A Model-Based Predictive Control Method for Controlling the Tension of Raw Fiber in the Carbon Fiber Drawing Process

Abstract

This invention provides a model predictive control method for controlling the tension of precursor fibers during carbon fiber drawing. Based on the carbon fiber production process requirements, the setpoint for precursor fiber tension during drawing is determined. A nonlinear dynamic model is established between the driving voltage and precursor fiber tension in a single-stage drawing process. Based on the dynamic model, an objective function is constructed that aims to jointly minimize tension tracking error and driving voltage energy consumption. An optimization algorithm is used to solve the objective function to obtain the optimal driving voltage sequence in the prediction time domain. The first term in the optimal driving voltage sequence is selected for control, and the above steps are repeated at the next sampling time to achieve dynamic and stable control of the precursor fiber tension. This method effectively solves the problems of insufficient model prediction accuracy and nonlinear coupling in traditional control methods, significantly improving the system control accuracy.

Description

Technical Field

[0001] This invention relates to the field of carbon fiber production technology, specifically to a method for controlling the tension of precursor fibers during the carbon fiber drawing process based on model predictive control. Background Technology

[0002] The initial fiber drawing process, a core step in carbon fiber production, plays a crucial role in stretching the still-forming fibers as they pass through drawing rollers driven by a motor at varying speeds. This stretching causes the molecular chains of the initial fibers to align more orderly and the crystal structure to become more compact, thus improving the tensile strength and elastic modulus of the resulting carbon fibers. Single-stage drawing, a critical phase in the process, is typically accomplished by a pair of driving rollers, consisting of a first roller and a second roller. In this process, the first roller serves as a reference axis, providing a stable linear velocity and initial tension; the second roller acts as a dynamic adjustment axis, its linear velocity dynamically adjusted via a driving voltage. By precisely controlling the driving voltage of the second roller, a difference in linear velocity is created between the two rollers, allowing the initial fiber to achieve stable tension and deform according to process requirements. Detailed analysis of the carbon fiber single-stage drawing process revealed a significant coupling between the controlled variables, precursor fiber speed and precursor fiber tension. This means that controlling one variable can affect the stability of others. This interplay between controlled variables introduces nonlinearity into the system, making the carbon fiber single-stage drawing process a complex system with both nonlinearity and coupling. Field production practice demonstrates that only long-term stable precursor fiber tension can produce high-performance precursor fibers; therefore, stable control of precursor fiber tension is of paramount importance.

[0003] Currently, tension control during the single-stage drawing process of carbon fiber mostly employs a separate speed regulation method. This involves using a motor as the primary drive source to move a roller and the unformed initial fiber in contact with it as the load. Sensors monitor changes in physical quantities such as speed and tension in real time, and the controller dynamically adjusts the voltage input to the drive motor based on the feedback information from the sensors, ensuring the roller operates at a set speed and thus stabilizing the tension of the raw fiber. However, this conventional feedback closed-loop control method struggles to handle complex control tasks involving nonlinear coupling and operational constraints. It requires repeated tuning of control parameters based on the dynamic equations of the nonlinear system, resulting in insufficient flexibility. In practical field applications, the system response often exhibits significant deviations, leading to unsatisfactory control performance.

[0004] Existing technologies simulate the actual water bath process in carbon fiber production lines by constructing a correlation model between operational variables such as coagulation bath solution concentration and performance indicators such as draw ratio. However, this system is an idealized production environment that does not consider external interference factors, making it unsuitable for real-world applications. Secondly, while a built-in temperature sensor in the drawing tank monitors water temperature changes in real time and dynamically adjusts the draw ratio of the carbon fiber precursor, the large volume of the tank and the time required for temperature changes, along with the placement of the temperature sensor affecting real-time monitoring, all contribute to a delay in the system's response to temperature signals. Furthermore, based on a tension variation model, the PLC receives surface tension information from the sensor and outputs control commands to the servo motor to control the fiber surface tension. However, this system does not consider future system state changes; control only occurs when there is an error between the measured surface tension value and the desired setpoint, making it difficult to achieve optimal control. Finally, the amount of demineralized water is controlled based on temperature and pressure measurements from the sensor to achieve stable control of steam humidity. However, the control system does not take into account drastic changes in the control quantity or the suppression of overshoot, making it difficult for the control output to transition smoothly and resulting in poor system stability. Summary of the Invention

[0005] This invention proposes a model predictive control-based method for controlling the tension of the precursor fiber in the carbon fiber drawing process. This method addresses the problem that traditional control methods are unable to effectively handle the nonlinear coupling characteristics in the carbon fiber drawing process, which leads to significant fluctuations in the precursor fiber tension, a key process parameter.

