A crystallizer liquid level control method and a surface wave filter structure

Abstract

The application discloses a crystallizer liquid level control method with a surface wave filtering structure and a surface wave filtering structure. In a feedback loop of crystallizer liquid level feedback control, a surface wave monitoring and filtering structure based on a liquid level measurement signal is arranged, and periodic real-time monitoring of a liquid level fluctuation signal is established through the arranged surface wave monitoring and filtering structure. When the monitoring result is greater than or equal to a set threshold value, surface wave filtering based on a wave trap is started, and a liquid level measurement signal feedback based on surface wave filtering is formed. Otherwise, direct feedback based on the liquid level measurement signal is formed. The crystallizer liquid level control method with the surface wave filtering structure and the surface wave filtering structure can effectively reduce the harmful influence of surface waves on the crystallizer liquid level control in the actual production process through the above technical arrangement.

Description

Technical Field

[0001] This invention belongs to the field of steelmaking continuous casting technology, specifically relating to a method for controlling the liquid level of a crystallizer with a surface wave filtration structure and the surface wave filtration structure. Background Technology

[0002] Stable control of the liquid level in the crystallizer is crucial for safe production and ensuring product quality in continuous casting. Molten steel is injected into the crystallizer through an immersion nozzle via a stopper rod mechanism in the tundish. Under the action of cooling water in the crystallizer, the molten steel forms a billet with a certain shell thickness. The continuous casting machine pulls the gradually solidifying billet out of the crystallizer at a speed set by the process. During continuous casting, the liquid level in the crystallizer must be controlled within a certain range. Excessive fluctuations in the liquid level can easily cause slag inclusions and cracks on the billet surface, resulting in quality loss, or even steel leakage, leading to serious production accidents. Therefore, methods for high-precision control of the liquid level in continuous casting crystallizers have received considerable attention.

[0003] In actual production, we observed a flow asymmetry caused by crystallizer vibration or branching of the submerged entry nozzle, resulting in sloshing of molten steel inside the crystallizer. The internal liquid level, detected by a VUHZ level gauge, exhibits periodic fluctuations, but the total volume of molten steel inside the crystallizer remains unchanged. Automatic adjustment of this process via PID control exacerbates this oscillation, a phenomenon known as surface oscillation. When this problem occurs in actual operation, operators typically switch to manual open-loop control or reduce the casting speed to ensure safe and stable production. However, suppressing surface oscillations through manual open-loop control or reduced casting speed not only significantly reduces production efficiency but also increases the workload for on-site operators.

[0004] The invention application with application number CN201310287655.7 discloses "a method for controlling liquid level fluctuations in a crystallizer". It utilizes the existing continuous casting liquid level measurement system, communication control system, and stopper rod control system, and adds a liquid level fluctuation analysis system. The liquid level detection unit of the crystallizer liquid level measurement system transmits fluctuation data in real time to the liquid level fluctuation analysis system based on spectral analysis. Fourier transform is used to decompose each frequency component, and the relative importance of each component is measured using the spectral density function. The main frequency components in the sequence are identified, thereby grasping the periodic fluctuation characteristics of the sequence. The liquid level fluctuation frequency range at the main locations causing slag entrapment in the crystallizer under steady-state and unsteady-state casting conditions is analyzed. This allows for real-time monitoring of liquid level fluctuations. The possibility of slag entrapment is reduced by controlling the stopper rod to decrease the casting speed and adjusting the protective slag and nozzle outlet angle.

[0005] The invention application with application number CN 202210767436.8 discloses "a method and system for identifying abnormal fluctuations in the liquid level of a crystallizer." This method can be applied to both offline historical data analysis and online assessment of liquid level fluctuations in the crystallizer, reducing the impact of liquid level fluctuations on billet quality, minimizing billet quality losses, and improving the efficiency of continuous casting production. Utilizing crystallizer liquid level fluctuation data, and based on an analysis method combining Fast Fourier Transform and wavelet entropy, it can comprehensively analyze the fluctuations of molten steel in the crystallizer over a period of time (different heats or different castings), accurately pinpointing the time of abnormal liquid level fluctuations and quickly tracing their causes. Summary of the Invention

[0006] To address the above problems, this invention provides a method for controlling the liquid level in a crystallizer with a surface wave filtration structure and the surface wave filtration structure itself. The specific technical solution of the method for controlling the liquid level in a crystallizer with a surface wave filtration structure is as follows:

[0007] In the feedback loop of the crystallizer level feedback control, a surface wave monitoring and filtering structure based on the level measurement signal is set up.

[0008] Periodic real-time monitoring of liquid level fluctuation signals is established by setting up surface wave monitoring and filtration structures;

[0009] When the monitoring result is greater than or equal to the set threshold, the surface wave monitoring and filtering structure based on the liquid level measurement signal is activated to form feedback based on the liquid level measurement signal after surface wave filtering; otherwise, direct feedback based on the liquid level measurement signal is formed.

