit depends on the reaction order and is s -1 or L·mol -1 ·s -1 .

[0049] κ j represents the tunneling correction factor for elementary reaction j. For reactions not involving light atom transfer, this value is usually close to 1.

[0050] k B represents the Boltzmann constant, which is 1.380649×10 -23 J.K. -1 .

[0051] T represents absolute temperature, the unit is K.

[0052] h represents Planck's constant, which is 6.62607015×10 -34 J.s.

[0053] represents the partition function for the transition state of elementary reaction j, excluding vibrational contributions along the reaction coordinate.

[0054] Q R,j represents the total partition function of reactant j in elementary reaction.

[0055] E a,j It represents the activation energy of elementary reaction j, in J·mol -1 .

[0056] R represents the ideal gas constant, which is 8.314 J·mol -1 ·K -1 By adding k TST,j By fitting within the SSP operating temperature range, the Arrhenius form parameters for the macrokinetic model, namely the pre-exponential factor A, can be obtained. j and activation energy E a,j .

[0057] In this example, a macroscopic reaction kinetic network model of the SSP process was established based on precise kinetic parameters obtained through quantum chemical calculations. This model is designed to track changes in the concentration of key substances or polymer characteristics.

[0058] Specifically, the species tracked by the model include the concentration of polymer end groups, carboxyl [-COOH] and hydroxyl [-OH]; the concentration of small molecule byproducts, water [H2O] and ethylene glycol [EG] (for PET systems); and the active concentration of the catalyst [Cat]. active For any species S k , the rate of change of its concentration over time can be expressed as: in: [S k ] indicates species S k The concentration, usually expressed in mol -1 or mol·kg -1 .

[0059] ν kj Indicates species S k The stoichiometric coefficient in an elementary reaction j is negative for reactants and positive for products.

[0060] r j Represents the reaction rate of elementary reaction j, usually in mol·L -1 ·s -1 or mol·kg -1 ·s -1 The forward rate r of the esterification reaction in the PET polycondensation reaction is f,est It can be approximately expressed as r f,est =k f,est [-COOH][-OH][Cat] active , where k f,est is the rate constant of the reaction.

[0061] At the same time, the method of moments is used to describe the evolution of the polymer molecular weight distribution (MWD). i Defined as: Among them [P n ] is the concentration of polymer chains with a degree of polymerization of n. By solving the differential equations for the time-varying low-order moments of λ0, λ1, and λ2, the number-average degree of polymerization DP can be obtained. n =λ1 / λ0 and weight average degree of polymerization DP w =λ2 / λ1.

[0062] The intrinsic viscosity IV can be related to the viscosity average molecular weight M by the Mark-Houwink-Sakurada equation. v Relationship: IV= where K MHS and α MHSis the Mark-Houwink parameter for a specific polymer / solvent / temperature system, M v Can be DP n and DP w And the degree of aggregation distribution function is approximated.

[0063] In this example, considering that the SSP process is carried out in a high-viscosity solid phase, the diffusion of small molecule byproducts and the crystallization behavior of the polymer have a significant impact on the reaction rate and the performance of the final product, so a coupled mass transfer-crystallization model was established. am,sm The free volume theory is used to describe it: in: A D,sm The pre-exponential factor of the diffusion of small molecules sm, in m 2 ·s -1 .

[0064] B D,sm is a dimensionless parameter related to the minimum local free volume required for small molecule sm transitions.

[0065] v f It represents the average fractional free volume of the polymer and is a dimensionless parameter whose value can be estimated by the Williams-Landel-Ferry (WLF) equation or similar forms. f (T) = v f,g +α f,v (TT g ). Here v f,g is the glass transition temperature of the polymer g The fractional free volume at f,v is the thermal expansion coefficient of the free volume fraction (K -1 ), T g (K) itself is also a function of molecular weight and crystallinity. For semi-crystalline polymers, the effective diffusion coefficient D eff,sm It is expressed as: where χ c is the crystallinity of the polymer (mass fraction or volume fraction), τ tor is the tortuosity factor, which is used to describe the obstruction of the crystalline region to the diffusion path. The crystallization kinetics of polymers are described by the extended Nakamura model or similar models, and the non-isothermal crystallization rate equation can be expressed as: in: n Avis the Avrami index, reflecting the nucleation mechanism and crystal growth dimension.