[0006] To address the aforementioned technical problems, this invention provides a method for controlling the tension of precursor fibers during the carbon fiber drawing process based on model predictive control, comprising the following steps:

[0007] Step S1: Determine the set value of the precursor tension during the drawing process according to the carbon fiber production process requirements;

[0008] Step S2: Establish a nonlinear dynamic model between the driving voltage and the yarn tension in single-stage drafting. The dynamic model includes a single input operating variable and two output controlled variables, wherein the input variable is the driving voltage of the dynamic adjustment shaft in single-stage drafting, and the output variables are the yarn tension and angular velocity of the dynamic adjustment shaft.

[0009] Step S3: Based on the dynamic model, construct an objective function that aims to jointly minimize tension tracking error and driving voltage energy consumption;

[0010] Step S4: Solve the objective function using an optimization algorithm to obtain the optimal driving voltage sequence in the prediction time domain;

[0011] Step S5: Select the first term in the optimal driving voltage sequence for control, and repeat steps S2 to S5 at the next sampling time to achieve dynamic and stable control of the original yarn tension.

[0012] Preferably, in step S2, the expression of the nonlinear dynamic model is:

[0013]

[0014] In the formula, u represents the driving voltage of the dynamic adjustment shaft during the single-stage drawing process of carbon fiber; x1 and x2 represent the filament tension and angular velocity on the dynamic adjustment shaft, respectively; L1 represents the distance between the two drive motors; E represents Young's modulus; A is the cross-sectional area of ​​the filament; R represents the radius of the dynamic adjustment shaft; J a represents the moment of inertia; f0 represents the coefficient of friction; n represents the transmission ratio between the drive motor transmission rod and the dynamic adjustment shaft; T0 and V0 represent the initial tension value and the linear velocity of the original yarn on the reference shaft, respectively.

[0015] Preferably, the objective function J in step S3 k The expression is:

[0016]

[0017] In the formula, y(k+i|k) represents the predicted value at time k+i obtained by the dynamic model at time k sampling time; y ref The system's original yarn tension setpoint is represented by u(k+i|k); u(k+i|k) represents the driving voltage at time k+i obtained through the dynamic model at time k sampling; p represents the number of time steps for future prediction; and Q represents a symmetric positive semi-definite matrix.

[0018] Preferably, step S4 uses an improved particle swarm optimization algorithm to solve the objective function, including the following steps:

[0019] Step S41: Initialize the particle swarm, where each particle represents the driving voltage sequence in the future prediction time domain;

[0020] Step S42: Calculate the objective function values ​​of all particles in the particle swarm and determine the globally optimal particle;

[0021] Step S43: Calculate the angle between the particle and the globally optimal particle, and update the particle swarm based on the minimum angle pruning strategy;

[0022] Step S44: Dynamically adjust the inertial weights based on the particle's achievement scalarization function value to update the particle's velocity and position;

[0023] Step S45: Repeat steps S42 to S44 to iterate until the termination condition is met, then output the optimal driving voltage sequence.

[0024] Preferably, the method for updating the particle swarm based on the minimum angle reduction strategy in step S43 includes: calculating the angle between a particle and the globally optimal particle; if the angle is less than a threshold, it is replaced with a random new particle; otherwise, it is retained.

[0025] Preferably, the expression for calculating the angle between the particle and the globally optimal particle is:

[0026]

[0027] In the formula, J(s1) and J(s2) represent particles s1 and s2 at the target value; J min Represents the globally optimal particle p g The corresponding minimum objective value; ||·|| represents the Euclidean norm.

[0028] Preferably, the expression for the achievement scalarization function value in step S44 is:

[0029]

[0030] In the formula, ASF(s) i ) represents the i-th particle s in the particle swarm. i The achievement of scalarized function value; J min Represents the globally optimal particle p g The corresponding minimum objective value; J max J(s) represents the maximum objective value in the particle swarm; ε represents a very small constant; i ) represents particle s i The target value.