[0010] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0011] The surface wave monitoring and filtering structure consists of a surface wave identification unit and a notch filter unit.

[0012] The surface wave identification unit is used to receive liquid level measurement signals and crystallizer width detection signals in real time, and determine the actual notch center frequency, notch depth, notch bandwidth and the amplitude of the wave signal corresponding to the actual notch center frequency based on these two signals.

[0013] The notch filter unit is used to receive the amplitude of the fluctuating signal corresponding to the actual notch center frequency, and to determine whether to start the notch filter based on the comparison result of the fluctuating signal amplitude and the set threshold.

[0014] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0015] The determination of the actual notch filter center frequency based on the liquid level measurement signal and the crystallizer width detection signal specifically includes the following steps:

[0016] S1: Determine the theoretical frequency of the surface wave based on the crystallizer width and the order of the notch filter;

[0017] S2: Perform zero-mean processing on the liquid level measurement signal to obtain the liquid level fluctuation signal;

[0018] S3: Perform time-frequency conversion on the liquid level fluctuation signal and combine it with the theoretical frequency of the surface wave to determine the actual notch wave center frequency.

[0019] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0020] Based on this, the specific steps for determining the notch depth and notch bandwidth are as follows:

[0021] SS1: Real-time determination of the phase margin of the current system with notch filter;

[0022] SS2: Calculate the difference between the theoretical phase margin of the system and the phase margin of the current system with notch filter. If the calculation result is greater than the set value, proceed to step SS3; otherwise, proceed to step SS4.

[0023] SS3: Determine the notch depth as 0.4 and the notch bandwidth as 0.26;

[0024] SS4: Determine the notch depth based on the actual surface wave amplitude, and determine the notch bandwidth based on the combined constraints of normal liquid level feedback and notch filter robustness.

[0025] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0026] The theoretical frequency of surface waves is determined by the following formula:

[0027]

[0028] In the above formula,

[0029] f: Theoretical frequency of surface waves, unit: Hz;

[0030] c: The order of the notch filter;

[0031] g: acceleration due to gravity, unit: m / s² 2 ;

[0032] L: width of the crystallizer, unit: m.

[0033] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0034] The aforementioned time-frequency conversion of the liquid level fluctuation signal is accomplished through spectral refinement analysis based on the frequency shift method.

[0035] Based on this, the actual notch wave center frequency is determined by combining the theoretical frequency of the surface wave. Specifically, a peak search is performed within a frequency range set near the theoretical frequency of the surface wave to obtain the maximum value of the amplitude spectrum of the liquid level fluctuation signal after time-frequency conversion within this frequency range. The actual notch wave center frequency is determined based on this maximum value.

[0036] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0037] The determination of notch depth based on the actual surface wave amplitude is specifically as follows:

[0038] Set the target amplitude Af of the notch filter center frequency after filtering.

[0039] Real-time determination of surface wave amplitude A;

[0040] The notch depth is determined by the ratio of Af to A.

[0041] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0042] The notch bandwidth ranges from [0.05, 0.4].

[0043] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0044] The notch filter unit includes a first notch filter and a second notch filter connected in series in the feedback loop.

[0045] A method for controlling the liquid level in a crystallizer with a surface wave filtration structure according to the present invention.

[0046] The first notch filter and the second notch filter are respectively a first-order notch filter and a second-order notch filter.

[0047] A surface wave filtration structure for liquid level in a crystallizer.

[0048] The surface wave filtering structure is installed in the feedback loop of the crystallizer liquid level feedback control system. The surface wave filtering structure establishes periodic real-time monitoring of surface waves based on the liquid level measurement signal. Based on the monitoring results, the surface wave filtering structure controls the formation of two feedback forms: when the monitored value exceeds the set threshold, the liquid level measurement signal after filtering the surface wave is fed back; or when the monitored value does not exceed the set threshold, the liquid level measurement signal is directly fed back.

[0049] Furthermore,

[0050] The surface wave filtering structure consists of a surface wave identification unit and a notch filter unit.

[0051] The surface wave identification unit is used to receive liquid level measurement signals and crystallizer width detection signals in real time, and determine the actual notch center frequency, notch depth, notch bandwidth and the amplitude of the wave signal corresponding to the actual notch center frequency based on these two signals.

[0052] The notch filter unit is used to receive the amplitude of the fluctuating signal corresponding to the actual notch center frequency, and to determine whether to start the notch filter based on the comparison result of the fluctuating signal amplitude and the set threshold.

[0053] Furthermore,

[0054] The determination of the actual notch filter center frequency based on the liquid level measurement signal and the crystallizer width detection signal specifically includes the following steps:

[0055] S1: Determine the theoretical frequency of the surface wave based on the crystallizer width and the order of the notch filter;

[0056] S2: Perform zero-mean processing on the liquid level measurement signal to obtain the liquid level fluctuation signal;

[0057] S3: Perform time-frequency conversion on the liquid level fluctuation signal and combine it with the theoretical frequency of the surface wave to determine the actual notch wave center frequency.

