An adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer

Abstract

The present application relates to a kind of for crystallizer hydraulic width adjustment displacement adaptive notch filter control method, belong to metallurgical automation technical field.The method real-time reads displacement sensor original value and electromagnetic stirring working state, constructs notch filter model;With displacement original value as input, according to electromagnetic stirring working frequency, i.e.target notch frequency, is filtered specifically;By comparing filter value and original value, real-time adjustment parameter is obtained to obtain the best effect.The present application can accurately suppress specific frequency periodic interference, strong adaptability, model is simple, effectively guarantee the stable and reliable operation of hydraulic width adjustment system under strong electromagnetic interference.

Description

Technical Field

[0001] This invention belongs to the field of metallurgical automation technology and relates to an adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer. Background Technology

[0002] Continuous casting is a comprehensive metallurgical process involving numerous physical phenomena such as flow, heat transfer, and solidification. The crystallizer, as a key piece of equipment in the continuous casting machine, directly affects the quality of the cast billet. When molten steel completes the solidification of the billet shell and the transport of bubbles and inclusions within the crystallizer, it can easily have an adverse impact on the quality of the cast billet. To improve billet quality, electromagnetic stirring technology has emerged and has been widely applied in continuous casting production.

[0003] Currently, electromagnetic stirring technology is mainly used in the crystallizer area, secondary cooling area, and the solidification end. However, during operation, the electromagnetic field generated by the crystallizer almost completely covers the entire crystallizer space, inevitably causing varying degrees of electromagnetic interference to the electrical equipment installed on and around the crystallizer. Typical manifestations of this electromagnetic interference include causing false temperature alarms in the slag leakage prediction system and causing drastic fluctuations in the displacement sensor measurements of the hydraulic width adjustment system.

[0004] Specifically, the displacement sensor of the hydraulic width adjustment system for the crystallizer is installed inside the hydraulic cylinder, behind the narrow-side copper plate of the crystallizer, within the range of a strong electromagnetic field. Under the influence of the alternating electromagnetic field generated by the electromagnetic stirring of the crystallizer, the measurement signal of the displacement sensor is severely interfered with, resulting in extremely unstable and highly volatile displacement values. This abnormal displacement fluctuation seriously affects the normal operation and control accuracy of the hydraulic width adjustment system, and may even trigger production accidents such as crystallizer cone slippage, ultimately threatening the stability of continuous casting production and the quality of the cast billet.

[0005] Therefore, in order to solve the problem of periodic electromagnetic interference signals caused by electromagnetic stirring in the crystallizer, it is urgent to study and design a method that can effectively suppress interference at specific frequencies, so as to ensure the accuracy and reliability of displacement detection signals and ensure the smooth operation of continuous casting production. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide an adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] An adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer includes the following steps:

[0009] S1: Real-time reading of the original displacement value of the hydraulic width adjustment displacement sensor of the crystallizer and the working status of the electromagnetic stirring of the crystallizer, and design of notch filter control model based on this.

[0010] S2: The original displacement value is used as the input signal of the notch filter control model, and the interference signal in the displacement signal is subjected to targeted notch filtering according to the working frequency of the electromagnetic stirring of the crystallizer, i.e. the target notch frequency.

[0011] S3: Compare the filtered displacement value with the original displacement value, and adjust the filtering parameters in real time accordingly to obtain the best filtering effect.

[0012] Furthermore, the specific method for designing the notch filter control model in S1 includes:

[0013] S11: Perform discrete angular frequency normalization calculation on the target notch frequency;

[0014] S12: Based on the orthogonality of sine and cosine functions, extract the sine and cosine components that are in phase with the target notch frequency from the input signal and establish their corresponding state equations.

[0015] S13: Weighted inverse coupling is applied to the extracted orthogonal components and projected onto the sinusoidal components;

[0016] S14: Weight the extracted orthogonal components and project them onto the cosine components;

[0017] S15: Add the sine projection component and the cosine projection component to synthesize the final filtered output signal.

[0018] Furthermore, the discrete angular frequency normalization calculation in S11 is achieved through the following formula:

[0019] ω0=ω0+2π·f0·T s

[0020]

[0021] Where ω0 is the discrete angular frequency in radians; f0 is the target notch frequency in Hertz (Hz); T s The sampling period of the input signal is expressed in seconds (s).