[0031] Preferably, the expression for dynamically adjusting the inertial weight based on the achievement scalarization function value of the particle in step S44 is as follows:

[0032] w(s i ) = w min +(w max -w min )·ASF(s i );

[0033] In the formula, w(s) i ) represents the inertial weight of the i-th particle; w min and w max These represent the minimum and maximum inertial weight values ​​in the current particle swarm, respectively.

[0034] Preferably, the expression for updating the particle's velocity and position in step S44 is:

[0035] v′ ij =w(s i )vij +c1r 1j (p ij -s ij )+c2r 2j (p gj -s ij );

[0036] s′ ij =s ij +v′ ij ;

[0037] In the formula, c1 and c2 represent acceleration constants; r 1j and r 2j p is a random number that follows a uniform distribution in the interval [0,1]. ij and p gj They represent particles s and s respectively. i The value of its own historical best position and the value of its global best position in the particle swarm in the (j+1)th dimension; v ij and v′ ij These represent the velocities of the particles before and after the update, respectively; s ij and s′ ij These represent the positions of the particles before and after the update.

[0038] The beneficial effects of the present invention include at least the following:

[0039] 1) This invention constructs a dynamic model reflecting the nonlinear relationship between the driving voltage and the yarn tension, and uses this model to predict the yarn tension output in the future prediction time domain online. This method effectively solves the problems of insufficient model prediction accuracy and nonlinear coupling in traditional control methods, and significantly improves the system control accuracy;

[0040] 2) In the objective function design, a term to minimize the error between the system output and the setpoint, and a term to minimize the input of the manipulated variables, are introduced. During the rolling optimization solution process, constraints such as limitations on the manipulated variables and the controlled variables are fully considered, which can overcome external disturbances and further enhance the dynamic stability of the system.

[0041] 3) At each sampling moment, the system dynamically adjusts the optimal operating variable based on the real-time monitored physical quantity status information such as velocity and tension, as well as the status prediction information for a period of time in the future. This continuously reduces the system control deviation, allowing the controlled variable to gradually approach and stabilize to the set value, thereby significantly improving the system's response speed. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0043] Figure 2This is a schematic diagram illustrating the changes in raw yarn tension and roller speed with voltage according to an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram illustrating the effect of model predictive control on the tension control of the carbon fiber drawing process in an embodiment of the present invention.

[0045] Figure 4 This is a schematic diagram illustrating the effect of PID-based carbon fiber drawing process tension control in an embodiment of the present invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0047] like Figure 1 As shown, this embodiment of the invention provides a method for controlling the tension of the precursor fiber during the carbon fiber drawing process based on model predictive control, including the following steps:

[0048] Step S1: Determine the set value of the precursor tension during the drawing process according to the carbon fiber production process requirements.

[0049] Specifically, in this embodiment, based on the requirements of the production process for the strength, orientation, and other performance indicators of the carbon fiber precursor, the tension setting value of the precursor during the carbon fiber drawing process is determined to be 0.025 cN, which remains unchanged in subsequent control steps.

[0050] Step S2: Establish a nonlinear dynamic model between the driving voltage and the original yarn tension in single-stage drafting. The dynamic model includes a single input operating variable and two output controlled variables. The input variable is the driving voltage of the dynamic adjustment shaft in single-stage drafting, and the output variables are the original yarn tension and angular velocity of the dynamic adjustment shaft.

[0051] Specifically, the dynamic model of the nonlinear relationship is expressed as follows:

[0052]

[0053] In the formula, the model represents a single-input, two-output control system. The single-input operating variable is u, which represents the driving voltage on the dynamic adjustment shaft during the single-stage carbon fiber drawing process. The two output operating variables are x1 and x2, which represent the filament tension and angular velocity on the dynamic adjustment shaft, respectively. L1, E, A, R, J af0, n, T0, and V0 are fixed parameters in the prediction model; L1 represents the distance between the two drive motors; E represents Young's modulus; A is the cross-sectional area of ​​the precursor filament; R represents the dynamic adjustment shaft radius; J a The moment of inertia is represented by f0; the coefficient of friction is represented by n; the transmission ratio between the drive motor transmission rod and the dynamic adjustment shaft is represented by n; T0 and V0 represent the initial tension value and the linear velocity of the original yarn on the first roller, i.e., the reference shaft, respectively.

