A Method and System for Frequency Control of Three-Phase Asynchronous Motors Based on Electromechanical Signal Analysis

Abstract

This invention relates to the field of frequency modulation control technology, and discloses a frequency modulation control method and system for a three-phase asynchronous motor based on electromechanical signal analysis. The method includes: real-time acquisition of the instantaneous values ​​of the three-phase current of the stator of the target controlled object; synthesis of a current vector based on the instantaneous values ​​of the three-phase current; identification of positive and negative abrupt changes in the synthesized current vector; and obtaining a current impact characteristic factor. This scheme generates a dynamic slip enhancement compensation value by analyzing the instantaneous values ​​of the three-phase current, dynamic torsional deformation signals, and terminal voltages. It can capture transient changes without sacrificing response speed, effectively suppressing stator current distortion and electromagnetic torque oscillation, reducing shaft vibration, and improving the anti-interference capability and control accuracy of the three-phase asynchronous motor. It is suitable for harsh transient conditions such as mine start-up and shutdown and sudden changes in material flow.

Description

Technical Field

[0001] This invention relates to the field of frequency modulation control technology, specifically to a frequency modulation control method and system for three-phase asynchronous motors based on electromechanical signal analysis. Background Technology

[0002] Currently, when performing frequency modulation control of a three-phase asynchronous motor based on electromechanical signal analysis, it is usually necessary to sample and analyze the electromechanical signals of the stable three-phase asynchronous motor, and adjust the output frequency and voltage of the frequency converter accordingly.

[0003] However, the above control methods still have the following drawbacks in the application of three-phase asynchronous motors in mine conveyor belts: During transient processes such as start-up, shutdown, and sudden changes in material loading, the three-phase asynchronous motors of mine conveyor belts will be subjected to severe load impacts. Such instantaneous changes in mechanical load will cause dynamic distortion of the stator current of the three-phase asynchronous motor, high-frequency oscillation of electromagnetic torque, and wideband vibration response of the mechanical structure. Existing analysis methods often sacrifice response speed for signal smoothing, resulting in the inability to accurately analyze the transient changes represented by the load impact in the electromechanical signal, thereby affecting the control effect of the three-phase asynchronous motor. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a frequency modulation control method and system for three-phase asynchronous motors based on electromechanical signal analysis, thus solving the aforementioned problems.

[0005] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0006] A frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis includes:

[0007] Step S1: Real-time acquisition of the instantaneous values ​​of the three-phase current of the stator of the target controlled object; synthesis of the current vector based on the instantaneous values ​​of the three-phase current; identification of the positive and negative abrupt changes in the synthesized current vector; and obtaining the current impact characteristic factor.

[0008] Step S2: Real-time acquisition of dynamic torsional deformation signal of the target controlled object shaft; extraction of torsional vibration alternating component related to load impact from preprocessed dynamic torsional deformation signal; analysis of instantaneous vibration intensity of shaft system based on torsional vibration alternating component to obtain shaft system torsional vibration threat level.

[0009] Step S3: Real-time acquisition of the terminal voltage and stator current of the target controlled object; calculation of the instantaneous power signal based on the preprocessed terminal voltage and stator current; analysis of the disordered fluctuation characteristics of the instantaneous power signal in the transient process; and obtaining the magnetic field disorder.

[0010] Step S4: Combine the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree to obtain the disturbance rejection stability index.

[0011] Step S5: Map the disturbance rejection stability index to a dynamic slip enhancement compensation value, and superimpose the slip enhancement compensation value with the reference slip frequency to generate the frequency modulation control command for the target controlled object.

[0012] Furthermore, based on the instantaneous values ​​of the three-phase currents, a synthesized current vector is obtained, and positive and negative abrupt changes in the synthesized current vector are identified to obtain current impact characteristic factors, including:

[0013] The instantaneous values ​​of the three-phase currents are orthogonally decomposed and current vectors are constructed. The instantaneous modal amplitudes of the current vectors are then calculated.

[0014] Set a transient observation window and calculate the instantaneous imbalance deviation between the instantaneous modal amplitude and the historical reference baseline within the window;

[0015] Within this window, based on the characteristics of instantaneous imbalance deviation, the weighted cumulative amounts of positive and negative imbalance deviations are calculated respectively, and the positive and negative impact intensities are obtained respectively.

[0016] Furthermore, based on the instantaneous values ​​of the three-phase currents, a synthesized current vector is obtained, and the positive and negative abrupt changes in the synthesized current vector are identified to obtain the current impact characteristic factor. This also includes:

[0017] The covariance relationship between positive and negative impact intensity is analyzed to obtain the impact covariance coefficient;

[0018] The positive impact intensity, negative impact intensity, and impact covariance coefficient are fused to generate the current impact characteristic factor.

[0019] Furthermore, torsional vibration alternating components related to load impact are extracted from the preprocessed dynamic torsional deformation signal. Based on the torsional vibration alternating components, the instantaneous vibration intensity of the shaft system is analyzed to obtain the torsional vibration threat level of the shaft system, including:

[0020] Stress wave propagation characteristics were analyzed on the preprocessed dynamic torsional deformation signal, and the stress wave components of a specific frequency band generated under impact load were extracted to obtain the shaft system response characteristic quantities.

[0021] Based on the characteristic quantities of shaft response, the stress cycle characteristics within the window are analyzed to obtain the transient damage index of the material.

[0022] The correlation between the frequency distribution of the shaft system response characteristic quantities and the shaft system characteristics is analyzed, and the coupling strength between the positive impact intensity, negative impact intensity and current impact characteristic factor is calculated to obtain the resonant excitation degree.

[0023] The shaft system response characteristic quantity, material transient damage index and resonance excitation degree are fused in multiple dimensions to generate the shaft system torsional vibration threat degree.

[0024] Furthermore, stress wave propagation characteristics are analyzed on the preprocessed dynamic torsional deformation signal to extract the stress wave components in a specific frequency band generated under impact load, thus obtaining shaft system response characteristic quantities, including:

[0025] Modal decomposition was performed on the preprocessed dynamic torsional deformation signal to obtain the structural disturbance wave group;

[0026] The energy transfer and dissipation of the structural disturbance wave group along the axis spatial path are analyzed, the degree of order in its transmission process is calculated, and the disturbance propagation entropy is obtained.