[0066] K cryst is the crystallization rate constant (s -1 ), whose temperature dependence is usually described by the Hoffman-Lauritzen theory: where K c0 is the pre-factor, U * is the activation energy associated with the diffusion of polymer segments to the crystal surface (J·mol -1 ), T g,∞ is the glass transition temperature of the polymer at infinite molecular weight (K), is the nucleation parameter related to the crystal surface free energy, is the degree of subcooling (K), is the equilibrium melting point (K), is the temperature correction factor.

[0067] In some embodiments, the lattice Boltzmann method (LBM) can be introduced to further elucidate mesoscopic transport phenomena within SSP particles and between particles. The LBM can be used to simulate the flow of inert gases within the pore structure of the particle bed, as well as the convection and diffusion behavior of small molecule byproducts within these pores. Furthermore, the LBM can be coupled with a phase field model (PFM) or cellular automaton (CA) model to dynamically simulate the evolution of pore structure (pore size, porosity, connectivity) due to polymer particle shrinkage, sintering, or crystal growth.

[0068] In this embodiment, at the scale of a single polymer particle (usually assumed to be spherical with a radius R p (t) shrinks as the reaction proceeds), and a parameter C describing the concentration of small molecule byproducts sm was established. sm,p (r p ,t p ) at radial position r inside the particle p and time t p Distributed mass transfer-reaction coupled partial differential equation: where R gen,sm and R deg,sm Represent the generation rate and consumption rate of small molecules inside the particle (provided by the macroscopic reaction kinetics model). The boundary conditions of this equation include the particle center symmetric boundary and the mass transfer boundary between the particle surface and the bulk gas phase: where k m,ext is the mass transfer coefficient of the particle outer surface (m·s -1 ), Csm,bulk is the concentration of small molecules in the bulk gas phase in the reactor (mol·m -3 ). At the same time, it is necessary to solve the energy conservation equation within the particle simultaneously, taking into account the effects of heat conduction, reaction heat, and latent heat of crystallization.

[0069] The multi-level, multi-scale mechanistic model constructed above enables a comprehensive and in-depth quantitative description of the complex physical and chemical phenomena in the SSP process. This not only provides a theoretical foundation for understanding the SSP process but also lays a critical mathematical foundation for the subsequent development of model-based intelligent control strategies to precisely control the properties of recycled fiber products (IV, MWD, color) and optimize the overall production process. Once these models are validated and calibrated with experimental data, their predictive accuracy will be guaranteed.

[0070] S3, intelligent optimization control of solid phase polycondensation viscosity increasing module: In this example, to ensure robust and efficient operation of the solid-state polycondensation (SSP) module in the face of uncertainties in feedstock properties and external disturbances, an advanced intelligent control unit was designed and deployed. The core technology of this unit is the stochastic model predictive control (SMPC) strategy.

[0071] Generally speaking, SMPC is a model-based optimization control algorithm. At each control sampling moment, it solves an open-loop optimization problem within a finite time domain to determine the optimal control input sequence for the current and future periods. However, only the first control action in this sequence is applied to the actual system. This process is repeated in a rolling time domain manner.

[0072] In this embodiment, the SMPC strategy aims to dynamically control the key operating parameters of the SSP reactor, including the reaction temperature profile, inert gas flow rate, reaction time, or particle bed movement rate (for a continuous SSP reactor), to synergistically optimize multiple performance indicators.

[0073] Specifically, the optimization objective function J of SMPC is SMPC In each control cycle k s is minimized and can be expressed as: in: In the prediction domain N pH The control input sequence to be optimized. c This may include temperature set points for each reactor zone and inert gas flow rates.

[0074] represents the random disturbance d on the raw material characteristics rw The mathematical expectation of the distribution of the raw material characteristics drw It may include the initial intrinsic viscosity IV0 of the incoming material, the end group concentration [-COOH]0, [-OH]0, the moisture content w c , Impurity Type and Content I c .

[0075] N pH is the length of the prediction horizon.

[0076] is the stage cost function at step j in the prediction horizon, which quantifies the current state and control inputs The comprehensive cost of It may include the intrinsic viscosity IV, number average molecular weight M n , weight average molecular weight M w , polydispersity index PDI (M w / M n ), color parameters (b of CIELAB system * value), as well as the temperature distribution and small molecule by-product concentration distribution in the reactor.