[0054] For example, the values ​​of key variables are shown in Table 1.

[0055] Table 1

[0056]

[0057]

[0058] When the driving voltage changes in the form of a piecewise function as shown below, the tension changes with the voltage as follows: Figure 2 As shown. From Figure 2 (a) in the diagram represents the change in raw yarn tension. It can be seen that the raw yarn tension decreases and then tends to stabilize as the voltage input of the roller increases. For example, when the roller voltage increases from 10V to 30V, the raw yarn tension decreases from 1.8 × 10⁻⁶ to 1.8 × 10⁻⁶. -3 cN decreased to 0.4 × 10 -3 cN tends to stabilize afterward; from Figure 2 (b) in the figure represents the change in roller speed. It can be seen that the roller speed increases or decreases synchronously with the voltage input.

[0059]

[0060] Step S3: Based on the dynamic model, construct an objective function that aims to jointly minimize the tension tracking error and the driving voltage energy consumption.

[0061] Specifically, first, the constraints, such as the operating variables and the controlled variables, are defined as follows:

[0062] u min ≤u≤u max ;

[0063] x 1min ≤x1≤x 1max ;

[0064] x 2min ≤x2≤x 2max ;

[0065] In the formula, u max and u min These represent the upper and lower limits of the operation variable u, with values ​​of 10 and -10 respectively; x1max and x 1min These represent the upper and lower limits of the controlled variable x1, with values ​​of 0.03 and 0 respectively; x 2max and x 2min These represent the upper and lower limits of another controlled variable, x2, with values ​​of 5 and -15, respectively.

[0066] To ensure that the tension of the precursor yarn can be stabilized to the set value while minimizing energy consumption, an objective function is defined as follows:

[0067]

[0068] In the formula, y(k+i|k) represents the predicted value at time k+i obtained by the dynamic model at time k sampling time; y ref denoted by ; u(k+i|k) represents the driving voltage value at time k+i obtained through the dynamic model at time k sampling; p represents the number of time steps for future prediction; and Q represents a symmetric positive semi-definite matrix.

[0069] Step S4: Use an optimization algorithm to solve the objective function to obtain the optimal driving voltage sequence in the prediction time domain.

[0070] For example, the optimization algorithms in this embodiment include, but are not limited to, ant colony optimization algorithm, genetic algorithm, artificial bee colony algorithm and differential evolution algorithm, which will not be described in detail here.

[0071] Preferably, this embodiment provides an improved particle swarm optimization algorithm to solve the above objective function, which includes the following steps.

[0072] 1) Algorithm Initialization. An initial particle swarm of n particles is randomly generated, and the velocity, position, and optimal position of each particle are set. In this algorithm, each particle represents the feasible region space. A potential solution in is the sequence of operational variables over p time steps, which is mathematically defined as:

[0073] s i =(u i (k),u i (k+1),…,u i (k+(p-1))),i∈{1,…,n};

[0074] Among them, u i (k+j) represents the value of the operation variable for the i-th particle at a future time k+j.

[0075] 2) Target value calculation: Calculate the target value of all particles in the particle swarm, compare the target values ​​of all particles one by one, determine the particle with the smallest target value in the current particle swarm, and update it as the globally optimal particle p. g .

[0076] 3) The particle swarm is updated. In this embodiment, a minimum angle pruning strategy is used to maintain particle diversity. The core idea of ​​this strategy is to measure particle diversity by calculating the angle between particles in the target space. For two particles s1 and s2 in the decision space, the angle formed by the line connecting their target value in the target space and the current minimum target value of the population is defined as follows:

[0077]

[0078] In the formula, J(s1) and J(s2) represent particles s1 and s2 at the target value; J min Represents the globally optimal particle p g The corresponding minimum objective value; ||·|| represents the Euclidean norm.

[0079] exist Based on the definition, through The diversity of particle s1 is measured and defined as follows:

[0080]

[0081] In the formula, P represents the current particle swarm. If Value less than threshold θ th This indicates that s1 and s2 are relatively close in the target space. The more concentrated the distribution of particle s1 in the target space, the worse the diversity of particle s1. Replacing it with randomly generated new particles increases the diversity of the particle swarm and avoids premature convergence; conversely, if... The value is greater than or equal to the threshold θ th This indicates that s1 is far from other solutions in the target space, and its diversity is relatively good, so it should be retained.