[0027] By fusing the structural disturbance wave group with the disturbance propagation entropy, a shaft system response characteristic quantity representing the overall dynamic response to the impact load is generated.

[0028] Furthermore, the instantaneous power signal is calculated based on the preprocessed terminal voltage and stator current. The disordered fluctuation characteristics of the instantaneous power signal during the transient process are analyzed to obtain the magnetic field turbulence, including:

[0029] The instantaneous power signal is calculated based on the preprocessed terminal voltage and stator current. The fast pulsation component in the instantaneous power signal is decomposed to obtain the electromagnetic topological pulsation quantity.

[0030] The oscillation intensity of electromagnetic topological pulsations is analyzed, the correlation between its oscillation intensity and magnetic field saturation characteristics is calculated, and the magnetic circuit saturation oscillation index is obtained by combining the material transient damage index.

[0031] The response delay characteristics of the instantaneous power signal at the moment of load change are calculated to obtain the magnetic field reconstruction delay.

[0032] The electromagnetic topological pulsation, magnetic circuit saturation oscillation index, and magnetic field reconstruction delay are combined to generate the magnetic field disorder.

[0033] Furthermore, the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree are aggregated to obtain the disturbance rejection stability index, including:

[0034] The electromagnetic-mechanical energy transfer path among the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree is established. The anomalies of the electromagnetic-mechanical energy transfer path are analyzed to obtain the instability propagation path coefficient.

[0035] Based on the instability propagation path coefficient, an anti-disturbance stability index is generated by analyzing the degree of erosion of the stability boundary by energy anomaly transfer.

[0036] Furthermore, the calculation process for the reference slip frequency is as follows:

[0037] Real-time acquisition of the target controlled object's real-time rotational speed and set operating frequency;

[0038] The reference slip frequency is obtained by calculating the real-time rotational speed and the set operating frequency after preprocessing.

[0039] Furthermore, the disturbance rejection stability index is mapped to a dynamic slip enhancement compensation value, and the slip enhancement compensation value is superimposed on the reference slip frequency to generate a frequency modulation control command for the target controlled object, including:

[0040] Based on the disturbance resistance stability index, the changing trend of the stability boundary is analyzed to obtain the dynamic stability margin;

[0041] Based on the dynamic stability margin, a mapping relationship between the slip frequency compensation and the electromagnetic torque increment is established to generate an adaptive slip compensation.

[0042] The adaptive slip compensation amount and the reference slip frequency are superimposed and optimized in the field to generate the frequency modulation control command for the target controlled object.

[0043] Furthermore, a three-phase asynchronous motor frequency modulation control system based on electromechanical signal analysis, applied to the aforementioned three-phase asynchronous motor frequency modulation control method based on electromechanical signal analysis, includes:

[0044] The current analysis unit is used to acquire the instantaneous values ​​of the three-phase current of the stator of the target controlled object in real time, synthesize the current vector based on the instantaneous values ​​of the three-phase current, identify the positive and negative abrupt changes in the synthesized current vector, and obtain the current impact characteristic factor.

[0045] The vibration analysis unit is used to acquire the dynamic torsional deformation signal of the target control object shaft in real time, extract the torsional vibration alternating component related to the load impact from the preprocessed dynamic torsional deformation signal, analyze the instantaneous vibration intensity of the shaft system based on the torsional vibration alternating component, and obtain the torsional vibration threat level of the shaft system.

[0046] The signal control unit is used to acquire the terminal voltage and stator current of the target controlled object in real time, calculate the instantaneous power signal based on the preprocessed terminal voltage and stator current, analyze the disordered fluctuation characteristics of the instantaneous power signal in the transient process, and obtain the magnetic field disorder.

[0047] The disturbance rejection control unit is used to aggregate the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree to obtain the disturbance rejection stability index;

[0048] The frequency modulation control unit is used to map the disturbance rejection stability index to a dynamic slip enhancement compensation value, and to superimpose the slip enhancement compensation value with the reference slip frequency to generate a frequency modulation control command for the target controlled object.

[0049] In summary, the present invention has the following main beneficial effects:

[0050] This solution synthesizes a current vector by real-time acquisition of the instantaneous values ​​of the three-phase stator current, accurately identifies positive and negative abrupt changes, and generates current impact characteristic factors. Simultaneously, it acquires the dynamic torsional deformation signal of the shaft system to extract the torsional vibration alternating component, calculates the instantaneous power signal based on the terminal voltage and stator current, and analyzes the disordered fluctuations of the magnetic field. This achieves a full-dimensional transient analysis of current dynamic distortion, high-frequency oscillation of electromagnetic torque, and wideband mechanical vibration response, avoiding the limitations of single signal analysis. Furthermore, by establishing an electromagnetic-mechanical energy transfer path, it aggregates the current impact characteristic factors, shaft torsional vibration threat level, and magnetic field disorder into an anti-disturbance stability index, accurately reflecting the dynamic stability state of the electromechanical coupling of the motor under load impact, overcoming the shortcoming of traditional analysis that ignores energy transfer anomalies.

[0051] The generated frequency modulation control commands can quickly respond to changes in the stability boundary caused by sudden load changes, reduce stator current distortion, suppress electromagnetic torque oscillation and shaft vibration, and improve the motor's anti-disturbance capability and control accuracy under transient conditions. This solution can achieve accurate analysis of transient signals without sacrificing response speed, adapt to the harsh dynamic load conditions of mine conveyor belts, effectively ensure the stability of three-phase asynchronous motor operation, and reduce mechanical damage and electromagnetic losses. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the steps of the frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to the present invention;

[0053] Figure 2 This is a schematic diagram of the frequency regulation control system for a three-phase asynchronous motor based on electromechanical signal analysis according to the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] refer to Figure 1 and Figure 2 A frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis includes:

[0056] Step S1 is used to collect the instantaneous values ​​of the three-phase current of the stator of the target controlled object in real time, synthesize the current vector based on the instantaneous values ​​of the three-phase current, identify the positive and negative abrupt changes in the synthesized current vector, and obtain the current impact characteristic factor.

