Dynamic liquid level detection system and method for stirred tanks

Abstract

The application discloses a dynamic liquid level detection system and method based on a stirred tank, and belongs to the field of liquid level detection. The system comprises a differential pressure sensor module, a rotating speed acquisition module and a signal processing unit. The signal processing unit comprises a vortex dynamic compensation module, an adaptive filtering module and a delay prediction compensation module connected in series. The application collects the differential pressure signal of the liquid column in the tank and converts it into an apparent liquid level value, and simultaneously collects the rotating speed signal of the stirring paddle. The liquid level deviation caused by the vortex at the tank wall is calculated according to the rotating speed signal, and a first-order recursive tracking output dynamic compensation is used to eliminate the vortex liquid level deviation. The low-pass filter cutoff frequency is adaptively determined according to the rotating speed signal to suppress the stirring fluctuation noise. The change rate of the filtered liquid level value and the group delay are used for forward prediction correction to reduce the filtering delay. The application realizes dynamic cooperation of each link by using the rotating speed signal as a link, and improves the accuracy and response speed of the liquid level measurement under the stirring condition.

Description

Technical Field

[0001] This invention relates to the field of liquid level detection technology, and more specifically to a dynamic liquid level detection system and method based on a stirred tank. Background Technology

[0002] Agitated reactors are core equipment for material mixing, dissolving, and reaction. Accurate measurement of the liquid level within the reactor is crucial for the safe operation and precise control of the production process. Common differential pressure level measurement technology indirectly estimates the liquid level by measuring the pressure difference between the bottom and top of the liquid column. However, during reactor operation, the rotation of the agitator generates forced eddies in the liquid, causing the liquid level near the reactor wall to rise due to centrifugal force, creating a vortex depression effect. Since the differential pressure sensor's pressure tap is typically located at the reactor wall, the eddying caused by the agitation vortex causes the differential pressure level gauge's measurement to systematically deviate from the true average liquid level within the reactor. Furthermore, this deviation dynamically changes with the agitator rotation speed. Existing differential pressure level detection solutions generally lack the ability to dynamically compensate for the vortex effect in real time, resulting in significant systematic errors in level measurement under agitation conditions.

[0003] Furthermore, the periodic disturbances to the liquid surface caused by the rotating impeller will superimpose fluctuation noise into the liquid level signal. The frequency characteristics of this noise are closely related to the impeller speed. Existing liquid level signal filtering solutions typically use low-pass filters with fixed parameters. However, filters with fixed cutoff frequencies struggle to simultaneously achieve both noise suppression and signal response speed under variable impeller speed conditions. At low speeds, the cutoff frequency may be too high relative to the stirring fluctuation frequency, leading to insufficient noise suppression. At high speeds, the cutoff frequency may be too low, introducing excessive signal delay. Simultaneously, low-pass filters inevitably introduce response delay during noise suppression, causing the filtered liquid level measurement to lag behind the actual liquid level. This delay can adversely affect the performance of the closed-loop liquid level control system during rapid level changes in feeding or discharging conditions. Existing solutions generally lack effective compensation measures for this filtering delay.

[0004] Therefore, designing a dynamic liquid level detection system and method to solve the above-mentioned technical problems is of great significance. Summary of the Invention

[0005] To address the problems existing in the background art, the present invention provides a dynamic liquid level detection method based on a stirred tank, comprising the following steps:

[0006] S1. Differential pressure level acquisition: The differential pressure signal of the liquid column in the vessel is acquired by a differential pressure sensor installed on the stirred vessel, and the differential pressure signal is converted into an apparent liquid level value;

[0007] S2, Rotation speed acquisition: The rotation speed signal of the agitator is acquired in real time by a rotation speed sensor installed at the drive end of the agitator.

[0008] S3, vortex depression dynamic compensation: The steady-state offset of the liquid level at the vessel wall caused by the stirring vortex is calculated based on the rotation speed signal as the steady-state compensation target value. The dynamic compensation amount is gradually approached to the steady-state compensation target value through a first-order recursive tracking loop. At the current sampling time, the dynamic compensation amount is subtracted from the apparent liquid level value to obtain the compensated liquid level value.

[0009] S4. Adaptive filtering: Determine the cutoff frequency of the low-pass filter based on the rotation speed signal, and adaptively adjust the cutoff frequency with the stirring speed to filter the compensated liquid level value to obtain the filtered liquid level value.

[0010] S5. Filter delay prediction compensation: Calculate the group delay of the low-pass filter based on the cutoff frequency, and use the rate of change of the filtered liquid level value and the group delay to perform forward prediction correction to obtain the final liquid level measurement value.

[0011] Furthermore, step S1 includes the following sub-steps:

[0012] S11. Pressure transmitters are installed at the bottom and top pressure measuring points of the stirred tank to collect the differential pressure value between the bottom and top pressure measuring points. This sub-step obtains the liquid column differential pressure signal, excluding the influence of the gas phase pressure inside the vessel;

[0013] S12, Based on the differential pressure value Based on the density of the material inside the vessel, the apparent liquid level value is calculated using the following formula: ;

[0014] in, The apparent liquid level value (m); The differential pressure value (Pa); Density of material inside the vessel (kg / m³) 3 ); Acceleration due to gravity (m / s²) 2 );

[0015] The apparent liquid level value corresponding to the height of the liquid column at the vessel wall is obtained.

[0016] Furthermore, step S3 includes the following sub-steps:

[0017] S31. Obtain the current rotation speed of the agitator based on the rotation speed signal. Calculate the angular velocity of the agitator using the following formula: ;

[0018] in, Angular velocity of the agitator (rad / s); The stirring speed is 60 r / min; 60 is the conversion factor between minutes and seconds.

[0019] Convert the rotational speed signal into angular velocity;

[0020] S32, based on the angular velocity of the stirring paddle and the inner radius of the stirring vessel The steady-state compensation target value is calculated using the following formula: ;

[0021] in, The steady-state compensation target value (m); The vortex compensation coefficient is determined by calibration, and the calibration process covers the influence of internal structural components on the vortex morphology. The angular velocity of the impeller is (rad / s). The inner radius of the stirred tank (m); Acceleration due to gravity (m / s²) 2 );

[0022] Calculate the steady-state offset of the liquid level at the vessel wall corresponding to the current rotational speed;

[0023] S33. The dynamic compensation amount is updated in each sampling period using the following first-order recursive formula, so that it gradually approaches the steady-state compensation target value: ;

[0024] in, For the first The dynamic compensation amount (m) at each sampling time; For the first The dynamic compensation amount (m) at each sampling time; For the first The steady-state compensation target value (m) calculated by step S32 at each sampling time; The tracking coefficient; The calculation formula is: ;

[0025] in, The sampling period is (s). The vortex response time constant (s) is determined by calibration.

[0026] S34. At the current sampling time, subtract the dynamic compensation amount from the apparent liquid level value according to the following formula to obtain the compensated liquid level value: ;

[0027] in, The compensated liquid level value (m); The apparent liquid level value (m); For the first The dynamic compensation amount (m) at each sampling time.

[0028] Furthermore, step S4 includes the following sub-steps:

[0029] S41. Obtain the current speed of the agitator based on the speed signal. The impeller rotation frequency is calculated using the following formula, and the cutoff frequency of the low-pass filter is determined: ;

[0030] in, The frequency of the stirring paddle (Hz); The stirring speed is 60 r / min; 60 is the conversion factor between minutes and seconds. ;

[0031] in, The cutoff frequency (Hz); This is a frequency proportionality coefficient, with a value less than 1, ensuring that the cutoff frequency is always lower than the rotational frequency of the stirring paddle. The impeller rotational frequency (Hz); the cutoff frequency is defined as follows: when the impeller rotational speed is lower than the rotational speed threshold determined by the characteristics of the stirring fluctuation noise. Take a preset fixed value;

[0032] S42, at the cutoff frequency A second-order Butterworth low-pass filter is constructed, and its discretization into a difference equation is performed using a bilinear transform. This discretization is then applied to the compensated liquid level value to obtain the filtered liquid level value. When the cutoff frequency... When changes occur, the filter coefficients are recalculated and a weighted smooth transition is applied to the old and new coefficients.

