Single crystal furnace diameter pulling speed PID control method based on ARX model

Abstract

The invention relates to a single crystal furnace diameter pulling speed PID (proportion integration differentiation) control method based on an ARX (autoregressive X) model, which comprises the following steps: identifying a single crystal furnace diameter pulling speed production data system to obtain parameters A, B and e in an ARX formula yn = AY + BU + e; reading data, including a diameter parameter Y and a pulling speed parameter U of the single crystal furnace, of the system before the nth moment, substituting the data into an ARX formula to obtain a predicted diameter yn, and substituting the predicted diameter yn as input into a PID formula to obtain a predicted pulling speed un; continuously substituting into an ARX formula to obtain a predicted diameter yn + 1; and performing loop iteration, performing recursion for 10 times in sequence, performing uninterrupted loop optimization, and gradually forming a predicted pulling speed sequence (un, un + 1, un + 2... un + 9). The method has the advantages that the precision, stability and reliability of diameter pulling speed control in the production process of the single crystal furnace can be effectively improved, solid technical support is provided for high-quality monocrystalline silicon production, and technical upgrading and innovative development of related industries are promoted.

Description

Technical Field

[0001] The present invention relates to a method for controlling the diameter and pulling speed of a single crystal furnace, and specifically to a PID control method for the diameter and pulling speed of a single crystal furnace based on an ARX model. Background Art

[0002] With the booming development of the semiconductor and photovoltaic industries, single crystal silicon, as a core basic material, the accuracy and stability of its preparation process are directly related to product quality and industrial benefits. As a key device for preparing single crystal silicon, precise control of the crystal diameter and pulling speed is a core process requirement.

[0003] When facing the complex thermal field changes, material property fluctuations, and external interference factors of a single crystal furnace, the existing PID control method gradually exposes defects such as poor stability, excessive overshoot, and difficulty in effectively reducing the deviation between the set value and the actual value.

[0004] In order to break through the limitations of traditional control methods, a collaborative control strategy of building an ARX model and PID is considered to improve the accuracy, stability, and reliability of diameter and pulling speed control during the production process of a single crystal furnace. Summary of the Invention

[0005] The present invention proposes a PID control method for the diameter and pulling speed of a single crystal furnace based on an ARX model, aiming to overcome the above-mentioned deficiencies of the existing technology and improve the accuracy, stability, and reliability of diameter and pulling speed control during the production process of a single crystal furnace.

[0006] The technical solution of the present invention: The PID control method for the diameter and pulling speed of a single crystal furnace based on an ARX model includes the following steps:

[0007] 1) After system identification of the production data of the single crystal furnace diameter and pulling speed, obtain the parameters A, B, and e in the ARX formula y n = AY + BU + e;

[0008] 2) Read the data before the nth moment of the system, including the single crystal furnace diameter parameter Y and the pulling speed parameter U, and substitute them into the ARX formula in step 1) to obtain the predicted diameter y n ;

[0009] 3) Take the predicted diameter y n obtained in step 2) as the input, substitute it into the PID formula, and obtain the predicted pulling speed u n ;

[0010] 4) Take y n , y n-1 , y n-2 , y n-3 , …, y n-k and u n , u n-1, u n-2 , u n-3 , …, u n-k Substitute into the ARX formula to obtain the predicted diameter y n+1 ;

[0011] 5) Take the predicted diameter y obtained in step 4) n+1 as the input and substitute it into the PID formula to obtain the predicted drawing speed u n+1 ;

[0012] 6) Perform iterative loop, recursively 10 times in sequence, continuously loop and optimize, and gradually form a predicted drawing speed sequence (u n , u n+1 , u n+2 … u n+9 ).

[0013] Take the predicted drawing speed u of the 10th time n+9 as the key parameter for PLC seed crystal drawing speed control, and high-precision coordinated control of the drawing speed and diameter can be achieved. The control effects of the drawing speed and diameter can be significantly optimized, and it is superior to the existing PID single control mode in core indicators such as stability improvement, overshoot reduction, and deviation control accuracy enhancement, and efficient control of the single-crystal silicon preparation process can be effectively realized.

[0014] Preferably, in step 1), e is an error parameter, A = [a1, a2, a3, …, a k , B = [b1, b2, b3, …, b k .[[]]

[0015] Preferably, in step 2), Y = [y n-1 , y n-2 , y n-3 , …, y n-k T , U = [u n- 1, u n-2 , u n-3 , …, u n-k T .