[0057] Step S2 is used to acquire the dynamic torsional deformation signal of the target controlled object shaft in real time, extract the torsional vibration alternating component related to the load impact from the preprocessed dynamic torsional deformation signal, analyze the instantaneous vibration intensity of the shaft system based on the torsional vibration alternating component, and obtain the torsional vibration threat level of the shaft system.

[0058] Step S3 is used to acquire the terminal voltage and stator current of the target controlled object in real time, calculate the instantaneous power signal based on the preprocessed terminal voltage and stator current, analyze the disordered fluctuation characteristics of the instantaneous power signal in the transient process, and obtain the magnetic field disorder.

[0059] Step S4 is used to aggregate the current impact characteristic factor, shaft torsional vibration threat degree and magnetic field disorder degree to obtain the disturbance rejection stability index.

[0060] Step S5 is used to map the disturbance rejection stability index to a dynamic slip enhancement compensation value, and to superimpose the slip enhancement compensation value with the reference slip frequency to generate a frequency modulation control command for the target controlled object.

[0061] In one embodiment, based on the instantaneous values ​​of the three-phase currents, a synthesized current vector is obtained, and positive and negative abrupt changes in the synthesized current vector are identified to obtain current impact characteristic factors, including:

[0062] The process involves orthogonally decomposing the instantaneous values ​​of three-phase currents and constructing current vectors, then calculating the instantaneous modal amplitudes of these current vectors. Specifically, this includes: converting the instantaneous values ​​of the three-phase currents into two orthogonal current components along the α and β axes using the Clarke transform, with these two components being Iα and Iβ, respectively; if Iα ≥ 0, then the sign function value Sα = 1; if Iα < 0, then the sign function value Sα = -1; if Iβ ≥ 0, then the sign function value Sβ = 1; if Iβ < 0, then the sign function value Sβ = -1; multiplying Sβ by Sα yields the dynamic weighting factor; summing the absolute values ​​of Iα and Iβ, and then adding this sum to the dynamic weighting factor, yields the instantaneous modal amplitudes.

[0063] A transient observation window is set up, and the instantaneous imbalance deviation between the instantaneous modal amplitude and the historical reference baseline is calculated within this window. Specifically, this includes: setting a transient observation window with a duration of N sampling periods, where N represents the number of sampling periods; storing the latest N data points within this window in real time, with each data point being the instantaneous modal amplitude; using the median of the first N-1 data points in this window as the historical reference baseline; calculating the difference between the Nth data point at the current time and the historical reference baseline; and dividing the difference by the absolute value of the difference between the historical reference baseline and the minimum value of all N-1 data points in the window to obtain the instantaneous imbalance deviation.

[0064] Within this window, based on the characteristics of instantaneous imbalance deviations, the weighted cumulative amounts of positive and negative imbalance deviations are calculated to obtain the positive and negative impact intensities, respectively. Specifically, this includes: within the transient observation window, first calculating the mean of the absolute differences of the first N-1 instantaneous imbalance deviations, and using the mean as the dynamic benchmark value; for each instantaneous imbalance deviation, dividing its absolute value by the dynamic benchmark value to obtain the corresponding ratio, then summing all such ratios to obtain the total, dividing each ratio by the total and normalizing it to the 0-1 interval to obtain the weight of each instantaneous imbalance deviation, and the sum of all weights is 1;

[0065] When the instantaneous imbalance deviation is greater than 0, the instantaneous imbalance deviation is multiplied by the corresponding weight, and then multiplied by the ratio of the next adjacent instantaneous imbalance deviation to the instantaneous imbalance deviation. If the ratio is less than 1, it is taken as 1 to obtain a single positive impact component. By accumulating all positive impact components, the positive impact intensity can be obtained.

[0066] When the instantaneous imbalance deviation is less than 0, the absolute value of the instantaneous imbalance deviation is multiplied by the corresponding weight, and then multiplied by the ratio of the absolute value of the next instantaneous imbalance deviation to the absolute value of the instantaneous imbalance deviation. If the ratio is less than 1, it is taken as 1 to obtain a single negative impact component. By accumulating all negative impact components, the negative impact intensity can be obtained.

[0067] When the instantaneous imbalance deviation is equal to 0, it indicates that there is no current imbalance deviation and it is not included in the calculation of positive and negative impact intensity.

[0068] In one embodiment, based on the instantaneous values ​​of the three-phase currents, a synthesized current vector is obtained by identifying positive and negative abrupt changes in the synthesized current vector to arrive at a current impact characteristic factor. The method further includes:

[0069] The covariance relationship between positive and negative impact intensity is analyzed to obtain the impact covariance coefficient. Specifically, this includes: calculating the mean of positive and negative impact intensity, multiplying this mean by the weighted mean of the first N-1 instantaneous imbalance deviations within the transient observation window to obtain the covariance reference value; then calculating the ratio of the difference between positive and negative impact intensity to the covariance reference value, and subtracting the absolute value of this ratio from 1 to obtain the initial covariance value.

[0070] The ratio of the number of non-zero instantaneous imbalance deviations within the statistical window to N-1 is used to multiply the initial covariant value by this ratio to obtain the shock covariant coefficient.

[0071] The positive impact intensity, negative impact intensity, and impact covariance coefficient are fused to generate a current impact characteristic factor. Specifically, this involves: dividing the positive impact intensity by the negative impact intensity to obtain the intensity ratio; if the intensity ratio is ≥1, its reciprocal is taken as the intensity matching coefficient; if the intensity ratio is <1, the intensity ratio is directly used as the intensity matching coefficient; multiplying the intensity matching coefficient by the impact covariance coefficient to obtain the covariance matching value; and superimposing the covariance matching value with the mean of the weights of the first N-1 imbalance deviations within the transient observation window to obtain the fusion correction factor.

[0072] The superposition process is as follows: calculate the mean of the weights of the first N-1 imbalance deviations within the transient observation window; if the covariance ratio value is greater than or equal to the mean, multiply the covariance ratio value by the mean and then add the mean to complete the superposition; if the covariance ratio value is less than the mean, add the covariance ratio value to the mean and then multiply it by the covariance ratio value to complete the superposition, and finally obtain the fusion correction factor.