[0058] Furthermore,

[0059] Based on this, the specific steps for determining the notch depth and notch bandwidth are as follows:

[0060] SS1: Real-time determination of the phase margin of the current system with notch filter;

[0061] SS2: Calculate the difference between the theoretical phase margin of the system and the phase margin of the current system with notch filter. If the calculation result is greater than the set value, proceed to step SS3; otherwise, proceed to step SS4.

[0062] SS3: Determine the notch depth as 0.4 and the notch bandwidth as 0.26;

[0063] SS4: Determine the notch depth based on the actual surface wave amplitude, and determine the notch bandwidth based on the combined constraints of normal liquid level feedback and notch filter robustness.

[0064] Furthermore,

[0065] The theoretical frequency of surface waves is determined by the following formula:

[0066]

[0067] In the above formula,

[0068] f: Theoretical frequency of surface waves, unit: Hz;

[0069] c: The order of the notch filter;

[0070] g: acceleration due to gravity, unit: m / s² 2 ;

[0071] L: width of the crystallizer, unit: m.

[0072] Furthermore,

[0073] The aforementioned time-frequency conversion of the liquid level fluctuation signal is accomplished through spectral refinement analysis based on the frequency shift method.

[0074] Based on this, the actual notch wave center frequency is determined by combining the theoretical frequency of the surface wave. Specifically, a peak search is performed within a frequency range set near the theoretical frequency of the surface wave to obtain the maximum value of the amplitude spectrum of the liquid level fluctuation signal after time-frequency conversion within this frequency range. The actual notch wave center frequency is determined based on this maximum value.

[0075] Furthermore,

[0076] The determination of notch depth based on the actual surface wave amplitude is specifically as follows:

[0077] Set the target amplitude Af of the notch filter center frequency after filtering.

[0078] Real-time determination of surface wave amplitude A;

[0079] The notch depth is determined by the ratio of Af to A.

[0080] Furthermore,

[0081] The notch bandwidth ranges from [0.05, 0.4].

[0082] Furthermore,

[0083] The notch filter unit includes a first notch filter and a second notch filter connected in series in the feedback loop.

[0084] Furthermore,

[0085] The first notch filter and the second notch filter are respectively a first-order notch filter and a second-order notch filter.

[0086] The present invention discloses a crystallizer level control method and surface wave filtering structure with surface wave filtering structure. By inserting a notch filter in series in the feedback loop, the narrow-band characteristics of the notch filter are used to establish a good response to surface wave fluctuations in actual working conditions, so as to establish fully automatic adaptive real-time control of surface waves, thereby improving the stability and control accuracy of crystallizer level control.

[0087] In the actual application of notch filters, the accuracy of the center frequency of the narrow-band notch filter affects its performance. Therefore, how to accurately determine the center frequency of the notch filter in real time becomes the primary technical problem to be solved. This technical solution addresses this problem from two aspects. First, based on the theoretical frequency of surface waves and the actual liquid level, a method for determining the actual center frequency in real time is established. Second, considering the picket fence effect, a spectrum refinement analysis based on the frequency shift method is adopted to complete the time-frequency conversion and obtain a more ideal spectrum.

[0088] Meanwhile, considering that notch filters can cause a certain phase margin loss, in order to ensure and maintain the stability of the system itself, this technical solution further optimizes the above technical solution and establishes a notch filter parameter determination method based on discriminant constraints. When the difference between the theoretical phase margin of the system and the current phase margin with the notch filter exceeds the set value, a fixed notch depth and notch bandwidth are used to determine the notch filter parameters; otherwise, the method established in this technical solution is used to determine the notch depth and notch bandwidth, thereby completing the determination of the notch filter parameters.

[0089] The present invention provides a crystallizer liquid level control method and a surface wave filtration structure. After the above technical settings are implemented and put into production, the harmful effects of surface waves on crystallizer liquid level control during actual production can be effectively reduced. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the surface wave monitoring and filtering structure in this invention;

[0091] Figure 2 This is a schematic diagram of the crystallizer level control system with surface wave monitoring and filtration structure in this invention;

[0092] Figure 3 This is a schematic diagram of the surface wave filtration process for the crystallizer liquid level in the working principle and process of the present invention;

[0093] Figure 4 This is a schematic diagram of a simulation model of a crystallizer level control system with surface wave monitoring and filtration structure in an embodiment of the present invention.

[0094] Figure 5 This is a schematic diagram comparing the liquid level signal before and after data preprocessing in an embodiment of the present invention;

[0095] Figure 6 This is a schematic diagram of the liquid level fluctuation signal in the embodiment of the present invention, and of performing FFT time-frequency conversion and refined FFT on the liquid level fluctuation signal respectively.

[0096] Figure 7This is a schematic diagram comparing the liquid level measurement signal and the liquid level feedback signal in an embodiment of the present invention. Detailed Implementation

[0097] The following is a detailed description of a crystallizer level control method with a surface wave filtration structure and the surface wave filtration structure of the present invention, based on the accompanying drawings and specific embodiments.