[0022] Furthermore, the state equation established in S12 is as follows:

[0023] I sin (k)=I sin (k-1)+GT s ·[e(k)-F(k-1)]·sinω0

[0024] I cos (k)=I cos (k-1)+GT s ·[e(k)-F(k-1)]·cosω0

[0025] Among them, I sin (k) represents the sinusoidal component that is in phase with the target frequency at the current moment; I cos (k) represents the cosine component that is in phase with the target frequency at the current moment; I sin (k-1) represents the sinusoidal component of the previous time step; I cos (k-1) represents the cosine component of the previous time step; e(k) represents the input signal at the current time step; F(k-1) represents the filtered output signal of the previous time step; G represents the gain coefficient; T s ω is the sampling period; ω0 is the discrete angular frequency.

[0026] Furthermore, the weighted back-coupled projection in S13 is achieved through the following formula:

[0027] F1 = [I cos (k)·bI sin (k)·a]·sinω0

[0028] The weighted forward coupling projection in S14 is achieved through the following formula:

[0029] F2 = [I cos (k)·a+I sin (k)·b]·cosω0

[0030] Where a and b are the frequency response adjustment coefficients of the filter; F1 is the sine projection component; and F2 is the cosine projection component.

[0031] Furthermore, the formula for synthesizing the filtered output signal in S15 is as follows:

[0032] F(k) = F1 + F2

[0033] Where F(k) is the filtered output signal at the current time.

[0034] Furthermore, when performing targeted notch filtering in S2, the selection of the filter frequency response adjustment coefficients $a$ and $b$ must satisfy the following relationship:

[0035]

[0036] The parameter a is a constant ranging from 0.1 to 1.0.

[0037] Furthermore, the z-domain transfer function H(z) of the notch filter control model is:

[0038]

[0039] Where K = acos2ω0 + bsin2ω0, and to ensure the stability of the filter, its poles satisfy |1-GT|. s K|<1.

[0040] Furthermore, through a bilinear transformation, the z-domain transfer function is mapped to the s-domain transfer function H(s):

[0041]

[0042] Furthermore, the real-time adjustment of the filtering parameters in S3 refers to dynamically adjusting the values ​​of the filter frequency characteristic adjustment coefficients a and b based on the comparison between the displacement filter value and the original displacement value, so as to adaptively obtain the best filtering effect.

[0043] The beneficial effects of this invention are as follows:

[0044] (1) The notch filter control model designed in this method innovatively introduces a calculation mechanism for the sine integral term and the cosine integral term. This mechanism can keep synchronized with the frequency of the interference signal, thereby achieving targeted processing of the periodic interference signal and specifically canceling the core interference. This method effectively avoids the indiscriminate attenuation of non-target frequency signals by traditional general filtering algorithms. While efficiently suppressing specific electromagnetic interference, it maximizes the preservation of the original dynamic response speed and control accuracy of the hydraulic width modulation system, ensuring the stability of system operation.

[0045] (2) This invention constructs a flexible parameter adjustment strategy through two key filter frequency characteristic adjustment coefficients. When the amplitude of electromagnetic interference encountered on site is large, the correction strength of the integral term can be enhanced by increasing the absolute value of the relevant parameters, thereby accelerating the error convergence speed and quickly eliminating fluctuations. Conversely, when the interference is weak, the relevant parameters can be reduced to avoid unnecessary oscillations in the system and ensure stability. More importantly, there is a scientific mathematical ratio between these parameters. This reasonable ratio can significantly reduce the system's sensitivity to phase changes of interference signals, thereby comprehensively improving the robustness of the entire anti-interference process and enabling the algorithm to adapt to complex and ever-changing on-site conditions.

[0046] (3) The core filtering model constructed in this invention is mathematically represented as a first-order discrete transfer function. The model structure is very simple, with low computational load and low requirements for the computing power of the controller. This simplicity makes the method easy to implement in existing industrial programmable logic controllers or embedded systems without increasing expensive hardware costs. The model can adapt to different operating frequencies and interference intensities by adjusting a few parameters, achieving an excellent balance between dynamic response speed, steady-state filtering accuracy, and system robustness. It is particularly suitable for solving the problem of hydraulic width adjustment displacement measurement under strong periodic interference from electromagnetic stirring in the crystallizer. It has high practical value and broad application prospects.