[0033] It can suppress stirring noise and retain true liquid level change information at different speeds.

[0034] Furthermore, step S5 includes the following sub-steps:

[0035] S51, according to the cutoff frequency The group delay of the low-pass filter in the passband is calculated using the following formula: ;

[0036] in, The group delay (s); The cutoff frequency (Hz); when the cutoff frequency The group delay varies with rotational speed. Synchronized updates;

[0037] Obtain the response delay under the current filtering conditions;

[0038] S52. Using the most recent sampled values ​​of the filtered liquid level, calculate the rate of change according to the following formula: ;

[0039] in, The estimated rate of change (m / s); For the first The filtered liquid level value (m) at each sampling time; For the first The filtered liquid level value (m) at each sampling time; The number of difference interval points, taken as a positive integer; The sampling period is (s).

[0040] Obtain the trend of the filtered liquid level value;

[0041] S53. Perform forward prediction correction on the filtered liquid level value according to the following formula to obtain the final liquid level measurement value: ;

[0042] in, The final liquid level measurement value (m); For the first The filtered liquid level value (m) at each sampling time; The group delay (s); The estimated rate of change (m / s); when and When the absolute value of the product exceeds the preset maximum correction amount, the preset maximum correction amount is taken as the actual correction amount, and its sign is the same as the preset maximum correction amount. Consistent; this sub-step reduces the response delay introduced by the low-pass filter to obtain the final liquid level measurement value.

[0043] The present invention also provides a dynamic liquid level detection system based on a stirred tank, comprising:

[0044] The differential pressure sensor module includes two pressure transmitters respectively set at the bottom and top pressure measuring points of the stirred tank, which are used to collect the differential pressure signal of the liquid column in the tank and output the apparent liquid level value.

[0045] The rotation speed acquisition module is located at the drive end of the agitator and is used to acquire the rotation speed signal of the agitator in real time.

[0046] The signal processing unit, connected to the differential pressure sensor module and the rotation speed acquisition module respectively, includes a vortex dynamic compensation module, an adaptive filtering module, and a delay prediction compensation module connected in series. The vortex dynamic compensation module calculates the steady-state offset of the liquid level at the vessel wall caused by the stirring vortex based on the rotation speed signal and outputs the dynamic compensation amount through a first-order recursive tracking loop to compensate the apparent liquid level value and output the compensated liquid level value. The adaptive filtering module determines the cutoff frequency based on the rotation speed signal and performs low-pass filtering on the compensated liquid level value before outputting the filtered liquid level value. The delay prediction compensation module calculates the group delay based on the cutoff frequency and performs forward prediction correction using the rate of change of the filtered liquid level value before outputting the final liquid level measurement value.

[0047] In a preferred embodiment, the input terminal of the vortex dynamic compensation module is connected to the differential pressure sensor module and the speed acquisition module, respectively, and its output terminal is connected to the adaptive filtering module; the adaptive filtering module is also connected to the speed acquisition module to receive the speed signal to determine the cutoff frequency, and its output terminal is connected to the delay prediction compensation module; the speed signal serves as the input parameter for both the vortex dynamic compensation module and the adaptive filtering module, forming a dual-channel signal processing architecture with the speed signal as the core.

[0048] The beneficial effects achieved by this invention are as follows:

[0049] This invention proposes a dynamic liquid level detection method based on a stirred tank. By introducing a dynamic compensation mechanism for vortex depressions on differential pressure liquid level acquisition, it effectively eliminates the systematic offset of the liquid level measurement value at the tank wall caused by the vortex effect generated by the rotating impeller. This compensation mechanism calculates the steady-state offset of the liquid level at the tank wall caused by the vortex in real time based on the impeller rotation speed signal. A first-order recursive tracking method is used to make the dynamic compensation amount gradually approach the steady-state compensation target value in an exponential response form each cycle, thus matching the rate of change of the compensation amount with the actual establishment process of the liquid vortex morphology within the tank. Compared to schemes without vortex compensation, this invention reduces the steady-state liquid level measurement error under stirring conditions to a level far smaller than the vortex offset. Compared to schemes that directly use the steady-state compensation target value as the compensation amount, the first-order recursive tracking mechanism of this invention can effectively avoid overcompensation or undercompensation when the impeller rotation speed undergoes a step change, significantly reducing the maximum transient measurement error during the sudden change in rotation speed.

[0050] This invention employs adaptive filtering technology to suppress noise in the compensated liquid level signal. The cutoff frequency of the low-pass filter is adaptively determined based on the agitator rotation speed signal, ensuring that the cutoff frequency maintains a predetermined proportional relationship with the agitator rotation frequency. When the agitator rotation speed increases, the agitation fluctuation frequency increases, and the cutoff frequency increases accordingly to reduce unnecessary filtering delay while maintaining noise suppression effectiveness. Conversely, when the agitator rotation speed decreases, the agitation fluctuation frequency decreases, and the cutoff frequency decreases accordingly to maintain effective suppression of low-frequency fluctuation noise. Compared to traditional low-pass filtering schemes using a fixed cutoff frequency, this invention's adaptive filtering scheme maintains stable and consistent noise suppression performance under different agitator rotation speeds, especially avoiding the insufficient noise suppression problem caused by fixed cutoff frequency filters having a cutoff frequency that is too high relative to the agitator rotation frequency at low speeds. Furthermore, when the cutoff frequency changes, this invention performs a weighted smooth transition on the filter coefficients, eliminating output transient shocks caused by abrupt coefficient changes and ensuring the continuity and stability of the filtered output.

[0051] This invention further introduces a filter delay prediction compensation stage, utilizing the changing trend of the filtered liquid level value and the group delay parameter of the low-pass filter for forward prediction correction, effectively reducing the response delay inevitably introduced by the low-pass filter during signal processing. This stage calculates the group delay in real time based on the current cutoff frequency and uses the finite differential rate of change of the filtered liquid level value for linear extrapolation, shifting the filtered output signal forward on the time axis to compensate for the lag. Compared to schemes that directly output the filtering result without delay compensation, this invention can significantly reduce tracking errors under conditions of uniform liquid level change and significantly improve tracking performance during transition phases with abrupt changes in the liquid level change rate. Simultaneously, this invention sets a safety limiting mechanism for the forward prediction correction amount, limiting the correction amount to a preset range when there are drastic fluctuations in liquid level or signal anomalies, ensuring the stability and safety of the system output while retaining the delay compensation function.

[0052] This invention uses the impeller speed signal as the core link, organically connecting three signal processing stages: vortex dynamic compensation, adaptive filtering, and delay prediction compensation. This forms a dual-channel signal processing architecture driven by the speed signal, ensuring that the entire signal processing chain's operating state remains dynamically synchronized with the actual operating conditions of the stirred tank. In this architecture, the speed signal simultaneously drives the vortex compensation channel to complete liquid level offset correction and the filtering channel to adaptively update noise suppression parameters. The parameter correlation between each stage ensures that the system maintains excellent measurement accuracy, noise suppression capability, and dynamic response speed across a wide speed range and various operating conditions. Attached Figure Description

[0053] Figure 1The graphs show the liquid level measurement response of Example 1, Comparative Example 1, and Comparative Example 2 when the rotation speed increases from 60 r / min to 120 r / min. (a) is a graph showing the change of the stirring paddle speed over time, (b) is a graph showing the change of the actual liquid level and the liquid level measurement values ​​of the three methods over time, and (c) is a graph showing the change of the liquid level measurement error of the three methods over time.

[0054] Figure 2 This is a grouped bar chart comparing the root mean square noise values ​​of Examples 1, 2, and 3 with Comparative Example 3 at three rotational speeds of 60 r / min, 90 r / min, and 120 r / min.

[0055] Figure 3 This is a comparison chart of the liquid level tracking performance of Example 1 and Comparative Example 4 under the condition of constant speed of 120 r / min during uniform feeding. (a) is a graph showing the change of the actual liquid level and the liquid level measurement values ​​of the two methods over time, and (b) is a graph showing the change of the liquid level tracking error of the two methods over time.