[0073] The current impact characteristic factor can be obtained by multiplying the sum of the absolute values ​​of the positive and negative impact intensities by the fusion correction factor and then dividing by half of the number of sampling periods N.

[0074] The instantaneous values ​​of three-phase current are converted into orthogonal current components along the α and β axes using the Clarke transform. Current vectors are constructed and instantaneous modal amplitudes are calculated. Simultaneously, by combining a transient observation window with N sampling periods, instantaneous imbalance deviations and positive and negative impact intensities are calculated in real time, avoiding response speed loss caused by signal smoothing. By analyzing the covariance relationship between positive and negative impact intensities, impact covariance coefficients are obtained, and current impact characteristic factors are generated. This can accurately capture the dynamic distortion of stator current when the mine conveyor belt starts and stops or when the material loading changes abruptly, understand the transient changes caused by load impacts, accurately correlate the coupling characteristics of high-frequency oscillations of electromagnetic torque and mechanical load impacts, improve the accuracy of transient analysis of electromechanical signals, and thus optimize the effect of frequency regulation control of three-phase asynchronous motors.

[0075] In one embodiment, torsional vibration alternating components related to load impact are extracted from the preprocessed dynamic torsional deformation signal. Based on the torsional vibration alternating components, the instantaneous vibration intensity of the shaft system is analyzed to obtain the torsional vibration threat level of the shaft system, including:

[0076] Stress wave propagation characteristics were analyzed on the preprocessed dynamic torsional deformation signal, and the stress wave components of a specific frequency band generated under impact load were extracted to obtain the shaft system response characteristic quantities.

[0077] Based on the shaft system response characteristic quantity, its stress cycle characteristics within the window are analyzed to obtain the material transient damage index. Specifically, this includes: calculating the sum of the absolute values ​​of the differences between adjacent data points of the shaft system response characteristic quantity within the window, and using it as the total amount of cycle fluctuation.

[0078] Obtain the material fatigue limit value of the target control object axis; divide the mean value of the axis system response characteristics by the material fatigue limit value to obtain the fatigue fit coefficient; divide the number of times the axis system response characteristics exceed the mean value of the axis system response characteristics within the window by N to obtain the over-limit ratio coefficient; multiply the total cyclic fluctuation by the fatigue fit coefficient, then multiply by the over-limit ratio coefficient, and then divide by (the number of peak values ​​of the axis system response characteristics within the window + 1) to obtain the material transient damage index.

[0079] The peak value determination process is as follows: calculate the standard deviation of all shaft system response characteristic quantities within the window, and set 0.3 times the standard deviation as the dynamic threshold for peak value determination;

[0080] Starting from the second axis response feature value within the window and ending at the second-to-last axis response feature value, neighborhood detection is performed on each data point: if an axis response feature value is simultaneously greater than both its preceding and following axis response feature values, and the difference between the axis response feature value and the preceding axis response feature value and the difference between the preceding and following axis response feature values ​​are both greater than the dynamic threshold, then it is determined to be the peak value of the axis response feature value.

[0081] The correlation between the frequency distribution of shaft system response characteristic quantities and shaft system characteristics is analyzed, and the coupling strength between positive impact intensity, negative impact intensity and current impact characteristic factor is calculated to obtain the resonant excitation degree. Specifically, based on the target control object, the analysis frequency band of shaft system response characteristic quantities is divided into torsional vibration sensitive sub-bands of 0-500Hz. The power density value of each frequency point in the torsional vibration sensitive sub-band is calculated, and the energy weight of each frequency point is obtained after normalization. The frequency point with the largest energy weight is determined as the dominant frequency value of the shaft system response.

[0082] Obtain the measured reference value of the first-order natural frequency of the shaft system of the target control object; calculate the absolute value of the difference between the main frequency value and the measured reference value, and divide the absolute value of the difference by the measured reference value to obtain the frequency deviation coefficient;

[0083] The difference between the positive and negative impact intensities is calculated and divided by the absolute values ​​of the positive and negative impact intensities to obtain the impact asymmetry coefficient; the current impact characteristic factor is divided by the material transient damage index to obtain the coupling correction coefficient; the frequency deviation coefficient is multiplied by the impact asymmetry coefficient, and then added to the coupling correction coefficient and multiplied by 100 to obtain the resonant excitation degree.

[0084] The shaft system response characteristic quantity, material transient damage index, and resonance excitation degree are fused in multiple dimensions to generate the shaft system torsional vibration threat degree. Specifically, this includes: dividing the peak value of the shaft system response characteristic quantity by the mean value of the shaft system response characteristic quantity to obtain the characteristic quantity strength coefficient; if the material transient damage index is > 0.5, the square of the material transient damage index is used as the damage correction coefficient; if the material transient damage index is ≤ 0.5, the square root of the material transient damage index is used as the damage correction coefficient.

[0085] Divide the degree of resonance excitation by 100 to obtain the resonance coefficient, and then divide the standard deviation of the shaft system response characteristic by the material fatigue limit of the target control object shaft to obtain the dynamic weight.

[0086] Multiply the characteristic strength coefficient by the damage correction coefficient and add it to the resonance coefficient, then multiply by the dynamic weight to obtain the shaft torsional vibration threat level.

[0087] In one embodiment, stress wave propagation characteristics are analyzed on the preprocessed dynamic torsional deformation signal to extract the stress wave components of a specific frequency band generated under impact load, thereby obtaining shaft system response characteristic quantities, including:

[0088] Modal decomposition is performed on the preprocessed dynamic torsional deformation signal to obtain the structural disturbance wave group. Specifically, this includes: the preprocessed dynamic torsional deformation signal is an amplitude sequence continuously acquired according to the sampling period; the amplitude attenuation rate of each data point in the preprocessed dynamic torsional deformation signal and its three preceding adjacent data points is calculated; the amplitude ratio of the same stress wave at two fixed distances in the shaft system is calculated; the amplitude ratio is divided by the fixed distance to obtain the stress wave attenuation value of the shaft system material; continuous signal segments with an amplitude attenuation rate lower than 20% of the stress wave attenuation value of the shaft system material are selected.