[0077] is the terminal cost function at the end of the prediction horizon.

[0078] In some embodiments, the stage cost and terminal costs It can be designed as a weighted sum of the following forms: where w (·) is the weight factor of each item, (·) target is the target value, E consumed is the energy consumption term, and Δt is the time term.

[0079] In this embodiment, a series of constraints need to be satisfied when solving the SMPC optimization problem.

[0080] These constraints include physical operating constraints, upper and lower limits on the temperature of each section of the reactor, and T min ≤T≤T max , upper and lower limits of inert gas flow F min ≤F≤F max , and voltage drop limitations.

[0081] At the same time, to ensure the reliability of product quality, chance constraints are introduced. It is required that at the end of the prediction time domain, the probability that the intrinsic viscosity reaches the target value is not less than a certain confidence level: Among them IV targetis the target intrinsic viscosity, α IV is the maximum allowed violation probability, 0.05 or 0.1.

[0082] Similar opportunity constraints can also be applied to other key quality indicators, such as PDI or color.

[0083] In one possible implementation, the calculation of expected values ​​and the processing of chance constraints can be converted into deterministic nonlinear programming (NLP) problems for solution through scenario approximation method (Scenario Approach), robust correspondence method (Robust Counterpart) or method based on polynomial chaos expansion (PCE).

[0084] In this embodiment, considering that the SSP high-fidelity mechanism model established in step S2 usually has high computational complexity and is not suitable for direct online iterative optimization and solution of SMPC, a physical information neural network (PINN) is used to construct a proxy model of the SSP process. PINN is a deep learning model whose training process not only uses data but also uses known physical laws (usually expressed in the form of partial differential equations (PDEs) or ordinary differential equations (ODEs)) to constrain the behavior of the network. The loss function L of the PINN is PINN These typically include the following: L PINN (W NN )=w data L data +w PDE L PDE +w BC L BC +w IC L IC ; in: W NN Represents the weight and bias parameters of the neural network.

[0085] L data is the data fitting loss term, mean squared error (MSE), which is used to minimize the difference between the predicted output of the PINN and the data points obtained from high-fidelity model simulation or experimental measurement.

[0086] L PDE is the physical residual loss term, which applies the governing equations of the high-fidelity model (the reaction kinetics and mass transfer-reaction coupling equations in step S2) to the output of the PINN and calculates its residual through automatic differentiation. This term penalizes the degree to which the network output deviates from the laws of physics.

[0087] L BC and L ICThey are the boundary condition loss term and the initial condition loss term, which are used to ensure that the solution of PINN meets the corresponding boundary and initial conditions.

[0088] w data , w PDE , w BC , w IC is the weight coefficient of each loss. The PINN proxy model obtained through training can significantly reduce the computation time of model evaluation while maintaining high prediction accuracy, meeting the real-time requirements of SMPC online optimization.

[0089] In this embodiment, in order to effectively process the raw material characteristics d rw To prevent random fluctuations, the intelligent control unit further integrates an online estimation module for raw material characteristics. This module uses real-time measurement data obtained by online sensors (near-infrared spectrometers, online viscometers, or raw material composition rapid detection devices installed at the inlet of the SSP reactor or in the pretreatment stage) to estimate the raw material characteristics. sens , and combined with the Bayesian inference method, the key characteristics of the current batch of raw materials are updated online rw The posterior probability distribution P rw (d rw |y sens ).

[0090] Specifically, the Bayesian update formula is: Among them, P prior (d rw ) is the prior distribution of raw material characteristics based on historical data statistics, P(y sens |d rw ) is the likelihood function, which describes the probability of a given raw material characteristic d rw The sensor reading y is observed sens The probability of this is usually based on a sensor model y sens =h sens (d rw )+v sens , where v sens is the sensor noise. P(y sens ) is the evidence factor, which serves as a normalizing constant.

[0091] In some embodiments, an extended Kalman filter (EKF), unscented Kalman filter (UKF), or particle filter (PF) recursive estimation algorithm can be used to implement online updates. The updated raw material characteristic distribution is then used for the expected value calculation and chance constraint evaluation of the SMPC.

[0092] In this embodiment, to further improve the energy efficiency and sustainability of the SSP process, constraints based on the principles of non-equilibrium thermodynamics (NET) are also incorporated into the SMPC strategy.