[0047] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0048] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0049] Figure 1 The displacement fluctuation diagram before filtering of the hydraulic width adjustment system subjected to electromagnetic stirring interference provided in the embodiment of the present invention;

[0050] Figure 2 A filtered displacement fluctuation diagram of a hydraulic width adjustment system subjected to electromagnetic stirring interference, provided in an embodiment of the present invention.

[0051] Figure 3 This is a data processing control flowchart provided for an embodiment of the present invention. Detailed Implementation

[0052] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0053] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0054] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0055] This invention provides an adaptive notch filter control method for hydraulic width adjustment displacement in a crystallizer. Under periodic disturbances from electromagnetic stirring in the crystallizer, the method ensures system stability by applying notch filtering to the displacement of the hydraulic width adjustment system. The method includes the following steps:

[0056] (1) Read the original displacement value of the hydraulic width adjustment displacement sensor of the crystallizer and the working status of the electromagnetic stirring of the crystallizer in real time, and design a notch filter control model.

[0057] (2) The original displacement value is used as the input signal of the notch filter control model, and the interference signal is subjected to targeted notch filtering according to the working frequency of the crystallizer electromagnetic stirring, i.e. the target notch frequency.

[0058] (3) Compare the filtered displacement value with the original displacement value and adjust the filtering parameters in real time to obtain the best filtering effect.

[0059] The specific method of step (1) is as follows:

[0060] Since the start-up of the electromagnetic stirrer in the crystallizer causes periodic interference to the width adjustment displacement, a corresponding notch filter algorithm is designed to filter the displacement data. First, the raw displacement values ​​from the crystallizer's hydraulic width adjustment displacement sensor and the working status of the crystallizer's electromagnetic stirrer, including the electromagnetic stirrer start signal and operating frequency, are read in real time.

[0061] Assume the input signal is e(k), the filtered output signal is F(k), and the sampling period of the input signal is set to T. s The unit is s, and the target notch frequency is f0, with the unit being Hz.

[0062] The control model for the notch filter is established below:

[0063] S11: First, perform discrete angular frequency normalization calculation on the target notch frequency:

[0064] ω0=ω0+2π*f0*T s (1)

[0065]

[0066] Where: ω0 is the discrete angular frequency, in radians.

[0067] S12: Based on the orthogonality of sine and cosine functions, the target frequency component is extracted from the complex signal. Therefore, by extracting the sine and cosine components in phase with the target notch frequency f0 from the input signal e(k), the state equations for the sine and cosine integral terms are established as follows:

[0068] I sin (k)=I sin (k-1)+GT s *[e(k)-F(k-1)]sinω0 (3)

[0069] I cos (k)=I cos (k-1)+GT s *[e(k)-F(k-1)]cosω0 (4)

[0070] Among them: I sin (k) represents the sinusoidal component that is in phase with the target frequency at the current moment, I cos (k) represents the cosine component that is in phase with the target frequency at the current moment, I sin (k-1) represents the sinusoidal component that was in phase with the target frequency at the previous moment, I cos (k-1) represents the cosine component in phase with the target frequency at the previous moment, G is the gain coefficient used to adjust the filter's response speed, and GT s This reflects the integral strength.

[0071] S13: Using the orthogonal components obtained above, namely the sine integral and cosine integral, we first perform weighted inverse coupling on them and project them onto the sine component, as follows:

[0072] F1 = [I cos (k)*bI sin (k)*a]*sinω0 (5)

[0073] S14: Using the sine and cosine integrals, a weighted forward coupling is performed and projected onto the cosine component, as follows:

[0074] F2 = [I cos (k)*a+I sin (k)*b]*cosω0 (6)

[0075] Where: a and b are the frequency response adjustment coefficients of the filter. By adjusting these two coefficients, the amplitude frequency response, phase frequency response, and bandwidth of the filter at the target frequency can be changed.