[0089] Obtain the trigger time of the load impact on the target controlled object; calculate the time difference between each signal segment and the trigger time of the load impact, and classify the signal segments with a time difference ≤ 2 sampling periods into one category to form multiple signal segment categories;

[0090] For each type of signal segment, divide its energy by the total energy of all categories to obtain the energy proportion coefficient. Multiply the amplitude of each data point in that category by the corresponding energy proportion coefficient to obtain the adjusted signal amplitude in each category.

[0091] Each signal segment category forms an independent perturbation wavelet group, and the set of all perturbation wavelet groups is the structured perturbation wavelet group. Each perturbation wavelet group itself is an amplitude sequence arranged according to the sampling period, and the amplitude in the sequence is the adjusted signal amplitude.

[0092] The energy transfer and dissipation of structural disturbance wave groups along the spatial path of the shaft system are analyzed, the degree of order of its transmission process is calculated, and the disturbance propagation entropy is obtained. Specifically, this includes: obtaining the propagation path of stress waves, dividing the shaft system into M equal-length spatial segments according to the propagation path of stress waves, where M represents the total number of spatial segments.

[0093] Calculate the deviation rate between the propagation velocity of each perturbation wave group in each segment and the average propagation velocity of all perturbation wave groups, and identify the spatial segments with a deviation rate exceeding 10%, which are the deviation segments; then calculate the energy dissipation rate of each perturbation wave group on the propagation path, and use the reciprocal of the energy dissipation rate as the dissipation correction coefficient; subtract the number of deviation segments from M and then divide by M to obtain the propagation order.

[0094] Multiply the propagation order by the dissipation correction factor and then divide by M to obtain the perturbation propagation entropy.

[0095] The structural disturbance wave group is fused with the disturbance propagation entropy to generate a shaft system response characteristic quantity representing the overall dynamic response to the impact load. Specifically, this includes: calculating the total energy of each disturbance wave subgroup and using the average total energy of all disturbance wave subgroups as the subgroup energy benchmark value.

[0096] Multiply the perturbation propagation entropy by the stress wave attenuation value of the shaft material to obtain the entropy correction coefficient;

[0097] Then, the amplitude sequence of each perturbation wave subgroup is multiplied by the entropy correction coefficient, and then multiplied by the ratio of the total energy of the perturbation wave subgroup to the subgroup energy reference value to generate the corrected subgroup amplitude.

[0098] Within the common sampling time range of all perturbation wave groups, for any sampling time, find the corrected subgroup amplitude of each perturbation wave group at that time, add these amplitudes together to obtain the superimposed amplitude at that time, traverse all sampling times to complete the superposition of amplitudes at all times, and finally form the superimposed amplitude sequence.

[0099] In the superimposed amplitude sequence, find the amplitude with the largest value and the amplitude with the smallest value, subtract the smallest amplitude from the largest amplitude, and use the absolute value of the calculation result as the characteristic quantity of the shaft system response.

[0100] By analyzing the stress wave propagation characteristics and performing mode decomposition on the preprocessed dynamic torsional deformation signal, the stress wave components of a specific frequency band under impact load are accurately extracted. Combined with the energy transfer orderliness of the shaft system spatial path, the shaft system response characteristic quantities are obtained, and the material transient damage index and resonance excitation degree are generated. Finally, the shaft system torsional vibration threat degree is obtained by fusion. This solution can accurately capture the transient changes of the broadband vibration response of mechanical structures without sacrificing response speed, accurately understand the shaft system torsional vibration risk and material damage trend caused by load impact, avoid resonance amplification, strengthen the transient adaptation of electromechanical coupling characteristics, and improve the control stability of three-phase asynchronous motors in transient scenarios of mining conveyor belts.

[0101] In one embodiment, the instantaneous power signal is calculated based on the preprocessed terminal voltage and stator current. The disordered fluctuation characteristics of the instantaneous power signal during the transient process are analyzed to obtain the magnetic field turbulence, including:

[0102] The instantaneous power signal is calculated based on the preprocessed terminal voltage and stator current. The fast pulsation component in the instantaneous power signal is decomposed to obtain the electromagnetic topological pulsation quantity. Specifically, the instantaneous values ​​of the preprocessed terminal voltage and stator current are multiplied point by point to obtain the original instantaneous power sequence.

[0103] Calculate the average power difference between each data point in the original instantaneous power sequence and the two data points before and after it to obtain the instantaneous power change rate. Use 1.8 times the median of the absolute values ​​of all instantaneous power change rates as the dynamic boundary value. Select data points whose instantaneous power change rate exceeds the dynamic boundary value, which are called boundary points. Calculate the interval between adjacent boundary data points. Group those with an interval ≤ 2 sampling periods into fast pulsation clusters. Calculate the cluster energy of each fast pulsation cluster. This energy is the sum of the squares of the instantaneous power change rates of all points within the fast pulsation cluster.

[0104] Divide the cluster energy by the number of supercritical points to obtain the cluster strength; multiply the maximum value of all cluster strengths by the number of clusters to obtain the electromagnetic topological pulsation.

[0105] The oscillation intensity of electromagnetic topological pulsations is analyzed, the correlation between its oscillation intensity and magnetic field saturation characteristics is calculated, and the magnetic circuit saturation oscillation index is obtained by combining the material transient damage index. Specifically, the oscillation period of electromagnetic topological pulsations is obtained, which is the sampling period between the peak values ​​of adjacent electromagnetic topological pulsations. The standard deviation of electromagnetic topological pulsations in all oscillation periods is divided by the mean of electromagnetic topological pulsations to obtain the oscillation disorder.

[0106] Calculate the average phase difference between the pre-processed terminal voltage and stator current, and divide the average by 90 degrees to obtain the saturation characteristic coefficient; subtract 0.5 from the material transient damage index to obtain the difference. If the difference is positive, multiply the saturation characteristic coefficient by (1 + difference) to obtain the saturation coefficient; if the difference is negative, multiply the saturation characteristic coefficient by (1 - absolute value of the difference) to obtain the saturation coefficient.