[0093] By performing entropy generation analysis on the SSP reactor model established in step S2, the main sources of irreversible losses are identified, including entropy generation caused by heat transfer temperature difference, mass transfer resistance, chemical reaction irreversibility, and fluid flow friction.

[0094] Based on this analysis, additional constraints can be set to limit the total entropy production rate or the entropy production of a specific fraction. Limit the maximum temperature gradient allowed within the reactor. Or limit the heating / cooling rate of the material (dT / dt) max , to reduce the entropy increase caused by thermal stress and inhomogeneity. These NET constraints are added as hard constraints in the SMPC optimization problem or as penalty terms in the objective function.

[0095] S4. Full-line automation collaboration and overall technical benefits: In this embodiment, the modular intelligent continuous regenerated fiber production line of the present invention is equipped with a comprehensive automated control system. This system not only provides intelligent optimization control for the solid-state polycondensation (SSP) module described in step S3, but more importantly, it ensures efficient coordination and seamless integration of all process units, from the sorting and cleaning module at the raw material inlet, the melt extrusion module, the impurity filtration module, the granulation module, the decolorization module, and finally the melt spinning module following the SSP module.

[0096] Generally, the automation control system adopts an architecture that combines a distributed control system (DCS) or a programmable logic controller (PLC) with an industrial computer.

[0097] In this embodiment, the automated control system integrates a wide range of sensor networks to collect status information and process parameters of key nodes of the production line in real time.

[0098] Specifically, in addition to the temperature, pressure, and gas flow sensors deployed in the SSP module and the near-infrared spectrometer used for online estimation of raw material characteristics, other modules are also equipped with corresponding sensors, including: In the sorting and cleaning module, image recognition sensors can be deployed for material classification, and turbidity sensors can be deployed to monitor the cleaning effect.

[0099] In the melt extrusion module, melt temperature sensors, melt pressure sensors and screw speed sensors are deployed.

[0100] In the impurity filtering module, a differential pressure sensor can be deployed to monitor the filter clogging condition.

[0101] In the pelletizing module, a pelletizing speed sensor and a cooling water temperature sensor can be deployed.

[0102] In the melt spinning module, a spinning box temperature sensor, a winding speed sensor, and an on-line fiber tension sensor are deployed.

[0103] All these sensor data are collected through an industrial bus (Profibus-DP, Ethernet / IP) into the database of the automation control system for processing, storage, and analysis.

[0104] In this embodiment, the automation control system schedules and coordinates the operation of each module based on the collected real-time data and the preset production plan.

[0105] When the intelligent control unit of the SSP module calculates that the reaction conditions need to be adjusted according to the predicted raw material characteristics and the target product specifications, the automation control system not only executes the instructions to the SSP module, but also adjusts the production tempo or material conveying rate of the upstream module (the pelletizing module or the decolorizing module) in advance according to the expected processing capacity change of the SSP module to ensure the smoothness of the material flow.

[0106] In a possible implementation, the automation control system can interact with the manufacturing execution system (MES) or the enterprise resource planning (ERP) system at the factory level. The MES / ERP system can issue high-level instructions such as production orders and quality standards to the automation control system of the production line, and the automation control system can upload real-time production data, equipment status, energy consumption information, and quality reports to the MES / ERP system to realize the transparency of production management and the intelligentization of decision-making.

[0107] In some embodiments, the automation control system can be further integrated with a cloud computing-based “Bottle-to-Bottle” (B2B) or “Textile-to-Textile” (T2T) full-process digitalization platform to realize a wider range of data traceability, supply chain collaboration, and full-life-cycle management.

[0108] In this embodiment, to further optimize the performance of the key modules (especially the SSP module) and guide the optimal configuration of the sensors and actuators thereof, the geometric nonlinear control theory is introduced to perform system-level analysis on the SSP system. Specifically, the dynamic behavior of the SSP process can be described by a set of nonlinear state space equations: y nl =h nl (x nl ); wherein: xnl It is the state vector of the system, whose elements may include the intrinsic viscosity IV of the polymer, the concentration of each end group, the temperature at key locations in the reactor, and the concentration distribution of small molecular by-products in the particles and in the gas phase.

[0109] u nl,i is the i-th control input, reactor heating power, inert gas flow rate, M u is the total number of control inputs.