[0098] This invention, combined with on-site process considerations, proposes a crystallizer level control method and surface wave (SW) filtering structure. In summary, this method, by modeling the crystallizer structure and considering the actual crystallizer width in production, can initially determine the theoretical frequency of the surface wave. Using advanced signal processing technology, the measured liquid level of the crystallizer level control system is analyzed, and combined with the calculated theoretical surface wave frequency, the activation and deactivation of the SW filtering structure, as well as the internal parameter settings of the SW filtering structure, are determined. Through this method, fully automatic adaptive control of the surface wave is achieved without human intervention, automatically removing the liquid level fluctuation components caused by these harmful interferences from the liquid level measurement data, thereby improving the stability and accuracy of the crystallizer level control.

[0099] The working principle and process of this technical solution are explained below to provide a clearer understanding of it:

[0100] Since first- and second-order surface waves are most common in actual production processes, the notch filter unit in this technical solution is composed of first- and second-order notch filters. (See [link to technical documentation]). Figure 1 .

[0101] The proposed technical solution combines width variation, theoretical frequency, and actual liquid level fluctuation under operating conditions with signal processing for combined analysis. The actual process involves roughly determining the frequency band of surface wave fluctuations by using the crystallizer width; automatically determining the presence and actual magnitude of surface waves by analyzing the liquid level fluctuations under actual operating conditions and using signal processing; and determining the opening and closing of the first and second notch filters based on the above analysis, and setting the notch filter parameters in real time. Through this control method, fully automatic online adaptive control is achieved for liquid level instability caused by surface waves.

[0102] The crystallizer level control system incorporating the surface wave monitoring and filtration structure designed in this technical solution is as follows: Figure 2 As shown, the module includes a PID controller, a level actuator, a crystallizer, a first notch filter, a second notch filter, and a surface wave recognition module. The control method and steps based on this are as follows: Figure 3As shown, the process includes: (1) calculating the theoretical frequency f of surface waves of different orders based on the crystallizer width information of the continuous casting process; (2) subtracting the average value from the liquid level measurement data to obtain the liquid level fluctuation signal; (3) using the liquid level fluctuation signal obtained in step 2, transforming the liquid level fluctuation signal from the time domain to the frequency domain by performing Zoom-FFT; (4) using the liquid level fluctuation frequency domain result obtained in step 3, finding the surface wave component in the current actual process, and determining the notch center frequency and notch attenuation factor based on the distribution of this component in the frequency domain; (5) using the notch center frequency determined in step 4. The rate and notch attenuation factor are calculated through parameters, and the parameters of the two notch filters are set respectively; (6) Analyze the change in phase margin of the open-loop transfer function after using the first and second notch filters, so as to infer the rationality of the notch filter parameter settings. If it is not reasonable, a set of default parameters is used. (7) Based on the surface wave component determined in the frequency domain by Zoom-FFT in step 3, determine the activation and deactivation of the two notch filters, calculate the deviation between the filtered liquid level feedback value and the liquid level set value, calculate the control adjustment amount through the PID controller, and use it for normal closed-loop liquid level control. The specific process is as follows:

[0103] (1) Theoretically, based on the internal structure of the crystallizer, the theoretical frequency of surface waves can be described by the following formula:

[0104]

[0105] Where c is the number of nodes (c = 1, 2, 3...); g is the gravitational acceleration, in m / s². 2 L represents the width of the crystallizer (which can be determined based on the current billet size information collected by the PLC), in meters (m). The theoretical dominant frequency of the surface wave in the current crystallizer is calculated based on the different orders c. The theoretical frequencies of the first two orders of surface waves are mainly considered: first-order surface wave frequency f1 (c=1) and second-order surface wave frequency f2 (c=2), and their relationship is generally f2>f1. However, in actual operating conditions, due to errors in width measurement, the actual fluctuation frequency of the surface wave often deviates from the theoretical frequency.

[0106] (2) Data preprocessing

[0107] To better analyze actual operating conditions, it is necessary to remove the DC component from the measured liquid level. The liquid level measurement values ​​from the crystallizer are preprocessed to obtain the liquid level fluctuation period signal, as follows:

[0108] Liquid level fluctuation signal y(n) = Liquid level measurement signal - Average value of liquid level measurement signal

[0109] (3) Zoom-FFT

[0110] In crystallizer level control, the sampling frequency of data acquisition is fs. To ensure the real-time performance of the analysis system, N data points are typically used for frequency domain transformation, resulting in a frequency resolution of Δf = fs / N. Due to the picket fence effect, the FFT of the level fluctuation signal only has values ​​at certain quantiles. However, the accuracy of the center frequency of the narrowband notch filter has a significant impact on the final notch filter performance. Considering these issues, without increasing the number of transform points, a Fast Fourier Transform (Zoom-FFT) that increases the frequency band resolution near the theoretical surface wave frequency is used. The process is as follows:

[0111] First, perform a Fourier transform on the liquid level fluctuation signal after preprocessing in step 2:

[0112]

[0113]

[0114] Generally, Zoom-FFT only refines a frequency band within a certain bandwidth. However, this technique considers the influence of the first two orders of surface waves simultaneously. The refined frequency band must at least include the frequency band between the theoretical frequencies of the first and second orders of surface waves, with a certain margin. The center frequency of the frequency band for refined analysis is determined as follows:

[0115] f c = [(f1-∈)+(f2+∈))] / 2,

[0116] Complex modulation of the original liquid level fluctuation signal

[0117]

[0118] Based on the frequency shifting characteristics of the Discrete Fourier Transform, the following relationship exists.

[0119] Y c (k)=Y(k+f c / Δf)

[0120] To better preserve the signal components within the refined frequency band, a low-pass filter is applied to the frequency-shifted signal.

[0121]

[0122] N(k) is a low-pass filter. The original fluctuating signal is resampled using the sampling frequency f′s = fs / D, expressed as follows:

[0123]

[0124] Where S = k / D, l = n / D. Perform a Discrete Fourier Transform on g(l) obtained from resampling.

[0125]

[0126]

[0127] Finally, the spectrum is restored to the actual frequency to obtain the final Zoom-FFT output:

[0128] Y(k)=Y(kf c / Δf)

[0129]

[0130] (4) Determine the actual notch center frequency and notch attenuation factor

[0131] Based on the frequency domain result Y(f) obtained by performing Zoom-FFT on the liquid level fluctuation signal in step 3, where Within a certain frequency range near the theoretical frequencies f1 and f2 of first- and second-order surface waves, Y(f) peak search is performed on fr1 and fr2 to obtain the Zoom-FFT maximum values ​​max(A(Y(fr1))) and max(A(Y(fr2))) of the liquid level fluctuation signals fr1 and fr2 within this frequency range. Based on this, the notch center frequencies N_f1 and N_f2 of the first and second notch filters are determined.

[0132] N_f2 satisfies the following conditions:

[0133] fr1={f1-ε≤fr1≤f1+ε}

[0134] fr2={f2-ε≤fr2≤f3+ε}

[0135] A(Y(N_f1))=max(A(Y(fr1)))

[0136] A(Y(N_f2))=max(A(Y(fr2)))

[0137] The notch attenuation factor σ should dynamically change according to the actual intensity of surface wave fluctuations under real operating conditions. When the surface wave is more intense, the notch attenuation factor σ should be smaller to effectively suppress it quickly. When the surface wave is relatively stable, the notch attenuation factor σ should be larger to reduce the impact of phase lag on the system. Analysis of the frequency domain characteristics of the notch filter shows that the notch attenuation factor is largest at the center frequency, where the signal component is attenuated to σ times its original value. The notch attenuation factor σ is set as follows:

[0138]

[0139]

[0140] Where Af A1 represents the target amplitude of the signal at the center frequency of the notch after filtering; A2 represents the first-order surface wave amplitude of the liquid level fluctuation signal identified online by Zoom-FFT; and A3 represents the second-order surface wave amplitude of the liquid level fluctuation signal identified online by Zoom-FFT.

[0141] (5) Parameters of the first and second notch filters

[0142] Using the notch center frequencies N_f1 and N_f2, and notch attenuation factors σ1 and σ2 of the first and second notch filters determined in step 4, the parameters of the first and second notch filters are set, including: setting the notch center frequency N_f, the notch attenuation factor σ, and the notch frequency range wb. The notch frequency range wb needs to be fixed empirically: generally, the range of notch frequency range wb should be 0.05 ≤ wb ≤ 0.4. If wb is too large, it will affect the normal feedback control of other liquid level fluctuation frequency bands; if wb is too small, the robustness of the notch filter will be poor.

[0143] The parameters of the first notch filter are as follows: 1) Notch center frequency N_f1; 2) Notch attenuation factor σ1, i.e., the attenuation factor σ1 of the center frequency; 3) Notch frequency range wb1. The parameters of the second notch filter are as follows: 1) Notch center frequency N_f2; 2) Notch attenuation factor σ2; 3) Notch frequency range wb2.

[0144] The general structures of the first and second notch filters are as follows (i.e., the basic transfer function of the notch filter):

[0145]

[0146] Where s is the Laplace transform operator; ω is the notch center frequency; m and n are notch coefficients, which are adjustable parameters depending on the notch center frequency, notch attenuation factor, and notch frequency range.

[0147] First notch filter structure and parameters:

[0148]

[0149] ω1=2π*N_f1,

[0150]

[0151] m1 = σ1 * n1,

[0152] Second notch filter structure and parameters:

[0153]

[0154] ω2=2π*N_f2,

[0155]

[0156] m2=σ2*n2,

[0157] (6) The rationality of the parameter settings of the first and second notch filters

[0158] The open-loop transfer function of the original system is G(s), where s is the Laplace differential operator. After obtaining the first and second notch filters in step 5, they are fed into the system. At this time, the open-loop transfer function of the system is Gn(s) = G(s) * N_F1(s) * N_F2(s).