[0016] Advantages of the present invention: The method is reasonably designed, can effectively improve the accuracy, stability and reliability of diameter and drawing speed control in the production process of single crystal furnaces, helps to provide solid technical support for high-quality single-crystal silicon production, and promotes the technological upgrading and innovative development of related industries. Description of the Drawings

[0017] Figure 1 is the flow chart of the PID control method for the diameter and drawing speed of the single crystal furnace based on the ARX model of the present invention. Detailed Embodiments

[0018] ​​The present invention will be further described in detail below in conjunction with embodiments and specific implementation manners.

[0019] In the equal-diameter growth stage of the single crystal furnace, first, on-site production data of the drawing speed and diameter are collected in all directions and in real time through sensors. These data contain various process information, such as the change trend of the thermal field distribution, the melt convection characteristics, and the dynamics of the crystal growth interface. Subsequently, in-depth mining and analysis are carried out through the system identification algorithm sampling the least squares method. In this process, operations such as denoising, normalization, and outlier removal are performed in the data preprocessing link to ensure the data quality. By continuously optimizing the algorithm parameters and adjusting the model structure, after strict evaluation and verification, reliable ARX parameters A, B, and the error term e are accurately determined. This data processing flow helps subsequent precise control and in-depth insight into the internal laws of the single crystal furnace production process.

[0020] The designed PID control method for the diameter and drawing speed of the single crystal furnace based on the ARX model includes: developing a dedicated program module FB_ARX in the PLC programmable logic controller. This module uses the drawing speed as the input quantity, relying on the ARX parameters, and calculates the predicted diameter according to the mathematical model y n = AY + BU + e. This predicted diameter is input into the PID controller as feedback information, and the predicted drawing speed is generated through the PID control algorithm operation. Then, the predicted diameter and predicted drawing speed data are grouped to form a feedback loop, continuously recursing in the PID controller, and looping more than 10 times. In each round of cyclic iteration process, based on the updated predicted diameter value, the PID controller fine-tunes the predicted drawing speed with its adaptive adjustment ability, gradually compresses the control deviation, and makes the control quantity continuously approach the optimal value. After multiple rounds of cyclic optimization, a stable and accurate diameter value is finally obtained, and the drawing speed instruction is inversely calculated based on this, so as to realize the dynamic, stable, and precise control of the drawing speed, and ensure that the single crystal growth process is stably approaching the ideal state.

[0021] Among them, the specific formula for the ARX parameters is:

[0022]

[0023] Among them,

[0024] y n is the ARX output value,

[0025] e is the error parameter,

[0026] A = [a1, a2, a3, …, a k ,

[0027] Y = [y n-1 , y n-2 , y n-3 , …, y n-k T ,​

[0028] B = [b1, b2, b3, …, b k ,

[0029] U = [u n-1 , u n-2 , u n-3 , …, u n-k T,

[0030] A, B, and e are all parameters obtained after system identification. Y and U are the input and output parameters of the system before the nth moment;

[0031] It can be expressed as:

[0032] y n = A * Y n-1 + B * U n-1 + e

[0033] The ARX model is specifically the ARX autoregressive exogenous input model, following the Y n = AY + BU + e mathematical paradigm. Among them, the coefficient matrices A = [a1, a2, a3, …, a k and B = [b1, b2, b3, …, b k are used as the core parameters of the model. The vector Y = [y n-1 , y n-2 , y n-3 , …, y n-k T covers the output values from the nth moment back to the previous k moments. These historical output values are concatenated into a time series, containing information on the inertia and hysteresis characteristics of the crystal growth system; U = [u n- 1, u n-2 , u n-3 , …, u n-k T then records the input values at the corresponding moments, reflecting the history of external control actions. The error term e is used as the accurate identification error value, and the algorithm is used to monitor and compensate the model prediction deviation in real time to ensure that the model output matches the actual working conditions. This model has a rigorous mathematical structure, can reflect the dynamic relationship between the system input and output, and provides a solid theoretical support for predictive control.

[0034] For the ARX system identification model parameters, the least squares method is used to identify the system parameters A, B, and e; let θ = [a1, a2, a3, …, a k , b1, b2, b3, …, b k T be the parameter vector, and the regression vector x t = [y n-1 , y n-2 , y n-3 , …, y​​​n-k , u n-1 , u n-2 , u n-3 , …, u n-k T , then y t = θ T x t + e t ;

[0035] Then the sum of the squares of the prediction errors can be expressed as:

[0036]

[0037] where N is the amount of data;

[0038] Take the partial derivative of J(θ):

[0039]

[0040] And set it equal to 0 to get:

[0041]

[0042] (X T X)θ = X T y

[0043] Then the vector solution parameter of θ is:

[0044] θ = (X T X) -1 X T y

[0045] where X T X is invertible.

[0046] The PID control principle is described in detail as follows, where the sampling period is 1 s.