[0056] Figure 4 The charts show the comprehensive performance indicators of Examples 1, 2, and 3 compared with Comparative Examples 1, 2, 3, and 4. Among them, (a) is a bar chart comparing steady-state measurement accuracy, (b) is a bar chart comparing maximum transient error of speed step, (c) is a bar chart comparing root mean square noise value, and (d) is a bar chart comparing uniform feed tracking error.

[0057] Figure 5 This is a flowchart of the dynamic liquid level detection method based on a stirred tank according to the present invention. Detailed Implementation

[0058] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. In addition, the forms of the various structures described in the following embodiments are merely illustrative. The present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The following specific embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0060] During the operation of a stirred tank, the vortex effect generated by the rotating impeller causes liquid level rise at the tank wall, leading to deviations from the actual liquid level readings of traditional differential pressure level gauges. Simultaneously, the periodic disturbances of the impeller add fluctuation noise to the liquid surface; while low-pass filtering can suppress this noise, it introduces response delay. This invention proposes a complete dynamic compensation and signal processing scheme to address these three error sources: vortex dip offset, stirring fluctuation noise, and filtering delay.

[0061] The dynamic liquid level detection system based on a stirred tank of the present invention includes a differential pressure sensor module, a rotation speed acquisition module, a signal processing unit, and an output interface module.

[0062] The differential pressure sensor module includes two pressure transmitters, one at the bottom and one at the top of the stirred tank. The bottom pressure point is typically located at the pressure tap interface on the bottom head or lower part of the tank body, and its position should be below the lowest operating liquid level inside the stirred tank. The top pressure point is located at the pressure tap interface on the upper part of the tank body or the top head, and its position should be above the highest operating liquid level inside the stirred tank. The two pressure transmitters measure the absolute or gauge pressure at the bottom and top pressure points, respectively; the difference between these measurements is the differential pressure signal of the liquid column inside the tank. Using a two-point differential pressure measurement method (top and bottom) eliminates common-mode interference from pressure fluctuations in the gas phase space inside the tank on the liquid level measurement, ensuring that the differential pressure signal only reflects the static pressure difference corresponding to the liquid column height, thus providing an accurate physical quantity input for subsequent liquid level calculations. The differential pressure sensor module converts the acquired differential pressure signal into a standard electrical signal output.

[0063] A speed acquisition module is installed at the drive end of the agitator to collect the agitator speed signal in real time. The drive end typically refers to the connection point between the agitator shaft and the reducer or motor output shaft. The speed acquisition module can use a magnetoelectric speed sensor, Hall effect speed sensor, or encoder to convert the mechanical rotation signal of the agitator into a pulse signal or analog signal output. By placing the speed acquisition module at the agitator drive end, the system can directly obtain the actual operating speed of the agitator, rather than relying on the inverter's setpoint or the motor's rated parameters, thus avoiding speed information distortion caused by factors such as reducer transmission ratio deviation and slip. The speed signal is a key input parameter for subsequent eddy compensation and adaptive filtering stages.

[0064] The signal processing unit is connected to the differential pressure sensor module and the speed acquisition module respectively. The signal processing unit can be implemented by hardware platforms such as embedded microcontrollers, digital signal processors, or industrial programmable logic controllers. Internally, it includes a vortex dynamic compensation module, an adaptive filtering module, and a delay prediction compensation module connected in series.

[0065] The input terminals of the vortex dynamic compensation module are connected to the differential pressure sensor module and the speed acquisition module, respectively, and its output terminal is connected to the adaptive filtering module. The vortex dynamic compensation module receives the apparent liquid level value output from the differential pressure sensor module and the speed signal output from the speed acquisition module. Based on the speed signal, it calculates the steady-state offset of the liquid level at the vessel wall caused by the stirring vortex, and outputs a dynamic compensation value through a first-order recursive tracking loop. After compensating the apparent liquid level value, it outputs the compensated liquid level value. The function of the first-order recursive tracking loop is that when the impeller speed changes abruptly, the vortex shape does not instantly form or disappear, but rather undergoes a transition process related to fluid inertia. The first-order recursive tracking loop simulates this transition process in an exponential response manner, allowing the dynamic compensation value to smoothly track the steady-state compensation target value corresponding to the speed change.

[0066] The adaptive filtering module is also connected to the speed acquisition module to receive the speed signal and determine the cutoff frequency. Its output is connected to the delay prediction and compensation module. The adaptive filtering module determines the cutoff frequency of the low-pass filter based on the speed signal, allowing the cutoff frequency to adaptively adjust with the impeller speed. It then performs low-pass filtering on the compensated liquid level value and outputs the filtered liquid level value. The correlation between the cutoff frequency and the speed signal enables the filter to effectively suppress surface fluctuation noise caused by periodic impeller disturbances under different stirring conditions, while preserving as much accurate liquid level change information as possible.

[0067] The delay prediction compensation module calculates the group delay introduced by the low-pass filter based on the cutoff frequency, and then performs forward prediction correction using the rate of change of the filtered liquid level value before outputting the final liquid level measurement value. The principle of forward prediction correction is: under the condition of slow liquid level change, the expected increment of the liquid level within the delay time period is extrapolated using the current trend of change, thereby shifting the filtered output signal forward on the time axis and reducing the response lag introduced by the low-pass filter.

[0068] The rotational speed signal serves as the input parameter for both the vortex dynamic compensation module and the adaptive filtering module, forming a dual-channel signal processing architecture centered on the rotational speed signal. In this architecture, the rotational speed signal drives the vortex compensation channel to complete liquid level offset correction, while simultaneously driving the filtering channel to adaptively update noise suppression parameters, ensuring that the entire signal processing chain's operating state remains synchronized with the actual operating conditions of the stirred tank.

[0069] The output interface module connects to the signal processing unit to output the final liquid level measurement value in a standard signal format. Standard signal formats can include 420mA current signals, 0.10V voltage signals, RS485 digital communication signals, or HART protocol signals, to adapt to different host systems or distributed control systems. The output interface module allows this system to be easily integrated into existing industrial automation control networks, enabling remote monitoring and closed-loop control of the stirred tank liquid level.

[0070] The dynamic liquid level detection method based on a stirred tank of the present invention is described in the following article. Figure 5 Specifically, it includes the following steps S1 to S5.

[0071] S1 is the differential pressure level acquisition step. A differential pressure sensor installed on the stirred tank acquires the differential pressure signal of the liquid column inside the tank and converts the differential pressure signal into an apparent liquid level value. The basic principle of differential pressure level measurement is based on fluid statics, that is, in a static or quasi-static state, the pressure difference between the bottom and top of the liquid column is equal to the product of the liquid column height, the liquid density, and the acceleration due to gravity. Therefore, the liquid column height can be indirectly obtained by measuring the differential pressure value. The apparent liquid level value referred to here is the liquid level value directly converted from the differential pressure signal. This value will deviate from the true liquid level due to the vortex effect when the agitator is running; subsequent steps will compensate for this deviation.

[0072] S1 specifically includes the following sub-steps S11 and S12.

[0073] S11 is the differential pressure acquisition sub-step. Pressure transmitters are installed at the bottom and top pressure measurement points of the stirred tank to collect the differential pressure value between the bottom and top pressure measurement points. The pressure at the bottom measuring point comprises both the hydrostatic pressure of the liquid column and the gas phase pressure inside the vessel, while the pressure at the top measuring point mainly comprises the gas phase pressure inside the vessel. The difference between the two measuring points eliminates the influence of the gas phase pressure, resulting in a differential pressure value. It only reflects the hydrostatic pressure difference corresponding to the liquid column height between two pressure measuring points. In actual installation, the length of the pressure tapping pipeline should be as appropriate as possible, and air bubbles or deposits should be avoided in the pipeline to ensure the accuracy of the differential pressure signal.

[0074] S12 is the level conversion step. Based on the differential pressure value... Based on the density of the material inside the vessel, the apparent liquid level value is calculated using the following formula.