[0110] f nl (x nl ) is the system's drift vector field, which describes the natural dynamics of the system in the absence of control input.

[0111] g nl,i (x nl ) is the control vector field associated with the i-th control input.

[0112] y nl It is the measurement output vector of the system, whose elements are the quantities that can be actually measured by the sensors, such as the online viscometer reading, the outlet gas composition analyzer reading, and the temperature sensor reading at a specific location.

[0113] h nl (x nl ) is the output function that maps the system state to the measured output. By calculating the controllability of the system Lie algebra (given by g nl,i and their relationship with f nl The distribution of the various order Lie brackets) and the observability codistribution (given by dh nl,k and along f nl The rank of the space spanned by the Lie derivatives of each order can be used to evaluate the local controllability and observability of the system at a specific operating point or operating region.

[0114] If the analysis shows that a key state variable (the concentration of a byproduct inside the polymer, which has a significant impact on the color of the final product) is poorly observable for the existing sensor combination, it can guide the addition of new sensor types or the optimization of the installation location of existing sensors to obtain more effective state information, thereby improving the closed-loop control performance.

[0115] Similarly, controllability analysis helps determine which control inputs are most effective for regulating a particular output variable, or whether there are certain state combinations that the system cannot achieve with existing actuators. In some embodiments, the controllability Gramian matrix W can be constructed. c or the observability Gramian matrix W o (for linearized systems or under certain approximations), and assist in the placement decisions of sensors and actuators by optimizing their determinants, minimum eigenvalues, or condition number indicators.

[0116] In this embodiment, through the above-mentioned modular design, intelligent connection between modules, deep optimization control of the core SSP module and coordinated operation of the full-line automation system, the modular intelligent continuous regenerated fiber production line and process described in the present invention can bring significant technical benefits.

[0117] Generally speaking, compared with traditional production methods, the automation rate of the production line has been greatly improved, which reduces manual intervention, operation intensity and the possibility of human error.

[0118] Through precise control of the SSP core process and effective response to raw material fluctuations, the batch-to-batch quality consistency and stability of regenerated fiber products are significantly improved, the fluctuation range of the intrinsic viscosity IV can be significantly reduced, and the molecular weight distribution can be controlled within a narrower range.

[0119] The production cycle is effectively shortened due to the smooth connection and optimized scheduling between modules.

[0120] The overall energy consumption is reduced due to the optimization of the SSP process (guided by NET constraints) and the full-line collaboration to reduce unnecessary waiting and idle consumption.

[0121] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. Modular intelligent continuous recycled fiber production line, characterized by: include: Sorting and cleaning module, melt extrusion module, impurity filtering module, granulation module, decolorization module, solid phase polycondensation and viscosity increasing module, and melt spinning module; Adaptive material distribution device, used to achieve material connection between modules; An automated control system for realizing the coordinated operation of the modules; The solid phase polycondensation viscosity increasing module is equipped with an intelligent control unit for dynamically optimizing its operation, and the intelligent control unit predicts and controls based on a physical and chemical model of the solid phase polycondensation process.

2. The modular intelligent continuous recycled fiber production line according to claim 1, characterized in that: The physicochemical model included in the intelligent control unit is a reaction kinetics network model refined based on quantum chemical calculations. The reaction kinetics network model calculates the rate constant of the elementary reaction j through transition state theory: in: k TST,j It represents the rate constant of elementary reaction j calculated based on transition state theory. Its unit depends on the reaction order and is s -1 or L·mol -1 ·s -1 ; κ j represents the tunneling correction factor for elementary reaction j. For reactions that do not involve light atom transfer, the value is usually close to 1; k B represents the Boltzmann constant, which is 1.380649×10 -23 J.K. -1 ; T represents absolute temperature, unit is K; h represents Planck's constant, which is 6.62607015×10 -34 J·s; represents the partition function of the transition state of elementary reaction j, which does not include the vibrational contribution along the reaction coordinate; Q R,j represents the total partition function of reactant j in elementary reaction; E a,j It represents the activation energy of elementary reaction j, in J·mol -1 ; R represents the ideal gas constant, which is 8.314 J·mol -1 ·K -1 .