[0159] The phase lag caused by the first-order notch filter to the system is:

[0160]

[0161] The phase lag caused by using a second-order notch filter in the system is

[0162]

[0163] If the phase margin differs by more than 10 0 It is believed that notch filters have a significant impact on the stability of the liquid level control system. Therefore, a set of default parameters is used for the notch attenuation factor and notch width of the first-order and second-order notch filters, as follows:

[0164]

[0165] Where ω0 is the amplitude crossover frequency of the original liquid level control system, ω f The amplitude crossover frequency after using a notch filter is given, but since the amplitude effect of the notch filter is relatively small in other frequency bands, ω0≈ω f Then we have β = -∠N_F1(ω0) -∠N_F2(ω0). Since β > 10°, we set the notch attenuation factors σ1 = 0.4, σ2 = 0.4, and the notch widths wb1 = 0.26, wb2 = 0.26, but without changing the notch center frequency, we recalculate the parameters of the first and second notch filters through step 5.

[0166] (7) Enabling and disabling conditions of the first and second notch filters

[0167] Step 3 is used to determine the surface wave component in the liquid level fluctuation signal in the frequency domain, that is, the surface wave amplitude A(Y(N_f2)) of the first and second order surface waves determined by Zoom-FFT. By comparing it with the set threshold δ, the activation and deactivation of the notch filter are determined.

[0168] Enabling and disabling the first notch filter:

[0169]

[0170] Enabling and disabling the second notch filter:

[0171]

[0172] When the amplitude of the surface wave exceeds a certain limit, the notch filter is activated; when the amplitude of the surface wave is suppressed, the notch filter is deactivated. This reduces the impact of the notch filter's phase hysteresis on normal liquid level feedback. However, the activation and deactivation thresholds are not equal, i.e., δ1 ≠ δ2. This is a dead-zone limitation set to avoid frequent activation and deactivation of the notch filter.

[0173] Example

[0174] Build a simulation model, such as Figure 4 As shown:

[0175] a) The liquid level setting is 64mm.

[0176] b) The expression for the PI controller is:

[0177]

[0178] c) The expression for the liquid level actuator is:

[0179]

[0180] d) Flow coefficient 0.35.

[0181] e) Time lag of 0.24s.

[0182] f) Crystallizer process objects:

[0183]

[0184] g) First-order surface wave model

[0185]

[0186] h) Second-order surface wave model

[0187]

[0188] i) The width of the crystallizer is L = 1.5m.

[0189] Surface wave filtration process

[0190] 1) Calculation of the theoretical frequency of surface waves

[0191] The theoretical formula for surface wave frequency is as follows:

[0192]

[0193] Theoretical frequency calculation of first-order surface waves (c = 1; L = 1.5m)

[0194] f1 = 0.721 Hz

[0195] Theoretical frequency calculation of second-order surface waves (c = 2; L = 1.5m)

[0196] f2 = 1.02 Hz

[0197] 2) Data preprocessing

[0198] The liquid level fluctuation signal is calculated as follows: Liquid level measurement signal = Liquid level measurement signal - Average value of liquid level measurement signals. Figure 5 As shown.

[0199] 3) Zoom-FFT

[0200] To improve the real-time performance of the system's surface wave detection, a sliding window was used to capture data from the aforementioned liquid level fluctuation signal. The window size was 204.8 s, and the sliding step size was 10 s. Zoom-FFT was then performed on the data within the window, and the results are as follows. Figure 6 As shown, Zoom-FFT significantly improves the frequency resolution near the surface wave frequency compared to ordinary FFT.

[0201] 4) Determine the notch center frequency and notch attenuation factor.

[0202] By using a certain frequency range fr1 and fr2 of the theoretical surface wave frequencies f1 and f2, a peak search is performed on the Zoom-FFT result Y(f) of the liquid level fluctuation signal to determine the surface wave frequency offset ∈ = 0.05. Within this frequency range, the maximum values ​​of the Zoom-FFT amplitude spectrum of the liquid level fluctuation signal correspond to the frequencies N_f1 and N_f2.

[0203] A(Y(N_f1))=max(A(Y(fr1)))

[0204] A(Y(N_f2))=max(A(Y(fr2)))

[0205] The notch center frequency of the first notch filter is determined to be N_f1 = 0.721 Hz; the notch center frequency of the second notch filter is determined to be N_f2 = 1.019 Hz.

[0206] The amplitude of the signal at the center frequency of the notch filter should be less than 0.1. Let A f =0.1,

[0207] Set the target amplitude A of the notch center frequency after filtering f=0.1, the recognition results of Zoom-FFT are A1=0.2007, A2=0.2736, so σ1=0.4982, σ2=0.3655.