[0075] ;

[0076] in, The apparent liquid level is in meters. The differential pressure value is expressed in Pa. Density of material inside the vessel (kg / m³) 3 ); Acceleration due to gravity (m / s²) 2 This formula is a direct application of the fundamental equations of fluid statics to an isodense liquid column. When the density of the material inside the vessel is known and relatively stable, the height of the liquid column can be obtained from the differential pressure and density. If the material density varies significantly with temperature or concentration, online density measurements or temperature compensation correction values ​​can be introduced to improve the conversion accuracy, but such corrections are not within the core scope of this invention. The apparent liquid level value obtained in S12... The equivalent value corresponding to the height of the liquid column between pressure measurement points on the vessel wall.

[0077] S2 is the speed acquisition step. The speed sensor installed at the agitator drive end acquires the agitator speed signal in real time. The agitator speed is a key parameter describing the flow field state inside the vessel, directly determining the vortex intensity and liquid surface fluctuation frequency. In each sampling cycle, the speed sensor outputs the current agitator speed value. This value is expressed in revolutions per minute (RPM). The sampling frequency of the speed signal should be consistent with or an integer multiple of the sampling frequency of the differential pressure signal, so as to synchronously acquire the differential pressure and speed signals at the same sampling time.

[0078] S3 is the dynamic compensation step for vortex depression. When the agitator rotates, the liquid inside the vessel is driven to rotate. Under the action of centrifugal force, the liquid level near the center of the agitator shaft drops while the liquid level near the vessel wall rises, forming a concave vortex. The pressure tap of the differential pressure sensor is usually located at the vessel wall, so the liquid level value measured by the differential pressure sensor includes the amount of bulging of the liquid surface at the vessel wall caused by the vortex effect. If this bulging is not compensated for, the apparent liquid level value output by the differential pressure sensor will be systematically higher than the true average liquid level. S3 is to dynamically compensate for the liquid level deviation caused by this vortex.

[0079] The steady-state offset of the liquid level at the vessel wall caused by the stirring vortex is calculated based on the rotation speed signal and used as the steady-state compensation target value. The dynamic compensation amount is gradually approached to the steady-state compensation target value through a first-order recursive tracking loop. At the current sampling time, the dynamic compensation amount is subtracted from the apparent liquid level value to obtain the compensated liquid level value.

[0080] S3 specifically includes the following sub-steps S31 to S34.

[0081] S31 is the angular velocity conversion sub-step. The current speed of the agitator is obtained based on the rotational speed signal. Calculate the angular velocity of the agitator using the following formula. ;

[0082] in, Angular velocity of the agitator (rad / s); The stirring speed is (r / min). 1 radian value corresponds to 1 revolution; 60 is the conversion factor between minutes and seconds. Angular velocity. It is a fundamental physical quantity in rotating flow field analysis, and the subsequent calculation of vortex offset requires angular velocity as input.

[0083] S32 is the sub-step for calculating the steady-state compensation target value. Based on the impeller angular velocity... and the inner radius of the stirring vessel The steady-state compensation target value is calculated using the following formula.

[0084] ;

[0085] in, The steady-state compensation target value (m); The vortex compensation coefficient is determined by calibration. Angular velocity of the agitator (rad / s); The inner radius of the stirred tank (m); Acceleration due to gravity (m / s²) 2 ); 4 is a constant factor. The physical background of the above formula originates from the rigid body rotation model in rotating fluid dynamics. Under ideal rigid body rotation conditions, the liquid surface shape is a paraboloid of revolution, and the increase in liquid level at the vessel wall relative to the central liquid surface is: However, in actual stirred tanks, due to the presence of internal components such as baffles, guide tubes, and thermometer sleeves, the liquid does not move entirely according to a rigid body rotation mode, and the vortex pattern will deviate. Therefore, a vortex compensation coefficient is introduced. The specific value of this coefficient was determined through calibration experiments. The calibration process covered the influence of internal structural components on the vortex morphology, specifically by comparing the deviation between the differential pressure level gauge reading and the reference level value at different rotational speeds, and then fitting the coefficient to obtain the result. For stirred tanks equipped with standard baffles, A value typically less than 1 indicates that the baffle suppresses the vortex; for a stirred tank without a baffle, The value may be close to 1 or slightly greater than 1.

[0086] S33 is the sub-step for updating the dynamic compensation amount. The dynamic compensation amount is updated in each sampling period using the following first-order recursive formula, gradually approaching the steady-state compensation target value.

[0087] ;

[0088] in, For the first Dynamic compensation amount (m) at each sampling time; For the first Dynamic compensation amount (m) at each sampling time; For the first The steady-state compensation target value (m) calculated by step S32 at each sampling time; For tracking coefficients. The essence of this first-order recursive formula is a first-order exponentially weighted filter, which is also equivalent to the discretized form of a first-order inertial element. Within each sampling period, the dynamic compensation amount... Take the value from the previous time step Compared with the current steady-state target value The weighted average, with weights determined by the tracking coefficients. Sure.

[0089] Tracking coefficient The calculation formula is:

[0090] ;

[0091] in, The sampling period is (s). Let be the vortex response time constant (s), determined by calibration. This formula is an approximate expression of the equivalent form of a first-order continuous system discretized with a zero-order hold. Vortex response time constant This reflects the characteristic time required for a liquid in a stirred tank to transition from one steady-state vortex pattern to another. This time is related to factors such as the tank size, liquid viscosity, and impeller type, and needs to be determined through calibration experiments. Much larger hour, When the value approaches zero, the rate of change of the dynamic compensation is slow, making it suitable for applications with high liquid viscosity or large vessel size; when When smaller, The dynamic compensation amount approaches 1, allowing it to quickly track changes in rotational speed. By employing a first-order recursive tracking method, overcompensation or undercompensation caused by transient deviations can be avoided during sudden changes in rotational speed, resulting in a smooth transition of the compensation amount over time.

[0092] S34 is the liquid level compensation sub-step. At the current sampling time, the dynamic compensation amount is subtracted from the apparent liquid level value according to the following formula to obtain the compensated liquid level value.

[0093] ;

[0094] in, The compensated liquid level value (m); The apparent liquid level is in meters. For the first The dynamic compensation amount (m) at each sampling time. Because the stirring vortex manifests as a liquid surface bulge at the vessel wall, the apparent liquid level value of the differential pressure sensor is systematically higher. Therefore, this deviation can be eliminated by subtracting the dynamic compensation amount. The compensated liquid level value obtained after processing by S34 is shown below. The static offset error caused by vortex depression has been eliminated, but the periodic fluctuation noise of the liquid surface caused by the rotation of the agitator still exists and requires further filtering.

[0095] S4 is the adaptive filtering step. During rotation, the agitator generates periodic disturbances to the liquid surface, with a fundamental frequency equal to the agitator's rotational frequency, accompanied by higher harmonic components. These periodic fluctuations are superimposed on the actual liquid level signal, constituting measurement noise. To suppress this noise, a low-pass filter is used in this step. However, a low-pass filter with a fixed cutoff frequency struggles to balance noise suppression and signal response speed when the agitator operates at varying speeds. As the rotational speed increases, the agitation fluctuation frequency increases, requiring a corresponding increase in the cutoff frequency to reduce filtering delay; conversely, as the rotational speed decreases, the agitation fluctuation frequency decreases, necessitating a corresponding decrease in the cutoff frequency to maintain suppression of low-frequency fluctuations. Therefore, this step adaptively adjusts the cutoff frequency based on the rotational speed signal, ensuring good filter performance under different rotational speed conditions.

[0096] S4 specifically includes the following sub-steps S41 and S42.

[0097] S41 is the sub-step for determining the cutoff frequency. The current speed of the agitator is obtained based on the speed signal. Calculate the agitator rotation frequency using the following formula, and determine the cutoff frequency of the low-pass filter. ;

[0098] in, The frequency of the stirring paddle (Hz); The impeller rotation speed (r / min); 60 is the conversion factor between minutes and seconds. Impeller rotation frequency. This represents the number of revolutions the agitator completes per second, and is the fundamental frequency of the liquid surface ripples caused by agitation. ;

[0099] in, Cutoff frequency (Hz); This is the frequency scaling factor, and its value is less than 1; The agitator rotation frequency (Hz). Frequency scaling factor. The value of is less than 1, making the cutoff frequency less than 1. Always below the stirring paddle rotation frequency This ensures that the low-pass filter can effectively attenuate the fluctuation noise of the stirring rotation frequency and higher frequency components. The specific value can be selected based on the number of impeller blades, the impeller type, and the required noise suppression level, with a preferred range of 0.3 to 0.8. When the impeller speed is lower than the speed threshold determined by the stirring fluctuation noise characteristics, the cutoff frequency... Use a preset fixed value. The purpose of setting the speed threshold is that when the speed is very low or even 0, the cutoff frequency calculated proportionally will be too small or approach 0, resulting in a narrow passband and extremely slow response speed of the filter. In this case, switching to a preset fixed value can ensure that the filter can still work normally at low speed and when the machine is stopped.