[0082] 4) Adaptive adjustment of inertia weights: Calculate the achievement scalarization function value for all particles, using the following formula:

[0083]

[0084] Among them, ASF(s) i J represents the achievement scalarization function value of the i-th particle in the particle swarm. max This represents the maximum objective value in the particle swarm, and ε represents a very small constant, here ε = 10. -6 This is used to prevent the denominator from being zero.

[0085] The inertial weight is dynamically adjusted based on the achievement scalarization function value of the particle, and its calculation formula is as follows:

[0086] w(s i ) = w min +(w max -w min )·ASF(s i );

[0087] Among them, w min and w max These represent the minimum and maximum inertial weight values ​​in the current particle swarm, respectively. When ASF(s) i When the value is small, it indicates that the particle s i If a particle is very close to the optimal individual in the particle swarm, its inertia weight should be reduced to increase its local search capability; conversely, if it is very close to the optimal individual in the swarm, it indicates that particle s... i To move away from the optimal individual in the particle swarm, inertia should be increased to enhance the particle's global exploration capability.

[0088] 5) Particle velocity and position update. During the algorithm's iterative optimization process, the velocity and position of each particle s are updated. i It will be based on its own historical best particle p i And the globally optimal particle p in the particle swarm g To update the current position and velocity. Let v ij and x ij Let represent the velocity and position of the i-th particle in the (j+1)-th dimension, respectively. Then, the velocity and position update formulas can be expressed as:

[0089] v′ ij =w(s i )v ij +c1r 1j (p ij -s ij )+c2r 2j (p gj -s ij );

[0090] s′ ij =s ij +v′ ij ;

[0091] Where w(x) i The inertial weights are represented by ), c1 and c2 represent the acceleration constants, and r... 1j and r 2j p is a random number that follows a uniform distribution in the interval [0,1]. ij and p gj They represent particles s and s respectively. i The values ​​of its own historical best position and the global best position in the particle swarm in the (j+1)th dimension, v′ij and x′ ij These represent the particle's updated velocity and position, respectively.

[0092] 6) Output the current optimal sequence of operational variables. Check if the algorithm has reached the maximum number of iterations. If the termination condition is met, end the algorithm optimization process, output the globally optimal particle in the particle swarm, and use it as the current optimal sequence of control variables. Otherwise, proceed to the next iteration.

[0093] Step S5: Select the first term in the optimal driving voltage sequence for control, and repeat steps S2 to S5 at the next sampling time to achieve dynamic and stable control of the original yarn tension.

[0094] Specifically, at the current sampling time k, the optimal sequence of operational variables is selected. The first item When applied to the raw yarn tension control system, the remaining control variable sequence is discarded, and the above control steps are repeated at the next sampling time based on the latest system state, thereby achieving stable control of the raw yarn tension.

[0095] Figure 3 The diagram shows the effect of carbon fiber drawing process precursor tension control based on model predictive control. It can be seen that under the action of the MPC controller corresponding to model predictive control, by adjusting the driving voltage of the manipulated variable, the controlled variable precursor tension can be stabilized to the production process set value of 0.025cN in about 6s. The controlled variable precursor tension output has a good smooth transition, and the controller has achieved a stable control effect.

[0096] Figure 4 The diagram shows the effect of PID-based control of the fiber tension in the carbon fiber drawing process. When dealing with the nonlinear coupled fiber tension control task with operational constraints, this conventional feedback closed-loop control method cannot stabilize the controlled variable, fiber tension, to the production process setpoint, resulting in overshoot and unsatisfactory control effect.

[0097] In summary, the carbon fiber drawing process precursor tension control method proposed in this invention can effectively solve the problem of significant fluctuations in precursor tension caused by the nonlinear coupling characteristics in the carbon fiber drawing process, and significantly improve the system's control accuracy, dynamic stability and response speed.