[0208] 5) Determine the notch filter structure and parameters

[0209] For the first notch filter, based on the notch center frequency N_f1 = 0.721Hz, the notch attenuation factor σ1 = 0.4982, and the notch frequency range wb1 = 0.1Hz, the structural parameters m1 = 0.0560, ω1 = 3.9235, and n1 = 0.1125 can be calculated. Therefore, the structural parameters of the first notch filter are as follows:

[0210]

[0211] For the second notch filter, based on the notch center frequency N_f2 = 1.019 Hz, the notch attenuation factor σ2 = 0.3655, and the notch frequency range wb2 = 0.1 Hz, the structural parameters m2 = 0.0241, ω2 = 5.5487, and n2 = 0.0660 can be calculated. Therefore, the structural parameters of the second notch filter are as follows:

[0212]

[0213] 6) The rationality of the parameter settings for the first and second notch filters

[0214] Open-loop transfer function of the original system

[0215]

[0216] With an amplitude crossover frequency ω0 = 0.868 rad / s and a phase margin of γ0 = 53.7°, after using the first and second notch filters, the amplitude crossover frequency ω f =0.868 rad / s, phase margin γ0 = 52°; therefore β = 53.7° - 52° = 1.7° < 10°. The parameters of the first and second notch filters are set within a reasonable range.

[0217] 7) Determine whether the notch filter is enabled or disabled.

[0218] The activation threshold δ1 = 0.5 mm and the deactivation threshold δ2 = 0.2 mm. The Zoom-FFT amplitude spectrum A(Y(N_f1)) of the liquid level fluctuation signal near the theoretical frequency of the surface wave and the thresholds δ1 and δ2 are used to determine whether the notch filter is turned on or off.

[0219] Enabling and disabling the first notch filter:

[0220]

[0221] Enabling and disabling the second notch filter:

[0222]

[0223] 7) Simulation Results

[0224] according to Figure 7 Simulation results from the liquid level feedback signal and liquid level measurement signal output by the simulation model show that at 2 minutes, the addition of first-order and second-order surface wave external signals leads to an interaction between the liquid level control action and the surface waves, resulting in increased liquid level fluctuations. At 10 minutes, activating the first and second notch filters effectively filters out the surface wave component in the liquid level feedback signal, reducing the liquid level fluctuations in the crystallizer caused by the interaction between the control action and the surface waves. This technology proposes a crystallizer liquid level control and method with a surface wave filtering structure, which can effectively remove the surface wave component from the original measured liquid level signal in a timely manner, prevent the interaction between liquid level control and surface waves, and successfully achieve fully automatic online adaptive control of surface waves.

Claims

1. A crystallizer level control method with surface wave filtering structure, characterized in that: a surface wave monitoring and filtering structure based on a level measurement signal is arranged in a feedback loop of a crystallizer level feedback control; periodic real-time monitoring of a level fluctuation signal is established through the arranged surface wave monitoring and filtering structure; when the monitoring result is greater than or equal to a set threshold, the surface wave monitoring and filtering structure based on the level measurement signal is started to form a feedback based on a level measurement signal filtered by surface waves; otherwise, a direct feedback based on the level measurement signal is formed; the surface wave monitoring and filtering structure is composed of a surface wave identification unit and a wave trap filtering unit; the surface wave identification unit is used to receive a level measurement signal and a crystallizer width detection signal in real time, and determine an actual wave trap center frequency, a wave trap depth, a wave trap bandwidth and a fluctuation signal amplitude corresponding to the actual wave trap center frequency according to the two signals; the wave trap filtering unit is used to receive the fluctuation signal amplitude corresponding to the actual wave trap center frequency, and determine whether to start wave trap filtering according to a comparison result of the fluctuation signal amplitude and a set threshold; in the above, the actual wave trap center frequency is determined according to the level measurement signal and the crystallizer width detection signal, and the specific steps include the following: S1: determining a theoretical frequency of surface waves according to a crystallizer width and an order of the wave trap; S2: performing zero mean processing on the level measurement signal to obtain a level fluctuation signal; S3: performing time-frequency conversion on the level fluctuation signal, and determining the actual wave trap center frequency in combination with the theoretical frequency of surface waves; the wave trap depth and the wave trap bandwidth are determined according to the following specific steps: SS1: determining a phase margin of a current system with the wave trap in real time; SS2: performing difference calculation on a theoretical phase margin of the system and the phase margin of the current system with the wave trap, when the calculation result is greater than a set value, entering step SS3, otherwise entering step SS4; SS3: determining that the wave trap depth is 0.4 and the wave trap bandwidth is 0.26; SS4: determining the wave trap depth according to an actual surface wave amplitude, and determining the wave trap bandwidth according to a common constraint of normal level feedback and robustness of the wave trap. 2.The crystallizer level control method with surface wave filtering structure according to claim 1, characterized in that: the theoretical frequency of surface waves is determined according to the following formula: in the formula, f: the theoretical frequency of surface waves, unit: Hz; c: the order of the wave trap; L: the crystallizer width, unit: m. 3.The crystallizer level control method with surface wave filtering structure according to claim 1, characterized in that: the time-frequency conversion on the level fluctuation signal is completed through frequency spectrum refinement analysis based on a frequency shift method; the determination of the actual wave trap center frequency in combination with the theoretical frequency of surface waves is completed by searching for a peak in a frequency range set near the theoretical frequency of surface waves to obtain a maximum value of an amplitude spectrum of the level fluctuation signal after time-frequency conversion in the frequency range, and the actual wave trap center frequency is determined according to the maximum value. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ g: acceleration due to gravity, unit: m / s 2 ; ​ ​ ​ ​ 4. The crystallizer liquid level control method with surface wave filtering structure according to claim 1, characterized in that: the notch depth is determined according to the actual surface wave amplitude, specifically: setting the target amplitude Af of the filtered notch center frequency, determining the surface wave amplitude A in real time, determining the notch depth according to the ratio of Af and A.