[0107] Multiplying the oscillation disorder by the saturation coefficient and then multiplying by 100 gives the magnetic circuit saturation oscillation index.

[0108] The response delay characteristics of the instantaneous power signal at the moment of load change are calculated to obtain the magnetic field reconstruction delay. Specifically, this includes: obtaining historical current impact characteristic factors and calculating the mean of historical current impact characteristic factors; taking the moment when the current impact characteristic factor exceeds twice the mean as the moment of load change; and taking the moment when the instantaneous power change rate is lower than the dynamic threshold as the moment when the magnetic field is stable.

[0109] Calculate the difference in sampling periods between the moment of load abrupt change and the moment of magnetic field stabilization;

[0110] For the continuous time period between the moment of load change and the moment of magnetic field stabilization, the cumulative sum of the instantaneous power change rate within this period is divided by the average instantaneous power change rate within the period to obtain the equivalent delay coefficient.

[0111] Multiplying the sampling period difference by the equivalent delay coefficient yields the magnetic field reconstruction delay.

[0112] The magnetic field disorder is generated by fusing the electromagnetic topological pulsation, the magnetic circuit saturation oscillation index, and the magnetic field reconstruction delay. Specifically, this involves: obtaining the historical maximum value of the electromagnetic topological pulsation; dividing the electromagnetic topological pulsation by the historical maximum value, dividing the magnetic circuit saturation oscillation index by 100, and dividing the magnetic field reconstruction delay by the sampling period difference to obtain the electromagnetic topological pulsation correction value, the magnetic circuit saturation oscillation correction value, and the magnetic field reconstruction delay correction value, respectively; dividing the magnetic circuit saturation oscillation correction value by the magnetic field reconstruction delay correction value to obtain the coupling weight; and multiplying the electromagnetic topological pulsation correction value by the coupling weight, and adding the average of the magnetic circuit saturation oscillation correction value and the magnetic field reconstruction delay correction value to obtain the magnetic field disorder.

[0113] By obtaining the original instantaneous power sequence, the rapid pulsation component can be accurately decomposed and the electromagnetic topological pulsation quantity can be obtained. At the same time, the magnetic field disorder can be generated, which can accurately capture the transient correlation between the high-frequency oscillation of electromagnetic torque caused by load impact and the dynamic distortion of stator current. The degree of magnetic field disorder fluctuation and reconstruction delay characteristics can be accurately understood, improving the response accuracy of frequency modulation control to transient scenarios in mining conveyor belts, effectively suppressing control deviations caused by magnetic field disorder, and ensuring the stability of three-phase asynchronous motor operation.

[0114] In one embodiment, the current impact characteristic factor, shaft torsional vibration threat level, and magnetic field disturbance level are aggregated to obtain an immunity stability index, including:

[0115] The electromagnetic-mechanical energy transfer path among the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree is established. The anomalies of the magnetic-mechanical energy transfer path are analyzed to obtain the instability propagation path coefficient. Specifically, based on the data of the first N-1 groups within the transient observation window, the ratio of current impact characteristic factor to magnetic field disorder degree and the ratio of magnetic field disorder degree to shaft torsional vibration threat degree are calculated respectively, and the historical electromagnetic side transfer ratio and historical magnetic-mechanical transfer ratio are obtained respectively.

[0116] Then calculate the ratio of the current impact characteristic factor to the magnetic field disorder and the ratio of the magnetic field disorder to the shaft torsional vibration threat at the current moment to obtain the electromagnetic side transmission ratio and the magneto-mechanical transmission ratio, respectively.

[0117] The first deviation rate is obtained by subtracting the historical average electromagnetic side transfer ratio from the electromagnetic side transfer ratio and then dividing by the historical average electromagnetic side transfer ratio; the second deviation rate is obtained by subtracting the historical average magnetic-mechanical transfer ratio from the magnetic-mechanical transfer ratio and then dividing by the historical average magnetic-mechanical transfer ratio.

[0118] For the first deviation rate and the second deviation rate, divide the number of times the two deviation rates exceed 20% by N, and then multiply by the reciprocal of the material transient damage index to obtain the instability propagation path coefficient.

[0119] Based on the instability propagation path coefficient, an anti-disturbance stability index is generated by analyzing the degree of erosion of the stable boundary by energy anomaly transfer. Specifically, this includes: using the first N-1 sets of data within the transient observation window as a basis, calculating the average product of the current impact characteristic factor, the shaft torsional vibration threat degree, and the magnetic field disorder degree, and using this as the anti-disturbance stability benchmark value; then calculating the ratio of the product of the current three sets of parameters to the anti-disturbance stability benchmark to obtain the energy erosion coefficient; multiplying the instability propagation path coefficient by the energy erosion coefficient to obtain the total erosion degree; and subtracting the total erosion degree from 1 and multiplying by (1 - material transient damage index) to obtain the anti-disturbance stability index.

[0120] By establishing electromagnetic-mechanical energy transfer paths based on current impact characteristic factors, shaft torsional vibration threat, and magnetic field disturbance, an instability propagation path coefficient is obtained. This coefficient is then combined with energy erosion degree and material transient damage index to generate an anti-disturbance stability index. This comprehensively reflects the multi-dimensional instability risk correlation caused by load impact, accurately captures the coupling effect of transient changes in electromechanical signals, enhances the ability to perceive abnormal energy transfer, effectively improves the impact resistance and operational stability of three-phase asynchronous motors in transient scenarios of mine conveyor belts, and optimizes control performance.

[0121] In one embodiment, the calculation process for the reference slip frequency is as follows:

[0122] Real-time acquisition of the real-time rotational speed and set operating frequency of the target controlled object; the set operating frequency is the operating frequency of the target controlled object set by the operator.

[0123] The real-time speed after preprocessing is calculated with the given operating frequency to obtain the reference slip frequency. Specifically, this includes: obtaining the inherent number of pole pairs of the target controlled object, multiplying the operating frequency by 60, and then dividing by the number of pole pairs of the motor to obtain the synchronous speed. For example, if the operating frequency is set to 50Hz and the number of pole pairs is 2, the synchronous speed is (50×60)÷2=1500 rpm.