[0100] S42 is the filtering sub-step. (Based on the cutoff frequency...) A second-order Butterworth low-pass filter was constructed and discretized into a difference equation using a bilinear transform. This discretization was then applied to the compensated liquid level value to obtain the filtered liquid level value. The second-order Butterworth low-pass filter exhibits the flattest amplitude-frequency response within its passband, preventing amplitude distortion of the useful signal and demonstrating good applicability in liquid level measurement. The bilinear transform is a method for mapping a continuous-time transfer function to a discrete-time transfer function. The substitution relationship will Domain transfer function transformed into The domain transfer function is then expanded into a difference equation form, facilitating real-time computation on a digital signal processor or microcontroller. After bilinear transformation, the difference equation of a second-order Butterworth low-pass filter contains three coefficients each for the input and output sequences, all of which are determined by the cutoff frequency. and sampling period Confirmed. When the cutoff frequency... When changes occur, the filter coefficients need to be recalculated. To avoid output jumps caused by coefficient switching, a weighted smooth transition is applied to the old and new coefficients, that is, the old coefficients are gradually transitioned to the new coefficients over several sampling periods. This weighted smooth transition method can eliminate transient shocks caused by abrupt coefficient changes and ensure the continuity of the filter output.

[0101] S5 is the filter delay prediction compensation step. While suppressing noise, the low-pass filter inevitably introduces signal delay, meaning the filtered output signal lags behind the input signal in time. In conditions of rapid liquid level changes, such as during feeding or discharging, this delay can cause the measured liquid level to fail to reflect the actual liquid level change trend in a timely manner, adversely affecting the performance of the closed-loop liquid level control system. This step uses the trend of the filtered liquid level value to perform forward prediction compensation for the filter delay, thereby reducing this response lag.

[0102] S5 specifically includes the following sub-steps S51 to S53.

[0103] S51 is the sub-step for calculating group delay. Based on the cutoff frequency... The group delay of the low-pass filter in the passband is calculated using the following formula.

[0104] ;

[0105] in, Group delay (s); Cutoff frequency (Hz); It is the arithmetic square root of 2, approximately equal to 1.414; Approximately 6.283. Group delay refers to the delay in time that a signal experiences after passing through a linear time-invariant system; it is defined as the negative derivative of the phase response with respect to angular frequency. For a second-order Butterworth low-pass filter, the group delay within its passband is approximately constant, numerically equal to... This approximation has high accuracy when the signal frequency is much lower than the cutoff frequency, and the frequency of liquid level change signals is usually much lower than the filter cutoff frequency, so this approximation is reasonable in this application scenario. When the cutoff frequency... Group delay as rotational speed changes Synchronous updates mean that the group delay decreases when the cutoff frequency increases, and the group delay increases when the cutoff frequency decreases.

[0106] S52 is the rate of change estimation sub-step. Using the most recent sampled values ​​of the filtered liquid level, the rate of change is calculated according to the following formula.

[0107] ;

[0108] in, The estimated rate of change (m / s); For the first Filtered liquid level value (m) at each sampling time; For the first Filtered liquid level value (m) at each sampling time; The number of difference interval points, taken as a positive integer; The sampling period is denoted by s. This formula uses the finite difference method to estimate the rate of change of liquid level, i.e., using the phase distance as denoted by s. The average rate of change is obtained by dividing the difference between two sampled values ​​in each sampling period by the time interval. (Number of difference interval points) The selection of the value needs to be balanced between the sensitivity of the rate of change estimation and the noise immunity. When the value is small, the rate of change estimation responds quickly to changes in liquid level, but it is easily affected by residual noise and fluctuates. Larger values ​​result in smoother rate-of-change estimates, but are less responsive to sudden changes in liquid level. Preferred... The value of is a positive integer between 3 and 10, and the specific value can be selected according to the sampling period and the actual noise level.

[0109] S53 is the forward prediction correction sub-step. The filtered liquid level value is forward predicted and corrected according to the following formula to obtain the final liquid level measurement value. ;

[0110] in, The final liquid level measurement (m); For the first Filtered liquid level value (m) at each sampling time; Group delay (s); This is the estimated rate of change (m / s). The physical meaning of this formula is: based on the current filtered liquid level value, using the rate of change... Group delay time The linear extrapolation within the time frame is used as the correction increment to shift the filtered output signal forward on the time axis. The forward prediction time is adjusted to compensate for the response delay introduced by the low-pass filter. In the ideal case of uniform liquid level change, this forward prediction can completely eliminate the filter delay. In the real case where the liquid level change rate is not constant, the forward prediction, while not completely eliminating the delay, can effectively reduce the amount of delay.

[0111] To prevent excessive forward prediction correction from distorting the output value during periods of drastic liquid level fluctuations or signal anomalies, a preset maximum correction amount is set as a safety limit. (When group delay...) With rate of change When the absolute value of the product exceeds the preset maximum correction amount, the preset maximum correction amount is taken as the actual correction amount, and its sign is the same as the preset maximum correction amount. Consistent. The specific value of the preset maximum correction amount can be determined according to the range of the stirred tank and the actual application requirements. This limiting processing ensures the stability and safety of the system's output value under abnormal operating conditions while retaining the delay compensation function.

[0112] In summary, the dynamic liquid level detection method based on a stirred tank of the present invention obtains the apparent liquid level value through differential pressure liquid level acquisition (S1), obtains the impeller speed signal through speed acquisition (S2), eliminates the liquid level deviation caused by stirring vortexes through dynamic compensation for vortex depression (S3), suppresses stirring fluctuation noise through adaptive filtering (S4), and reduces the response delay introduced by filtering through filter delay prediction compensation (S5), ultimately obtaining a measurement value that accurately reflects the true liquid level in the stirred tank. Each step is organically linked by the impeller speed signal, enabling the entire signal processing process to dynamically adapt to the actual operating conditions of the stirred tank. In this method, the application scenario of differential pressure liquid level measurement is consistent throughout, and all signal processing links serve to improve the accuracy and response speed of liquid level measurement, reflecting the core attributes of this invention in the field of fluid measurement technology.

[0113] Example 1: This example uses a standard stirred tank with an inner diameter of 1.0m as the object. The tank is equipped with four standard baffles and a set of four-bladed horizontal paddles. The material in the tank is water with a density of... 1000 kg / m 3 The stirring paddle speed ranges from 60 to 120 r / min, and the sampling period is... The time is 0.1s. The specific detection steps are as follows:

[0114] In step S1, differential pressure level acquisition, install one pressure transmitter at the bottom end cap and one at the top cylinder pressure port of the stirred tank, respectively, according to step S11. The measurement accuracy is 0.075%FS, and the vertical distance between the two pressure points is 2.0m. Then, according to step S12, the differential pressure value... Material density and gravitational acceleration According to the formula Calculate the apparent liquid level value .

[0115] In the S2 speed acquisition step, a Hall speed sensor is installed at the output shaft end of the agitator reducer, with the same sampling period as the differential pressure signal. Acquire impeller speed signal .

[0116] In the S3 vortex depression dynamic compensation step, press S31 to adjust the rotational speed. Convert to angular velocity According to S32, the vortex compensation coefficient is used. The inner radius of the stirring vessel is 0.08. Calculate the steady-state compensation target value for 0.5m. Under the parameter conditions of this embodiment, when the rotational speed is 60 r / min Approximately 0.020m, at a rotational speed of 120 r / min. Approximately 0.080 m. Based on S33, the vortex response time constant... Calculate the tracking coefficient for 3.0s And according to the first-order recursive formula Update the dynamic compensation amount. Calculate the compensated liquid level value according to S34. .