5. The crystallizer liquid level control method with surface wave filtering structure according to claim 1, characterized in that: the notch bandwidth is in the range of [0.05, 0.4].

6. The crystallizer liquid level control method with surface wave filtering structure according to claim 1, characterized in that: the notch filter unit includes a first notch filter and a second notch filter connected in series in the feedback loop.

7. The crystallizer liquid level control method with surface wave filtering structure according to claim 6, characterized in that: the first notch filter and the second notch filter are a first-order notch filter and a second-order notch filter, respectively.

8. A crystallizer liquid surface wave filtering structure, characterized in that: the surface wave filtering structure is arranged in the feedback loop of the crystallizer liquid level feedback control system, and the surface wave periodicity is monitored in real time based on the liquid level measurement signal according to the surface wave filtering structure; the monitoring result is used to control the formation of the liquid level measurement signal feedback after filtering the surface wave when the monitoring value exceeds the set threshold, or the direct feedback based on the liquid level measurement signal when the monitoring value does not exceed the set threshold; the surface wave filtering structure is composed of a surface wave identification unit and a notch filter unit, the surface wave identification unit is used to receive the liquid level measurement signal and the crystallizer width detection signal in real time, and determine the actual notch center frequency, the notch depth, the notch bandwidth and the fluctuation signal amplitude corresponding to the actual notch center frequency according to the two signals; the notch filter unit is used to receive the fluctuation signal amplitude corresponding to the actual notch center frequency, and determine whether to start the notch filter according to the comparison result of the fluctuation signal amplitude and the set threshold; the actual notch center frequency is determined according to the liquid level measurement signal and the crystallizer width detection signal, specifically including the following steps: S1: determining the theoretical frequency of the surface wave according to the crystallizer width and the order of the notch filter; S2: performing zero mean processing on the liquid level measurement signal to obtain the liquid level fluctuation signal; S3: completing the determination of the actual notch center frequency by performing time-frequency conversion on the liquid level fluctuation signal and combining the theoretical frequency of the surface wave; the notch depth and the notch bandwidth are determined according to the actual surface wave amplitude, and the notch bandwidth is determined according to the common constraints of the normal liquid level feedback and the robustness of the notch filter.

9. The crystallizer liquid surface wave filtering structure according to claim 8, characterized in that: ​ ​ ​ ​ The theoretical frequency of the surface wave is determined according to the following formula: In the above formula, f: the theoretical frequency of the surface wave, unit: Hz; c: the order of the notch filter; g: acceleration due to gravity, unit: m / s 2 ; L: the width of the crystallizer, unit: m.

10. The crystallizer liquid surface wave filtering structure according to claim 8, characterized in that: the time-frequency conversion of the liquid level fluctuation signal is completed through frequency spectrum refinement analysis based on the frequency shift method, and the actual notch center frequency is determined according to the theoretical frequency of the surface wave, specifically: the maximum value of the amplitude spectrum of the liquid level fluctuation signal after time-frequency conversion in the frequency range near the theoretical frequency of the surface wave is obtained through peak searching, and the actual notch center frequency is determined according to the maximum value.

11. The crystallizer liquid surface wave filtering structure according to claim 8, characterized in that: the notch depth is determined according to the actual surface wave amplitude, specifically: a target amplitude Af of the filtered notch center frequency is set, the surface wave amplitude A is determined in real time, and the notch depth is determined according to the ratio of Af to A.

12. The crystallizer liquid surface wave filtering structure according to claim 8, characterized in that: the notch bandwidth is in the range of [0.05, 0.4].

13. The crystallizer liquid surface wave filtering structure according to claim 8, characterized in that: the notch filter filtering unit comprises a first notch filter and a second notch filter connected in series in a feedback loop.

14. The crystallizer liquid surface wave filtering structure according to claim 13, characterized in that: the first notch filter and the second notch filter are a first-order notch filter and a second-order notch filter, respectively.

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