[0124] Obtain the real-time speed sequence within the transient observation window; divide the standard deviation of the first N-1 real-time speeds in the real-time speed sequence by the synchronous speed to obtain the speed fluctuation correction coefficient; subtract the real-time speed from the synchronous speed to obtain the base speed difference;

[0125] Multiply the base speed difference by (1 + speed fluctuation correction coefficient) and then divide by the synchronous speed to obtain the reference slip frequency.

[0126] In one embodiment, the disturbance rejection stability index is mapped to a dynamic slip enhancement compensation value, and the slip enhancement compensation value is superimposed on the reference slip frequency to generate a frequency modulation control command for the target controlled object, including:

[0127] Based on the disturbance rejection stability index, the changing trend of the stability boundary is analyzed to obtain the dynamic stability margin. Specifically, this includes: taking the mean of the first N-1 groups of disturbance rejection stability indices within the transient observation window as the historical stability benchmark value; calculating the deviation rate between the current disturbance rejection stability index and the historical stability benchmark value; subtracting the deviation rate from 1 and then multiplying it by (1 - instability propagation path coefficient) to obtain the dynamic stability margin.

[0128] Based on the dynamic stability margin, a mapping relationship between the slip frequency compensation and the electromagnetic torque increment is established to generate an adaptive slip compensation. Specifically, this includes: dividing the instantaneous power change rate by the synchronous speed to obtain the electromagnetic torque increment; dividing the dynamic stability margin by the shaft torsional vibration threat level as the stability-vibration compatibility coefficient; and using the reciprocal of the current impact characteristic factor as the impact suppression coefficient.

[0129] Multiply the stability-vibration compatibility coefficient by the shock suppression coefficient, then multiply by the electromagnetic torque increment, and then multiply by (the reference slip frequency divided by the set operating frequency) to obtain the adaptive slip compensation amount.

[0130] The adaptive slip compensation amount and the reference slip frequency are superimposed and optimized in the field to generate the frequency modulation control command of the target control object. Specifically, this includes: calculating the absolute value of the difference between the magnetic field disorder and the dynamic stability margin, and subtracting the absolute value of the difference from 1 to obtain the field adaptation coefficient.

[0131] The adaptive slip compensation is multiplied by the field adaptation coefficient and then added to the reference slip frequency to obtain the output frequency of the target controlled object.

[0132] Obtain the rated voltage and rated frequency of the target controlled object, divide the rated voltage by the rated frequency, and multiply by the output frequency to obtain the output voltage of the target controlled object;

[0133] Among them, the output frequency and the output voltage together constitute the frequency modulation control command of the target controlled object.

[0134] By combining the dynamic stability margin with the electromagnetic torque increment, stability-vibration coordination coefficient, and impact suppression coefficient, an adaptive slip compensation is generated. After optimization by the field adaptation coefficient, it is superimposed with the reference slip frequency to output frequency modulation control commands. This can accurately adapt to the load impact in transient scenarios of mining conveyor belts, effectively suppress the dynamic distortion of stator current and high-frequency oscillation of electromagnetic torque, reduce the wideband vibration response of mechanical structures, improve the real-time performance and accuracy of frequency modulation control, strengthen the impact resistance of three-phase asynchronous motors, and ensure the stability and control effect of three-phase asynchronous motor operation during transient processes.

[0135] In one embodiment, a three-phase asynchronous motor frequency modulation control system based on electromechanical signal analysis is applied to the aforementioned three-phase asynchronous motor frequency modulation control method based on electromechanical signal analysis, including:

[0136] The current analysis unit is used to acquire the instantaneous values ​​of the three-phase current of the stator of the target controlled object in real time, synthesize the current vector based on the instantaneous values ​​of the three-phase current, identify the positive and negative abrupt changes in the synthesized current vector, and obtain the current impact characteristic factor.

[0137] The vibration analysis unit is used to acquire the dynamic torsional deformation signal of the target control object shaft in real time, extract the torsional vibration alternating component related to the load impact from the preprocessed dynamic torsional deformation signal, analyze the instantaneous vibration intensity of the shaft system based on the torsional vibration alternating component, and obtain the torsional vibration threat level of the shaft system.

[0138] The signal control unit is used to acquire the terminal voltage and stator current of the target controlled object in real time, calculate the instantaneous power signal based on the preprocessed terminal voltage and stator current, analyze the disordered fluctuation characteristics of the instantaneous power signal in the transient process, and obtain the magnetic field disorder.

[0139] The disturbance rejection control unit is used to aggregate the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree to obtain the disturbance rejection stability index;

[0140] The frequency modulation control unit is used to map the disturbance rejection stability index to a dynamic slip enhancement compensation value, and to superimpose the slip enhancement compensation value with the reference slip frequency to generate a frequency modulation control command for the target controlled object.

[0141] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis, characterized in that, include: Step S1: Real-time acquisition of the instantaneous values ​​of the three-phase current of the stator of the target controlled object; synthesis of the current vector based on the instantaneous values ​​of the three-phase current; identification of the positive and negative abrupt changes in the synthesized current vector; and obtaining the current impact characteristic factor. Step S2: Real-time acquisition of dynamic torsional deformation signal of the target controlled object shaft; extraction of torsional vibration alternating component related to load impact from preprocessed dynamic torsional deformation signal; analysis of instantaneous vibration intensity of shaft system based on torsional vibration alternating component to obtain shaft system torsional vibration threat level. Step S3: Real-time acquisition of the terminal voltage and stator current of the target controlled object; calculation of the instantaneous power signal based on the preprocessed terminal voltage and stator current; analysis of the disordered fluctuation characteristics of the instantaneous power signal in the transient process; and obtaining the magnetic field disorder. Step S4: Combine the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disturbance degree to obtain the disturbance rejection stability index, including: The electromagnetic-mechanical energy transfer path among the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree is established. The anomalies of the electromagnetic-mechanical energy transfer path are analyzed to obtain the instability propagation path coefficient. Based on the instability propagation path coefficient, an anti-disturbance stability index is generated by analyzing the degree of erosion of the stability boundary by energy anomaly transfer. Step S5: Map the disturbance rejection stability index to a dynamic slip enhancement compensation value, and superimpose the slip enhancement compensation value with the reference slip frequency to generate a frequency modulation control command for the target controlled object, including: Based on the disturbance resistance stability index, the changing trend of the stability boundary is analyzed to obtain the dynamic stability margin; Based on the dynamic stability margin, a mapping relationship between the slip frequency compensation and the electromagnetic torque increment is established to generate an adaptive slip compensation. The adaptive slip compensation amount and the reference slip frequency are superimposed and optimized in the field to generate the frequency modulation control command for the target controlled object.