[0076] S15: Add the above sine projection and cosine projection to synthesize the sine and cosine components, generating the final filtered signal output:

[0077] F(k) = F1 + F2 = [I cos (k)*bI sin (k)*a]*sinω0+[I cos (k)*a+I sin (k)*b]*cosω0(7)

[0078] The transfer function of the filtered output signal F(k) in step S15 includes:

[0079] S16: Simplifying equation (7) above, we get:

[0080] F(k)=C1*I cos (k)+C2*I sin (k) (8)

[0081] Where: C1 = acosω0 + bsinω0, C2 = bcosω0 - asinω0

[0082] S17: Perform z-transform on state equations (3), (4) and (8):

[0083] I sin (z)=z -1 I sin (z)+GT s *[E(z)-z -1 F(z)]sinω0 (9)

[0084] I cos (z)=z -1 I cos (z)+GT s *[E(z)-z -1 F(z)]cosω0 (10)

[0085] F(z)=C1*I cos (z)+C2*I sin (z) (11)

[0086] S18: Combining equations (9), (10), and (11), the z-domain transfer function H(z) of the filtered output signal is obtained as follows:

[0087]

[0088] Where: K = acos2ω0 + bsin2ω0, thus the function is a first-order discrete function. To ensure the stability of the filter, its poles must satisfy |z| < 1, that is, |1-GT| s K|<1. Furthermore, the z-term in the molecule exhibits "leading characteristics," being related to the target notch frequency, thus enabling the filter to be selective for specific frequencies.

[0089] S19: Mapping relationship through bilinear transformation: Substituting into equation (12), the s-domain transfer function H(s) of the filtered output signal is obtained as follows:

[0090]

[0091] The specific method for step (2) is as follows:

[0092] To achieve good filtering results, targeted notch filtering should be performed. The selection of filtering parameters a and b must satisfy the following relationship:

[0093] S21: According to equation (12), and z = e jω The frequency response H(e) is obtained jω ):

[0094]

[0095] S22: Using Euler's formula e jω =cosω +jsinω, the magnitude response is calculated as follows:

[0096]

[0097] Therefore, to achieve notch filtering at the target frequency, when ω=ω0, the amplitude response |H(e) needs to be... jω If |→0, then the numerator of equation (15) needs to approach 0, that is, GT s K→0, that is, K=acos2ω0+bsin2ω0→0.

[0098] Therefore, a and b satisfy the following relationship:

[0099]

[0100] Wherein: parameter a is usually a constant between 0.1 and 1.0, and parameters a and b satisfy the above formula to ensure that the target notch frequency can be suppressed.

[0101] S23: Use the original displacement value of the pulse width modulation system as the input signal of the notch filter, and read the working frequency of the electromagnetic stirring of the crystallizer in real time, i.e. the target notch frequency, match the corresponding filtering parameters a and b, and perform notch filtering on its interference signal.

[0102] The specific method of step (3) is as follows: compare the filtered displacement value with the original displacement value to obtain the filtering control effect, and adjust the parameters a and b in real time according to the filtering effect to obtain the best filtering effect.

[0103] In this embodiment, the specific implementation steps are as follows:

[0104] 1) Let the sampling period of the system be T. s =0.02s, the working frequency of the electromagnetic stirrer in the crystallizer, i.e. the target notch frequency, is f0 = 5Hz, and the gain coefficient G = 10.0;

[0105] 2) Based on the above basic data, and combined with formulas (1) and (16), the discrete angular frequency ω0≈0.6283rad is calculated. Therefore, cos2ω0≈0.309rad and sin2ω0≈0.951rad, thus obtaining... If we choose a = 0.5, then b ≈ -0.16245;

[0106] 3) Real-time reading of the original displacement value of the width adjustment system. When the electromagnetic stirrer in the crystallizer is started, the change in the displacement value of the width adjustment system before and after being disturbed, such as... Figure 1 As shown, the displacement value fluctuates greatly after the electromagnetic stirrer in the crystallizer is turned on, exceeding 50 mm. Based on the above calculation results and values, and combined with formulas (3) to (7), the filtered signal output is calculated in real time, as shown below. Figure 2 The curve shows that the displacement value fluctuates within ±0.1mm, indicating a good filtering effect.

[0107] 4) The control flow of the entire data processing is as follows: Figure 3 As shown, in addition, the filtering parameters a and b can be adjusted in real time by observing the displacement value after filtering. If the working frequency of the electromagnetic stirrer of the crystallizer changes, the filtering control model will automatically update the filtering output according to its frequency, so as to obtain the best filtering effect.