3. The modular intelligent continuous recycled fiber production line according to claim 1, characterized in that: The physical and chemical model included in the intelligent control unit further includes a coupled mass transfer-crystallization model, which uses free volume theory to describe the diffusion coefficient of small molecule byproducts in the polymer amorphous phase: in: A D,sm The pre-exponential factor of the diffusion of small molecules sm, in m 2 ·s -1 ; B D,sm It is a dimensionless parameter related to the minimum local free volume required for small molecule sm transition; v f It represents the average fractional free volume of the polymer and is a dimensionless parameter; v f (T) = v f,g +α f,v (TT g ), where v f,g is the glass transition temperature of the polymer g The fractional free volume at f,v is the thermal expansion coefficient of the free volume fraction (K -1 ), T g (K) itself is also a function of molecular weight and crystallinity.

4. The modular intelligent continuous recycled fiber production line according to claim 1, characterized in that: The intelligent control unit adopts a stochastic model predictive control (SMPC) strategy. The objective function of the SMPC strategy includes optimization items for the intrinsic viscosity IV, molecular weight distribution MWD and color index of the regenerated fiber, and takes into account the raw material characteristics d rw random fluctuations.

5. The modular intelligent continuous recycled fiber production line according to claim 4, characterized in that: The optimization problem of the SMPC strategy is expressed as: in: In the prediction time domain N pH The control input sequence to be optimized is u c This may include temperature setpoints for each section of the reactor and inert gas flow rates; represents the random disturbance d on the raw material characteristics rw The mathematical expectation of the distribution of the raw material characteristics d rw It may include the initial intrinsic viscosity IV0 of the incoming material, the end group concentration [-COOH]0, [-OH]0, the moisture content w c , Impurity Type and Content I c ; N pH is the length of the prediction horizon; is the stage cost function at step j in the prediction horizon, which quantifies the current state and control inputs The comprehensive cost of the state It may include the intrinsic viscosity IV, number average molecular weight M n , weight average molecular weight M w , polydispersity index PDI (M w / M n ), color parameters, as well as temperature distribution and small molecule by-product concentration distribution in the reactor; is the terminal cost function at the end of the prediction horizon.

6. The modular intelligent continuous recycled fiber production line according to claim 1, characterized in that: The intelligent control unit uses a physical information neural network PINN as the proxy model of the physical and chemical model, and the loss function L of the PINN is PINN Contains the residual term L based on the control equation of the physical and chemical model PDE .

7. The modular intelligent continuous recycled fiber production line according to claim 1, characterized in that: The intelligent control unit further includes a raw material characteristics online estimation module, which is based on online sensor data y sens and Bayesian inference to update the key characteristics of raw materials d rw The posterior probability distribution P rw (d rw |y sens ).

8. The modular intelligent continuous recycled fiber production line according to claim 1, characterized in that: The automated control system further performs a geometric nonlinear control theory analysis on the nonlinear system model of the solid phase polycondensation viscosity increasing module to optimize the sensor layout or evaluate the controllability and observability of the system. The nonlinear system model is expressed as: y nl =h nl (x nl ); Among them, x nl is the state vector, u nl,i is the control input, f nl (x nl ) is the drift vector field, g nl,i (x nl ) is the control vector field, y nl is the measured output, h nl (x nl ) is the output function.

9. A process based on the production line according to claim 1, characterized in that: The process includes the following steps: The waste fiber raw materials are sorted, cleaned, melt-extruded, filtered for impurities, granulated, and decolorized to obtain recycled polymer chips; Inputting the regenerated polymer slices into a solid phase polycondensation viscosity increasing module to carry out viscosity increasing reaction; The viscosified polymer is melt-spinned to obtain regenerated fibers; Among them, during the viscosity-increasing reaction process of the solid-phase polycondensation viscosity-increasing module, an intelligent control unit is used to dynamically regulate the reaction temperature, reaction time and inert gas flow based on real-time estimation of the random fluctuations in the characteristics of the regenerated polymer chips and the use of the random model prediction control SMPC strategy to synergistically optimize the intrinsic viscosity, molecular weight distribution and color of the resulting polymer.

10. The process of the production line according to claim 9, characterized in that: The SMPC strategy further considers the entropy generation constraint obtained based on non-equilibrium thermodynamic analysis when dynamically controlling reaction parameters. The entropy generation constraint is used to limit the maximum temperature gradient or the heating rate or cooling rate of the material in the reactor.

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