[0117] In the S4 adaptive filtering step, according to S41 with the frequency scaling factor... Calculate the cutoff frequency with a value of 0.5. The low-speed threshold is 30 r / min, and the cutoff frequency is a preset fixed value of 0.25 Hz when the speed is below this threshold. A second-order Butterworth low-pass filter is constructed according to S42 and discretized by bilinear transform. The compensated liquid level value is then filtered to obtain the filtered liquid level value.

[0118] In the S5 filter delay prediction compensation step, the group delay is calculated according to S51. Number of points at differential intervals according to S52. Calculate the rate of change for 5. Calculate the final liquid level measurement according to S53. The preset maximum correction value is 0.020m.

[0119] In terms of the system, the signal processing unit is implemented using an ARM Cortex-M4 microcontroller, the differential pressure sensor module is input via a 420mA signal, the speed acquisition module is input via a pulse count, and the output interface module outputs the final liquid level measurement value via a 420mA standard signal.

[0120] Example 2: This example uses a stirred tank with an inner diameter of 1.6m as the object. No baffles are installed inside the tank. It is equipped with one set of anchor-type stirring paddles. The material inside the tank is mineral slurry with a density of... 1200 kg / m 3 The stirring paddle speed range is 30–90 r / min, and the sampling period is... The value is 0.1s. The difference from Example 1 lies in the following parameter: vortex compensation coefficient. The inner radius of the stirring vessel is 0.42. 0.8m, vortex response time constant 6.0s, frequency scaling factor 0.4, number of difference interval points The preset maximum correction value is 0.030m. Since the stirred tank in this embodiment does not have baffles, the vortex effect is more pronounced than in Embodiment 1; therefore, the vortex compensation coefficient is... The value is relatively large; at the same time, the vessel body is large and the material is slurry, resulting in large fluid inertia and a large vortex response time constant. The corresponding increase.

[0121] Example 3: This example uses a stirred tank with an inner diameter of 0.6m as the object. The tank is equipped with three baffles and one set of half-tube coils. The stirring impeller is a three-bladed swept-back impeller. The material in the tank is an organic solvent with a density of... 850kg / m 3 The stirring paddle speed ranges from 120 to 300 r / min, and the sampling period is... The value is 0.05s. The difference from Example 1 lies in the following parameter: vortex compensation coefficient. The inner radius of the stirring vessel is 0.12. 0.3m, vortex response time constant 1.5s, frequency scaling factor 0.65, number of difference interval points 3. The preset maximum correction value is 0.015m. Because the stirring impeller speed is high and the vessel body is small in this embodiment, the stirring fluctuation frequency is high; therefore, the frequency proportionality coefficient is... The value is set to be larger to retain more useful signal information; the number of differential interval points Smaller values ​​are chosen to improve the response speed of the rate of change estimation.

[0122] Comparative Example 1: The structure of the stirred tank, sensor configuration, and system hardware of this comparative example are exactly the same as those of Example 1. The difference is that the S3 vortex indentation dynamic compensation step is not performed during signal processing, that is, no compensation is made for the liquid level deviation at the tank wall caused by the stirring vortex. The apparent liquid level value output by the differential pressure sensor... After only undergoing S4 adaptive filtering and S5 filtering delay prediction compensation, the final liquid level measurement value is directly output.

[0123] Comparative Example 2 is identical to Example 1 in terms of stirred tank structure, sensor configuration, and system hardware. The difference lies in the fact that step S3 does not employ a first-order recursive tracking loop, but instead uses the steady-state compensation target value... It is used directly as a dynamic compensation quantity, that is, at each sampling time, let Equivalent to tracking coefficient Take 1. When the rotational speed changes abruptly, the vortex shape of the liquid inside the vessel needs to undergo a transition process related to fluid inertia to reach a new steady state. However, the compensation amount in this comparative example jumps instantaneously to the new steady-state target value, thus causing overcompensation during the transition period. The remaining steps S1, S2, S4, and S5 are the same as in Example 1.

[0124] Comparative Example 3: The structure of the stirred tank, sensor configuration, and system hardware of this comparative example are exactly the same as those of Example 1. The difference is that the cutoff frequency of the low-pass filter in step S4 is fixed at 0.8Hz instead of adaptively adjusting with the rotation speed. The remaining steps S1, S2, S3, and S5 are the same as those in Example 1.

[0125] Comparative Example 4: The structure of the stirred tank, sensor configuration, and system hardware of this comparative example are exactly the same as those of Example 1. The difference is that the S5 filter delay prediction compensation step is not performed; that is, the output of the S4 adaptive filter is directly used as the final liquid level measurement value without forward prediction correction. The remaining steps S1, S2, S3, and S4 are the same as those in Example 1.

[0126] Experimental Example 1 verifies the effectiveness of step S3 in the dynamic compensation of vortex depression. Using the methods of Example 1, Comparative Example 1, and Comparative Example 2, with the liquid level in the stirred tank maintained at a constant 1.500 m, the impeller speed was increased in a step from 60 r / min to 120 r / min. Liquid level measurements were recorded for 30 seconds, 15 seconds before and after the speed increase. No feeding or discharging operations were performed during the experiment, and the actual liquid level in the tank remained constant. After the speed increase, the vortex morphology in the tank needs to undergo a transition process related to fluid inertia to reach a new steady state. The characteristic time of this transition process is related to the vortex response time constant. Consistent. Evaluation indicators include steady-state level measurement error and the maximum transient error during a speed step transition. The steady-state level measurement error is defined as the absolute value of the mean difference between the measured level and the true level within 10 seconds after the speed stabilizes. The maximum transient error is defined as the maximum absolute value of the difference between the measured level and the true level within 5 seconds after the speed step occurs. Experimental results are as follows: Figure 1 As shown.

[0127] Figure 1 The graphs show a comparison of the step response of liquid level measurement with rotational speed in Example 1 and Comparative Examples 1 and 2. (a) shows the curve of the impeller rotational speed changing with time, where the speed increases from 60 r / min to 120 r / min at 15 s. (b) shows the curves of the measured liquid level of the actual liquid level, Example 1, Comparative Examples 1 and 2, and the measured liquid level over time. (c) shows the curves of the liquid level measurement error of Example 1, Comparative Examples 1 and 2, and the measured liquid level over time, where the liquid level measurement error is defined as the measured value of each method minus the actual liquid level.

[0128] from Figure 1 The following can be observed in (b) and (c). In Comparative Example 1, due to the lack of vortex compensation, the measured value stabilized at approximately 20 mm above the actual liquid level at a rotation speed of 60 r / min. After the rotation speed increased to 120 r / min, as the vortex gradually built up inside the vessel, the measured value gradually increased and eventually stabilized at approximately 80 mm above the actual liquid level. The steady-state error increased significantly with increasing rotation speed. In Comparative Example 2, although vortex compensation was performed, the first-order recursive tracking was not introduced because the steady-state compensation target value was directly used. At the instant of the rotation speed increase, the actual vortex was still at the old steady-state offset of approximately 20 mm, but the compensation amount had already jumped instantaneously to the new steady-state target value of approximately 80 mm. This resulted in the compensation amount exceeding the actual vortex offset by approximately 60 mm, leading to a negative transient deviation of approximately 60 mm in the measured value, i.e., overcompensation. Subsequently, as the actual vortex gradually built up to the new steady state, this overcompensation deviation gradually decreased and eventually disappeared. Example 1 uses a first-order recursive tracking method to update the dynamic compensation amount, ensuring that the rate of change of the compensation amount matches the actual vortex formation process. After a speed jump, the maximum transient error is approximately 6 mm, and the transition process is smooth with no over-compensation or under-compensation. These results indicate that the vortex concavity dynamic compensation step S3 can effectively eliminate the liquid level shift caused by the stirring vortex, while the first-order recursive tracking step avoids over-compensation during sudden speed changes by matching the rate of change of the compensation amount to the actual vortex formation process.