[0108] As can be seen from the above embodiments, the filtering method can accurately suppress periodic interference, improve the filtering targeting, and the algorithm is simple, easy to implement, widely applicable, and highly practical.

[0109] The present invention provides an adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer. Its core lies in using a cleverly designed notch filter control model to filter out the periodic displacement interference signal introduced by the electromagnetic stirring operation of the crystallizer in real time and in a targeted manner, thereby ensuring the accuracy and stability of the displacement feedback value of the hydraulic width adjustment system.

[0110] Example 1

[0111] This embodiment demonstrates the application process of the method of the present invention in a specific hydraulic width adjustment system of a continuous casting machine crystallizer. The sampling period of the system displacement sensor is set to 0.02 seconds, and the operating frequency of the crystallizer electromagnetic stirrer, i.e., the notch filter frequency to be filtered out, is 5 Hz. The gain coefficient of the system controller is set to 10.

[0112] First, based on the aforementioned basic parameters, the discrete angular frequency is normalized. Substituting the target notch frequency and sampling period into the formula, the discrete angular frequency is calculated to be approximately 0.6283 radians. Then, the sine and cosine values ​​of twice the discrete angular frequency are calculated; the cosine value is approximately 0.309, and the sine value is approximately 0.951. Using the filter parameter relationship determined according to this invention, the ratio of parameter b to parameter a is calculated to be approximately -0.3249. Selecting parameter a as 0.5, the corresponding parameter b is approximately -0.16245.

[0113] Figure 1 This figure shows the displacement sensor reading curves before filtering when the hydraulic width adjustment system is subjected to electromagnetic stirring interference in this embodiment. As shown in the figure, the horizontal axis represents time, and the vertical axis represents the displacement measurement value. After the electromagnetic stirring of the crystallizer is started, the displacement signal, which should have been stable, exhibits large-amplitude periodic fluctuations, with fluctuation amplitudes exceeding fifty millimeters. This violent fluctuation truly reflects the serious impact of electromagnetic interference on the measurement system, making it impossible for the control system to obtain accurate crystallizer narrow edge position information, seriously threatening production safety.

[0114] Then, the calculated parameters a, b, discrete angular frequency, and gain coefficient are substituted into the notch filter control model. The system reads the original displacement value e(k) in real time and iteratively calculates the sine and cosine integral terms at the current moment according to the state equation. Next, these two orthogonal components are weighted and coupled in reverse and forward directions, respectively projected onto the sine and cosine components, resulting in two projected components F1 and F2. Finally, the two projected components are added together to synthesize and output the filtered signal F(k) at the current moment.

[0115] Figure 2 The output curve of the displacement signal after the above notch filtering process is shown. It can be clearly seen from the figure that the originally violent periodic fluctuations have been largely filtered out. The filtered displacement curve becomes very smooth, with fluctuations suppressed within a range of ±0.1 mm, consistent with... Figure 1 The unfiltered signal in the image contrasts sharply with the actual signal. This demonstrates that the method of this invention successfully extracts and cancels interference at a specific frequency, outputting a stable and reliable displacement value, thus providing a solid foundation for the stable control of the hydraulic width adjustment system.

[0116] Figure 3 This paper discloses the control flowchart of the entire data processing process of this invention. The flowchart clearly illustrates the core steps and logical relationships of the method. The process begins with system initialization, setting initial parameters. Then, the main loop begins. The first step is signal acquisition, i.e., real-time reading of the original displacement value and the electromagnetic stirring operating status. The second step is frequency normalization, updating the target discrete angular frequency based on the real-time operating frequency of the electromagnetic stirring. The third step is model calculation, the core step, which includes calculating the sine and cosine integral terms, performing orthogonal component coupling and projection, and finally synthesizing the filtered output. The fourth step is sending the filtered output value to the control system for use. The fifth step is effect evaluation and parameter adaptation. This step compares the filtered displacement value with the original value, intelligently judges the current filtering effect according to preset evaluation criteria, and if the effect is not optimal, automatically fine-tunes the value of parameter a or parameter b and feeds it back to the model calculation step, forming a closed-loop optimization circuit to ensure the best filtering effect under any operating condition. The entire process is executed cyclically, achieving continuous adaptive filtering of periodic interference.