[0098] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0099] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for controlling the tension of precursor fibers during carbon fiber drawing based on model predictive control, characterized in that: Includes the following steps: Step S1: Determine the set value of the precursor tension during the drawing process according to the carbon fiber production process requirements; Step S2: Establish a nonlinear dynamic model between the driving voltage and the yarn tension in single-stage drafting. The dynamic model includes a single input operating variable and two output controlled variables, wherein the input variable is the driving voltage of the dynamic adjustment shaft in single-stage drafting, and the output variables are the yarn tension and angular velocity of the dynamic adjustment shaft. Step S3: Based on the dynamic model, construct an objective function that aims to jointly minimize tension tracking error and driving voltage energy consumption; Step S4: Solve the objective function using an optimization algorithm to obtain the optimal driving voltage sequence in the prediction time domain; Step S5: Select the first term in the optimal driving voltage sequence for control, and repeat steps S2 to S5 at the next sampling time to achieve dynamic and stable control of the original yarn tension. In step S2, the expression for the nonlinear dynamic model is: ； In the formula, This indicates the driving voltage of the dynamic adjustment shaft during the single-stage carbon fiber drawing process. and These represent the filament tension and angular velocity on the dynamic adjustment shaft, respectively. E represents the distance between the two drive motors; A represents Young's modulus; R represents the cross-sectional area of ​​the precursor filament; and R represents the radius of the dynamically adjustable shaft. Indicates the moment of inertia; represents the coefficient of friction; n represents the transmission ratio between the drive motor transmission rod and the dynamic adjustment shaft. and These represent the initial tension value and the linear velocity of the primary yarn on the first reference axis, respectively. The objective function described in step S3 The expression is: ； In the formula, This represents the predicted value at time k+i obtained through the dynamic model at time k sampling time; This indicates the system's raw yarn tension setting value; denoted by k, represents the driving voltage at time k+i obtained through the dynamic model at time k sampling; p represents the number of time steps for future prediction; and Q represents a symmetric positive semi-definite matrix.

2. The method for controlling the tension of precursor fibers in the carbon fiber drawing process based on model predictive control according to claim 1, characterized in that: Step S4 uses an improved particle swarm optimization algorithm to solve the objective function, including the following steps: Step S41: Initialize the particle swarm, where each particle represents the driving voltage sequence in the future prediction time domain; Step S42: Calculate the objective function values ​​of all particles in the particle swarm and determine the globally optimal particle; Step S43: Calculate the angle between the particle and the globally optimal particle, and update the particle swarm based on the minimum angle pruning strategy; Step S44: Dynamically adjust the inertial weights based on the particle's achievement scalarization function value to update the particle's velocity and position; Step S45: Repeat steps S42 to S44 to iterate until the termination condition is met, then output the optimal driving voltage sequence.

3. The method for controlling the tension of precursor fibers in the carbon fiber drawing process based on model predictive control according to claim 2, characterized in that: The method for updating the particle swarm based on the minimum angle reduction strategy in step S43 includes: calculating the angle between a particle and the globally optimal particle; if the angle is less than a threshold, it is replaced with a random new particle; otherwise, it is retained.

4. The method for controlling the tension of the precursor fiber in the carbon fiber drawing process based on model predictive control according to claim 3, characterized in that: The expression for calculating the angle between a particle and the globally optimal particle is: ； In the formula, and Represents particles and At the target value; Represents the globally optimal particle The corresponding minimum target value; This represents the Euclidean norm.

5. The method for controlling the tension of the precursor fiber in the carbon fiber drawing process based on model predictive control according to claim 4, characterized in that: The expression for the achievement scalarization function value mentioned in step S44 is: ； In the formula, Represents the i-th particle in the particle swarm. The achievement of scalarized function value; Represents the globally optimal particle The corresponding minimum target value; This represents the maximum objective value in the particle swarm. To represent a very small constant; Represents particles The target value.

6. The method for controlling the tension of precursor fibers in the carbon fiber drawing process based on model predictive control according to claim 5, characterized in that: The expression for dynamically adjusting the inertial weight based on the achievement scalarization function value of the particle in step S44 is as follows: ； In the formula, This represents the inertial weight of the i-th particle; and These represent the minimum and maximum inertial weight values ​​in the current particle swarm, respectively.

7. The method for controlling the tension of the precursor fiber in the carbon fiber drawing process based on model predictive control according to claim 6, characterized in that: The expression for updating the particle's velocity and position in step S44 is: ； ； In the formula, and Indicates the acceleration constant; and These are random numbers that follow a uniform distribution in the interval [0,1]. and They represent particles respectively The value of its own historical best position and the global best position in the particle swarm in the (j+1)th dimension; and These represent the velocities of the particles before and after the update; and These represent the positions of the particles before and after the update.

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