[0047] PID control realizes precise adjustment based on error feedback. The error is calculated according to the formula E = SV - PV, where E is the precise quantification of the deviation degree, SV is the preset diameter value, and PV is the real-time diameter value, reflecting the actual state of the current process. The differential error quantity δE = E - E last captures the error change rate, monitors the slope change of the control trajectory, anticipates the system dynamic trend in advance, and helps the controller respond quickly. The integral term ΣE = E n + E n-1 + E n-2 + … + E n-2700 By summing the errors within 45 minutes back from the current moment, historical error accumulation and correction are realized, ensuring that the integral term plays a stable role within a reasonable range and avoiding control instability caused by excessive accumulation. The final control output PID Out = K​p *E + K i *ΣE + K d *δE, K p 、K i 、K d are PID control coefficients obtained through repeated tests and calibrations. The coordinated linkage of the three can dynamically optimize the control efficiency according to different working conditions, ensuring accurate, rapid, and stable and precise system response.

[0048] As Figure 1 shown, the PID control method for the diameter pulling speed of a single crystal furnace based on the ARX model, namely the recursive prediction control process, specifically includes:

[0049] 1) After system identification of the production data of the single crystal furnace diameter pulling speed, the parameters A, B, and e in the ARX formula y n = AY + BU + e are obtained;

[0050] 2) Starting from the nth moment, the control system follows a predefined algorithm to mine the data at historical moments (n - 1 to n - k), that is, the data before the nth moment, specifically the single crystal furnace diameter parameter y n-1 , y n-2 , y n-3 , …, y n-k , and the pulling speed parameter u n- 1, u n-2 , u n-3 , …, u n-k . Through the ARX model operation, the predicted diameter y n is obtained;

[0051] 3) The predicted diameter y n is connected to the PID controller, and through the PID formula operation, the predicted pulling speed u n is output;

[0052] 4) A new vector Y1 = [y n , y n-1 , y n-2 … y n-(k-1 )]^T and U1 = [u n , u n-1 , u n-2 … u n-(k-1) ^T are constructed and injected into the ARX model for calculation again, and the predicted diameter y n+1 and the predicted pulling speed u n+1 are iteratively deduced.

[0053] 5) Through cyclic iteration, recursively 10 times in sequence, continuously loop-optimized, gradually forming a predicted pulling speed sequence (u n , u n+1 , u n+2 … u n+9 ), the predicted pulling speed un+9 。

[0054] Take the 10th predicted drawing speed u n+9 As a key parameter for PLC seed crystal drawing speed control, high-precision coordinated control of the drawing speed and diameter can be achieved.

[0055] The above method has been verified by a large number of experiments and production practices, can significantly optimize the control effects of the drawing speed and diameter, and is superior to the existing PID single control mode in core indicators such as improved stability, reduced overshoot, and enhanced deviation control accuracy, and can effectively achieve efficient control of the single-crystal silicon preparation process.

[0056] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the inventive concept of the present invention, several modifications and improvements can be made, and these all belong to the protection scope of the present invention.

Claims

1. A PID control method for the diameter and drawing speed of a single crystal furnace based on an ARX model, characterized in that, Including the following steps: 1) After identifying the production data system of the single crystal furnace diameter and pulling speed, the parameters A, B, and e in the ARX formula y n = AY + BU + e are obtained; 2) Read the data before the nth moment of the system, including the single crystal furnace diameter parameter Y and the pulling speed parameter U, and substitute them into the ARX formula in step 1) to obtain the predicted diameter y n ; 3) Substitute the predicted diameter y obtained in step 2) n as the input into the PID formula to obtain the predicted casting speed u n ; 4) Substitute y n , y n-1 , y n-2 , y n-3 , …, y n-k and u n , u n- 1, u n-2 , u n-3 , …, u n-k into the ARX formula to obtain the predicted diameter y n+1 ; 5) Use the predicted diameter y obtained in step 4) n+1 as the input and substitute it into the PID formula to obtain the predicted casting speed u n+1 ; 6) Perform cyclic iteration, recursively 10 times in sequence, continuously optimize the loop, and gradually form the predicted casting speed sequence (u n , u n+1 , u n+2 … u n+9 ).

2. The PID control method for the diameter and drawing speed of a single crystal furnace based on the ARX model according to claim 1, wherein, In the said step 1), e is an error parameter, A = [a1, a2, a3, …, a k , B = [b1, b2, b3, …, b k .

3. The PID control method for the diameter pulling speed of a single crystal furnace based on the ARX model according to claim 1, wherein In the said step 2), Y = [y n-1 , y n-2 , y n-3 , …, y n-k T , U = [u n- 1, u n-2 , u n-3 , …, u n-k T .​​

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