[0117] Example 2

[0118] This embodiment illustrates the adaptive capability of the method of the present invention when the electromagnetic stirring frequency changes. It is assumed that during production, the process requires adjusting the operating frequency of the crystallizer's electromagnetic stirring from five Hz to six Hz.

[0119] At this point, no manual intervention is required. The control model reads the new target notch frequency value of six Hz in real time. Subsequently, it automatically performs the discrete angular frequency normalization calculation step to update the discrete angular frequency value. Then, based on the new discrete angular frequency, it recalculates the ratio between parameter b and parameter a, and automatically updates the filter parameters.

[0120] After the entire update process is completed, the center frequency of the notch filter automatically tracks and locks onto the new interference frequency of six Hz, continuing to effectively filter out displacement interference signals at that frequency. This demonstrates the powerful adaptive capability of the method of this invention to changes in operating conditions, ensuring the continuous optimal filtering effect without requiring downtime for resetting.

[0121] In summary, the present invention demonstrates significant advantages through the above embodiments, including precise suppression of fixed-frequency interference, flexible parameter adjustment, and simple and easy-to-implement model, effectively ensuring the stable and reliable operation of the crystallizer hydraulic width adjustment system under strong electromagnetic interference environment.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer, characterized in that: Includes the following steps: S1: Real-time reading of the raw displacement values ​​from the hydraulic width adjustment displacement sensor of the crystallizer and the working status of the electromagnetic stirrer in the crystallizer, and designing a notch filter control model based on this; specific methods include: S11: Perform discrete angular frequency normalization calculation on the target notch frequency; S12: Based on the orthogonality of sine and cosine functions, extract the sine and cosine components in phase with the target notch frequency from the input signal, and establish their corresponding state equations; the established state equations are: in, It is the sinusoidal component that is in phase with the target frequency at the current moment; It is the cosine component that is in phase with the target frequency at the current moment; This is the sinusoidal component from the previous moment; It is the cosine component of the previous moment; This is the input signal at the current moment; This is the filtered output signal from the previous moment; This is the gain coefficient; The sampling period; Discrete angular frequencies; S13: Weighted inverse coupling is applied to the extracted orthogonal components and projected onto the sinusoidal components; S14: Weight the extracted orthogonal components and project them onto the cosine components; The weighted reverse coupling projection in S13 is achieved by the following formula: The weighted forward coupling projection in S14 is achieved through the following formula: in, and This is the frequency response adjustment coefficient for the filter; For sinusoidal projection components; For the cosine projection component; S15: Add the sine projection component and the cosine projection component to synthesize the final filtered output signal; S2: The original displacement value is used as the input signal of the notch filter control model, and the interference signal in the displacement signal is subjected to targeted notch filtering according to the working frequency of the electromagnetic stirring of the crystallizer, i.e. the target notch frequency. S3: Compare the filtered displacement value with the original displacement value, and adjust the filtering parameters in real time accordingly to obtain the best filtering effect.

2. The adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer according to claim 1, characterized in that: The discrete angular frequency normalization calculation in S11 is achieved through the following formula: in, These are discrete angular frequencies, expressed in radians. The target notch filter frequency is expressed in Hertz (Hz). The sampling period of the input signal, in seconds. s .

3. The adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer according to claim 1, characterized in that: The formula for synthesizing the filtered output signal in S15 is as follows: in, This is the filtered output signal at the current moment.

4. The adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer according to claim 1, characterized in that: When performing targeted notch filtering in S2, the filter frequency response adjustment coefficient a and b The selection must satisfy the following relationship: Among them, parameters The value of is a constant between 0.1 and 1.

0.

5. The adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer according to claim 1, characterized in that: The notch filter control model z Domain transfer function for: in, To ensure filter stability, its poles satisfy... .

6. The adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer according to claim 5, characterized in that: Through bilinear transformation, the z Domain transfer function mapped to s-domain transfer function : 。 7. The adaptive notch filter control method for hydraulic width adjustment displacement of a crystallizer according to claim 1, characterized in that: The real-time adjustment of the filter parameters in S3 refers to dynamically adjusting the filter frequency response adjustment coefficient based on the comparison between the displacement filter value and the original displacement value. a and b The value of is selected to adaptively obtain the best filtering effect.

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