[0129] Experimental Example 2 verifies the effectiveness of the adaptive filtering step S4. Using the methods of Examples 1, 2, 3, and Comparative Example 3, liquid level data were continuously collected for 60 seconds under three steady-state conditions with impeller speeds of 60 r / min, 90 r / min, and 120 r / min, respectively. The root mean square (RMS) value of the liquid level measurement noise under each condition was calculated. The RMS value was calculated by subtracting the mean value from the final liquid level measurement sequence during steady-state operation. This indicator reflects the magnitude of the residual noise after filtering. The experimental results are as follows: Figure 2 As shown.

[0130] Figure 2 This is a comparison chart of the root mean square noise values ​​of Examples 1, 2, and 3 with Comparative Example 3 at different rotational speeds. It is a grouped bar chart, with the horizontal axis representing the impeller rotational speed and the vertical axis representing the root mean square noise value (mm). Figure 2 As can be seen, the root mean square noise values ​​of Example 1 at 60 r / min, 90 r / min, and 120 r / min are 0.9 mm, 1.2 mm, and 1.5 mm, respectively. They increase slightly with increasing rotational speed, but the increase is gradual. This is because the cutoff frequency of the adaptive filter increases synchronously with the rotational speed, and the ratio of the cutoff frequency to the stirring rotational frequency remains constant. In Example 2, due to the larger vessel size and lack of baffles, the stirring fluctuation amplitude was larger, resulting in noise root mean square values ​​of 1.3 mm, 1.6 mm, and 2.0 mm, slightly higher than in Example 1 but still controlled at a low level. In Example 3, due to the smaller vessel size and shorter sampling period, the noise root mean square values ​​were 0.7 mm, 0.9 mm, and 1.2 mm. In Comparative Example 3, with a fixed cutoff frequency of 0.8 Hz, the stirring rotation frequency was 1.0 Hz at 60 r / min, resulting in a cutoff frequency to rotation frequency ratio of 0.8, which was insufficient to suppress the fundamental stirring frequency, leading to a noise root mean square value as high as 3.2 mm. At 90 r / min and 120 r / min, the rotation frequencies were 1.5 Hz and 2.0 Hz, respectively, reducing the cutoff frequency to rotation frequency ratio to 0.53 and 0.4, respectively, thus improving the noise suppression effect, with noise root mean square values ​​of 1.8 mm and 1.3 mm, respectively. The above results show that adaptive filtering can maintain a stable noise suppression effect at different speeds by adjusting the cutoff frequency synchronously with the rotational speed, while the fixed cutoff frequency scheme has significantly insufficient noise suppression performance at low speeds.

[0131] Experimental Example 3 verifies the effectiveness of the filter delay prediction compensation step S5. Using the methods of Example 1 and Comparative Example 4, with the agitator speed stable at 120 r / min, a feed pump is used to uniformly feed the liquid into the vessel, causing the liquid level to rise linearly from 1.000 m to 1.800 m. The feeding duration is approximately 50 s, and the liquid level change rate is approximately 16.0 mm / s. During the experiment, a reference liquid level value provided by a high-precision radar level gauge is recorded simultaneously as the true liquid level benchmark. The evaluation index is the liquid level tracking error, defined as the difference between the final liquid level measurement value and the reference liquid level value at each moment. Under the 120 r / min operating condition, the adaptive cutoff frequency... Hz, corresponding to group delay s, the theoretical uniform tracking error is mm. Experimental results are as follows: Figure 3 As shown.

[0132] Figure 3 The graphs show a comparison of liquid level tracking during the feeding process of Example 1 and Comparative Example 4. (a) shows the curves of the actual liquid level, the measured value of Example 1, and the measured value of Comparative Example 4 changing over time. (b) shows the curves of the liquid level tracking error of Example 1 and Comparative Example 4 changing over time, where the tracking error is defined as the measured value minus the actual liquid level value. The liquid level ranges from 1.000m to 1.800m, while the tracking error is only on the order of a few millimeters. In (a), the two measurement curves are visually nearly identical, while in (b), the difference is shown by magnifying the vertical axis to the order of millimeters.

[0133] from Figure 3 As shown in (b), the tracking error of Comparative Example 4 during the uniform feeding stage stabilizes at approximately -3.6 mm. This negative value indicates that the measured value lags behind the actual liquid level, and its absolute value matches the theoretically calculated value of 3.6 mm. After adopting forward prediction correction, the tracking error of Example 1 during the uniform feeding stage is reduced to approximately -0.8 mm, which is about 78% less than the absolute value of the tracking error of Comparative Example 4. In the transition section at the beginning and end of feeding, due to the sudden change in the rate of liquid level change, there is a brief lag in the rate of change estimation. The maximum absolute value of the tracking error of Example 1 in the transition section is approximately 2.5 mm, which is still significantly better than the approximately 5.2 mm of Comparative Example 4 in the transition section. The above results show that the filter delay prediction compensation step S5 can effectively reduce the response delay introduced by the low-pass filter. In (b), the tracking error of Comparative Example 4 exhibits a stable negative bias in the uniform feeding stage, reflecting the physical effect of the low-pass filter group delay, while the tracking error of Example 1 is close to 0 in the uniform feeding stage, indicating that the forward prediction correction effectively compensates for this group delay.

[0134] Experiment 4 is used to compare and evaluate the comprehensive performance of Examples 1, 2, 3, Comparative Examples 1, 2, 3, and 4. Each example and comparative example was tested completely on its corresponding stirred tank according to the experimental conditions of Examples 1 to 3. The following four performance indicators were extracted for comparison: steady-state measurement accuracy, maximum transient error of speed step, root mean square noise value, and uniform feed tracking error. The definitions of each indicator are consistent with those in Examples 1 to 3. The steady-state measurement accuracy and maximum transient error of speed step are taken from the data after the speed step reaches the highest operating speed of each stirred tank; the root mean square noise value is taken from the data under the condition of the lowest operating speed of each stirred tank to reflect the filtering difference at low speeds; and the uniform feed tracking error is taken from the steady-state value of the uniform feed stage at the corresponding highest speed. The experimental results are as follows: Figure 4 As shown.

[0135] Figure 4 The following graphs compare the comprehensive performance indicators of each embodiment and comparative example: (a) compares the steady-state measurement accuracy, (b) compares the maximum transient error of speed step, (c) compares the root mean square value of noise, and (d) compares the tracking error of uniform feed. The horizontal axis of each graph represents the number of each embodiment and comparative example, and the vertical axis represents the corresponding indicator value (mm).

[0136] from Figure 4 As shown in (a), the steady-state measurement accuracies of Examples 1, 2, and 3 are 1.2 mm, 1.8 mm, and 0.9 mm, respectively. Comparative Example 1, lacking vortex compensation, has a steady-state error as high as 80.5 mm. The steady-state measurement accuracies of Comparative Examples 2, 3, and 4 are 1.3 mm, 1.4 mm, and 1.2 mm, respectively. As shown in (b), the maximum transient errors of the speed step in Examples 1, 2, and 3 are 6.0 mm, 9.5 mm, and 4.2 mm, respectively. Comparative Example 1, due to uncompensated vortex offset continuously increasing during the transition period, has a maximum transient error of 69.0 mm. Comparative Example 2, due to overcompensation, has a maximum transient error of 60.0 mm. Comparative Examples 3 and 4, possessing dynamic compensation functions, have maximum transient errors of 6.5 mm and 6.0 mm, respectively. As shown in (c), the root mean square noise values ​​of Examples 1, 2, and 3 at low speeds are 0.9 mm, 1.3 mm, and 0.7 mm, respectively, while that of Comparative Example 3 is 3.2 mm, and those of Comparative Examples 1, 2, and 4 are 0.9 mm, 0.9 mm, and 0.9 mm, respectively. As shown in (d), the uniform feed tracking errors of Examples 1, 2, and 3 are 0.8 mm, 1.1 mm, and 0.6 mm, respectively, while that of Comparative Example 4 is 3.6 mm, and those of Comparative Examples 1, 2, and 3 are 0.8 mm, 0.8 mm, and 1.5 mm, respectively.