2. The frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to claim 1, characterized in that, Based on the instantaneous values ​​of the three-phase currents, the synthesized current vector is analyzed, identifying positive and negative abrupt changes in the synthesized current vector to obtain current impact characteristic factors, including: The instantaneous values ​​of the three-phase currents are orthogonally decomposed and current vectors are constructed. The instantaneous modal amplitudes of the current vectors are then calculated. Set a transient observation window, and calculate the instantaneous imbalance deviation between the instantaneous modal amplitude and the historical reference baseline within the transient observation window; Within this transient observation window, based on the characteristics of the instantaneous imbalance deviation, the weighted cumulative amount of the positive imbalance deviation and the negative imbalance deviation are calculated respectively, and the positive impact intensity and the negative impact intensity are obtained respectively.

3. The frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to claim 2, characterized in that, Based on the instantaneous values ​​of three-phase currents, a synthesized current vector is obtained, identifying positive and negative abrupt changes in the synthesized current vector to derive current impact characteristic factors. This also includes: The covariance relationship between positive and negative impact intensity is analyzed to obtain the impact covariance coefficient; The positive impact intensity, negative impact intensity, and impact covariance coefficient are fused to generate the current impact characteristic factor.

4. The frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to claim 3, characterized in that, The torsional vibration alternating component related to the load impact is extracted from the preprocessed dynamic torsional deformation signal. Based on the torsional vibration alternating component, the instantaneous vibration intensity of the shaft system is analyzed to obtain the torsional vibration threat level of the shaft system, including: Stress wave propagation characteristics were analyzed on the preprocessed dynamic torsional deformation signal, and the frequency band stress wave components generated under impact load were extracted to obtain the shaft system response characteristic quantities. Based on the characteristic quantities of shaft system response, the stress cycle characteristics of the system within the transient observation window are analyzed to obtain the transient damage index of the material. The correlation between the frequency distribution of shaft system response characteristic quantities and shaft system characteristics is analyzed, and the coupling strength between positive impact intensity, negative impact intensity and current impact characteristic factor is calculated to obtain the resonant excitation degree. The shaft system response characteristics, material transient damage index, and resonant excitation degree are fused in multiple dimensions to generate the shaft system torsional vibration threat level.

5. The frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to claim 4, characterized in that, Stress wave propagation characteristics were analyzed on the preprocessed dynamic torsional deformation signal to extract the frequency band stress wave components generated under impact load, thus obtaining shaft system response characteristic quantities, including: Modal decomposition was performed on the preprocessed dynamic torsional deformation signal to obtain the structural disturbance wave group; The energy transfer and dissipation of the structural disturbance wave group along the axis spatial path are analyzed, the degree of order in its transmission process is calculated, and the disturbance propagation entropy is obtained. By fusing the structural disturbance wave group with the disturbance propagation entropy, a shaft system response characteristic quantity representing the overall dynamic response to the impact load is generated.

6. The frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to claim 4, characterized in that, The instantaneous power signal is calculated based on the preprocessed terminal voltage and stator current. The disordered fluctuation characteristics of the instantaneous power signal during the transient process are analyzed to obtain the magnetic field turbulence, including: The instantaneous power signal is calculated based on the preprocessed terminal voltage and stator current. The fast pulsation component in the instantaneous power signal is decomposed to obtain the electromagnetic topological pulsation quantity. The oscillation intensity of electromagnetic topological pulsations is analyzed, the correlation between its oscillation intensity and magnetic field saturation characteristics is calculated, and the magnetic circuit saturation oscillation index is obtained by combining the material transient damage index. The response delay characteristics of the instantaneous power signal at the moment of load change are calculated to obtain the magnetic field reconstruction delay. The electromagnetic topological pulsation, magnetic circuit saturation oscillation index, and magnetic field reconstruction delay are combined to generate the magnetic field disorder.

7. The frequency modulation control method for a three-phase asynchronous motor based on electromechanical signal analysis according to claim 1, characterized in that, The calculation process for the reference slip frequency is as follows: Real-time acquisition of the target controlled object's rotational speed and set operating frequency; The reference slip frequency is obtained by calculating the real-time rotational speed and the set operating frequency after preprocessing.

8. A frequency control system for a three-phase asynchronous motor based on electromechanical signal analysis, applied to the frequency control method for a three-phase asynchronous motor based on electromechanical signal analysis as described in any one of claims 1-7, characterized in that, include: The current analysis unit is used to acquire the instantaneous values ​​of the three-phase current of the stator of the target controlled object in real time, synthesize the current vector based on the instantaneous values ​​of the three-phase current, identify the positive and negative abrupt changes in the synthesized current vector, and obtain the current impact characteristic factor. The vibration analysis unit is used to acquire the dynamic torsional deformation signal of the target control object shaft in real time, extract the torsional vibration alternating component related to the load impact from the preprocessed dynamic torsional deformation signal, analyze the instantaneous vibration intensity of the shaft system based on the torsional vibration alternating component, and obtain the torsional vibration threat level of the shaft system. The signal control unit is used to acquire the terminal voltage and stator current of the target controlled object in real time, calculate the instantaneous power signal based on the preprocessed terminal voltage and stator current, analyze the disordered fluctuation characteristics of the instantaneous power signal in the transient process, and obtain the magnetic field disorder. The disturbance rejection control unit is used to aggregate the current impact characteristic factor, shaft torsional vibration threat degree, and magnetic field disorder degree to obtain the disturbance rejection stability index; The frequency modulation control unit is used to map the disturbance rejection stability index to a dynamic slip enhancement compensation value, and to superimpose the slip enhancement compensation value with the reference slip frequency to generate a frequency modulation control command for the target controlled object.

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