[0137] comprehensive Figure 4 The data in the figures show that Examples 1 to 3 outperform or approach the best results among the comparative examples in all four indicators, indicating that the method of the present invention has good applicability and feasibility under different stirred tank structures, different materials, and different operating conditions. The steady-state and transient errors of Comparative Example 1 are significantly greater than those of the other examples, indicating that the vortex depression dynamic compensation step S3 is the key step in eliminating the liquid level deviation of the stirred vortex. The transient error of Comparative Example 2 is significantly greater than that of Example 1, and the transient deviation direction is negative, i.e., overcompensation, indicating that the first-order recursive tracking step plays an irreplaceable role in avoiding overcompensation during sudden changes in rotational speed by matching the rate of change of the compensation amount with the actual vortex establishment process. The noise performance of Comparative Example 3 at low speeds is significantly worse than that of the other examples, indicating that adaptive adjustment of the cutoff frequency plays a crucial role in ensuring noise suppression at different speeds. The feed tracking error of Comparative Example 4 is significantly greater than that of the other examples, indicating that the filter delay prediction compensation step S5 is of great significance in improving the dynamic response of the system.

[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic liquid level detection method for stirred tank, characterized in that, Includes the following steps: S1. Differential pressure level acquisition: The differential pressure signal of the liquid column in the vessel is acquired by a differential pressure sensor installed on the stirred vessel, and the differential pressure signal is converted into an apparent liquid level value; S2, Rotation speed acquisition: The rotation speed signal of the agitator is acquired in real time by a rotation speed sensor installed at the drive end of the agitator. S3, vortex depression dynamic compensation: The steady-state offset of the liquid level at the vessel wall caused by the stirring vortex is calculated based on the rotation speed signal as the steady-state compensation target value. The dynamic compensation amount is gradually approached to the steady-state compensation target value through a first-order recursive tracking loop. At the current sampling time, the dynamic compensation amount is subtracted from the apparent liquid level value to obtain the compensated liquid level value. Step S3 includes the following sub-steps: S31. Obtain the current rotation speed of the agitator based on the rotation speed signal. Calculate the angular velocity of the agitator using the following formula: ; in, The angular velocity of the agitator; The speed of the agitator is 60; 60 is the conversion factor between minutes and seconds. Convert the rotational speed signal into angular velocity; S32, based on the angular velocity of the stirring paddle and the inner radius of the stirring vessel The steady-state compensation target value is calculated using the following formula: ; in, The steady-state compensation target value; The vortex compensation coefficient is determined by calibration, and the calibration process covers the influence of internal structural components on the vortex morphology. The angular velocity of the stirring impeller; The inner radius of the stirring vessel; It is the acceleration due to gravity; Calculate the steady-state offset of the liquid level at the vessel wall corresponding to the current rotational speed; S33. The dynamic compensation amount is updated in each sampling period using the following first-order recursive formula, so that it gradually approaches the steady-state compensation target value: ; in, For the first The dynamic compensation amount at each sampling time; For the first The dynamic compensation amount at each sampling time; For the first The steady-state compensation target value is calculated by step S32 at each sampling time. The tracking coefficient; The calculation formula is: ; in, The sampling period; The vortex response time constant is determined by calibration; S34. At the current sampling time, subtract the dynamic compensation amount from the apparent liquid level value according to the following formula to obtain the compensated liquid level value: ; in, The compensated liquid level value; The apparent liquid level value; For the first The dynamic compensation amount at each sampling time; S4. Adaptive filtering: Determine the cutoff frequency of the low-pass filter based on the rotation speed signal, and adaptively adjust the cutoff frequency with the stirring speed to filter the compensated liquid level value to obtain the filtered liquid level value. S5. Filter delay prediction compensation: Calculate the group delay of the low-pass filter based on the cutoff frequency, and use the rate of change of the filtered liquid level value and the group delay to perform forward prediction correction to obtain the final liquid level measurement value.

2. The method according to claim 1, characterized in that, Step S1 includes the following sub-steps: S11. Pressure transmitters are installed at the bottom and top pressure measuring points of the stirred tank to collect the differential pressure value between the bottom and top pressure measuring points. This sub-step obtains the liquid column differential pressure signal, excluding the influence of the gas phase pressure inside the vessel; S12, Based on the differential pressure value Based on the density of the material inside the vessel, the apparent liquid level value is calculated using the following formula: ; in, The apparent liquid level value; The differential pressure value; This refers to the density of the material inside the vessel. It is the acceleration due to gravity; The apparent liquid level value corresponding to the height of the liquid column at the vessel wall is obtained.

3. The method according to claim 1, characterized in that, Step S4 includes the following sub-steps: S41. Obtain the current speed of the agitator based on the speed signal. The impeller rotation frequency is calculated using the following formula, and the cutoff frequency of the low-pass filter is determined: ; in, The rotational frequency of the agitator; The speed of the agitator is 60; 60 is the conversion factor between minutes and seconds. ; in, The cutoff frequency; This is the frequency scaling factor; The impeller rotation frequency; the cutoff frequency when the impeller rotation speed is lower than the rotation speed threshold determined by the stirring fluctuation noise characteristics. Take a preset fixed value; S42, at the cutoff frequency A second-order Butterworth low-pass filter is constructed, and its discretization into a difference equation is performed using a bilinear transform. This discretization is then applied to the compensated liquid level value to obtain the filtered liquid level value. When the cutoff frequency... When changes occur, the filter coefficients are recalculated and a weighted smooth transition is applied to the old and new coefficients. It can suppress stirring noise and retain true liquid level change information at different speeds.

4. The method according to claim 3, characterized in that, Step S5 includes the following sub-steps: S51, according to the cutoff frequency The group delay of the low-pass filter in the passband is calculated using the following formula: ; in, For the group delay; The cutoff frequency is the cutoff frequency; when the cutoff frequency is... The group delay varies with rotational speed. Synchronized updates; Obtain the response delay under the current filtering conditions; S52. Using the most recent sampled values ​​of the filtered liquid level, calculate the rate of change according to the following formula: ; in, This is an estimate of the rate of change; For the first The filtered liquid level value at each sampling time; For the first The filtered liquid level value at each sampling time; The number of difference interval points, taken as a positive integer; The sampling period; Obtain the trend of the filtered liquid level value; S53. Perform forward prediction correction on the filtered liquid level value according to the following formula to obtain the final liquid level measurement value: ; in, The final liquid level measurement value; For the first The filtered liquid level value at each sampling time; For the group delay; The estimated rate of change; when and When the absolute value of the product exceeds the preset maximum correction amount, the preset maximum correction amount is taken as the actual correction amount, and its sign is the same as the preset maximum correction amount. Consistent; this sub-step reduces the response delay introduced by the low-pass filter to obtain the final liquid level measurement value.

5. A dynamic liquid level detection system based on a stirred tank for implementing the method according to any one of claims 1-4, characterized in that, include: The differential pressure sensor module includes two pressure transmitters respectively set at the bottom and top pressure measuring points of the stirred tank, which are used to collect the differential pressure signal of the liquid column in the tank and output the apparent liquid level value. The rotation speed acquisition module is located at the drive end of the agitator and is used to acquire the rotation speed signal of the agitator in real time. The signal processing unit, connected to the differential pressure sensor module and the rotation speed acquisition module respectively, includes a vortex dynamic compensation module, an adaptive filtering module, and a delay prediction compensation module connected in series. The vortex dynamic compensation module calculates the steady-state offset of the liquid level at the vessel wall caused by the stirring vortex based on the rotation speed signal and outputs the dynamic compensation amount through a first-order recursive tracking loop to compensate the apparent liquid level value and output the compensated liquid level value. The adaptive filtering module determines the cutoff frequency based on the rotation speed signal and performs low-pass filtering on the compensated liquid level value before outputting the filtered liquid level value. The delay prediction compensation module calculates the group delay based on the cutoff frequency and performs forward prediction correction using the rate of change of the filtered liquid level value before outputting the final liquid level measurement value.

6. The system according to claim 5, characterized in that, The input terminals of the vortex dynamic compensation module are connected to the differential pressure sensor module and the speed acquisition module, respectively, and its output terminal is connected to the adaptive filtering module. The adaptive filtering module is also connected to the speed acquisition module to receive the speed signal to determine the cutoff frequency, and its output terminal is connected to the delay prediction compensation module. The speed signal serves as the input parameter for both the vortex dynamic compensation module and the adaptive filtering module, forming a dual-channel signal processing architecture with the speed signal as the core.

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