Multi-motor coordinated control method and system based on speed compensation

Abstract

The present invention discloses a multi-motor collaborative control method and system based on speed compensation, which specifically relates to the field of industrial multi-motor control technology, and is used to solve the problems of compensation misalignment and system oscillation caused by existing parameter asynchronous drift conditions; by real-time acquisition of the current and voltage signals of each motor and online solution of the dynamic resistance and inductance parameters; constructing a parameter variation causal entropy network to quantify the causal influence of single-machine anomalies on the system, and synchronously generating a system collaborative vulnerability index to achieve risk penetration perception; when detecting low-frequency oscillations, extracting harmonic components to establish a sensitivity grading model for parameter mismatch and oscillation frequency; integrating the leading compensation role based on causal entropy allocation to focus on key disturbance sources, generating dynamic limiting instructions based on collaborative vulnerability to adapt system stability, and optimizing resource allocation by allocating resonance suppression priorities according to sensitivity levels; finally reconstructing the torque instructions and issuing them synchronously to achieve precise transmission of compensation energy across devices and eliminate mechanical coupling oscillations.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial multi-motor control, and more particularly, to a multi-motor coordinated control method and system based on speed compensation. Background Art

[0002] In industrial multi-motor coordinated control systems, real-time compensation based on speed feedback is a key approach to ensuring synchronization accuracy. Existing methods rely on preset parameter models, such as motor resistance and inductance, to generate compensation values ​​and adjust torque output to eliminate speed deviations. However, in actual operation, motor parameters continuously drift due to independent factors such as local temperature rise and differences in magnetic saturation. Furthermore, due to the varying physical locations and cooling conditions of each motor, parameter drift exhibits significant asynchrony.

[0003] The current speed compensation mechanism adheres to the preset parameter model, which causes systemic defects under the condition of asynchronous drift of multi-motor parameters: the compensator cannot adapt to the real-time dynamic characteristics of each motor, resulting in response lag or overcompensation; the torque conflict caused by compensation misalignment is transmitted through mechanical coupling, causing system-level low-frequency oscillation and accumulation of synchronization errors. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a multi-motor coordinated control method and system based on speed compensation to solve the problems raised in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The multi-motor coordinated control method based on speed compensation includes:

[0007] S1, real-time acquisition of the operating current signal and terminal voltage signal of each motor in the system;

[0008] S2. Calculate the real-time resistance and inductance parameters of each motor online based on the operating current signal and terminal voltage signal;

[0009] S3. Based on the real-time resistance parameters and real-time inductance parameters, the transfer entropy algorithm is used to calculate the causal entropy of parameter changes between the motors, and the system collaborative vulnerability is determined based on Granger causal network analysis;

[0010] S4. When low-frequency oscillation is detected in the system, extract the harmonic components of the operating current signal at the detected low-frequency oscillation frequency, and analyze the sensitivity level of each motor parameter mismatch to the current oscillation frequency;

[0011] S5. Assign the leading compensation role according to the causal entropy of parameter variation, generate dynamic limiting instructions according to the system collaborative vulnerability, assign resonance suppression priority according to the sensitivity level, and integrate them into a collaborative compensation strategy;

[0012] S6. Reconstruct the output torque command of the speed compensator according to the collaborative compensation strategy and send it to the corresponding motor for execution simultaneously.

[0013] Furthermore, the operating current signal and terminal voltage signal of each motor in the system are collected in real time, including:

[0014] Synchronously sample the instantaneous current value of each motor's three-phase winding to generate a running current signal;

[0015] The instantaneous value of the input voltage of each motor drive terminal is synchronously sampled to generate a terminal voltage signal.

[0016] Furthermore, the sampling of the operating current signal and the terminal voltage signal maintains the same time reference and is updated and stored in a continuous cycle.

[0017] Furthermore, the real-time resistance parameters and inductance parameters of each motor are calculated online based on the operating current signal and the terminal voltage signal, including:

[0018] A parameter calculation model is established based on the motor stator voltage equation. The parameter calculation model expresses the terminal voltage signal as a function of the operating current signal and its derivative.

[0019] Perform central difference calculation on the operating current signal of multiple consecutive sampling periods to obtain current change rate data;

[0020] Input the terminal voltage signal, operating current signal and current change rate data into the parameter solution model to construct an overdetermined equation group;

[0021] Iteratively solving the overdetermined equations by using the recursive least squares method to update the estimated values ​​of the real-time resistance parameters and the real-time inductance parameters;

[0022] When the relative change of the estimated value is less than the convergence threshold for a set number of consecutive times, the real-time resistance parameter and the real-time inductance parameter are output.

[0023] Furthermore, based on the real-time resistance and inductance parameters, the transfer entropy algorithm is used to calculate the causal entropy of parameter variations between the motors. The system collaborative vulnerability is then determined based on Granger causal network analysis, including:

[0024] Extract the real-time resistance parameters and real-time inductance parameters of each motor according to the set time window to form a parameter time series;

[0025] The transfer entropy is calculated for the parameter time series of each two motors, and the delay order of the transfer entropy is determined according to the minimum point of the mutual information;

[0026] The transfer entropy value is normalized to the parameter variation causal entropy, which represents the parameter variation transmission intensity.

[0027] A directed weighted network is constructed based on the causal entropy of parameter variation among all motors, where nodes represent motors and edge weights represent the causal entropy of parameter variation;

[0028] Perform Granger causality test on the network and add causal edges when the test statistic exceeds the set significance threshold;

[0029] The variance of the betweenness centrality of network nodes is calculated as the system collaborative vulnerability.

[0030] Furthermore, when low-frequency oscillation is detected in the system, the harmonic components of the operating current signal at the detected low-frequency oscillation frequency are extracted, and the sensitivity level of each motor parameter mismatch to the current oscillation frequency is analyzed, including:

[0031] Identify low-frequency components in the operating current signal whose amplitude exceeds the set ratio of the fundamental amplitude through spectrum analysis. If the low-frequency component frequency is within the set low-frequency range, determine that low-frequency oscillation exists.

[0032] When there is low-frequency oscillation, the harmonic components of the positive and negative set percentage bandwidth are extracted with the oscillation frequency as the center;

[0033] Based on the real-time resistance parameters and real-time inductance parameters, the relative deviation between the measured parameters of each motor and the reference parameters is calculated as the parameter mismatch;

[0034] A linear mapping relationship between parameter mismatch and harmonic component amplitude is established, and the sensitivity coefficient is obtained through least square fitting;

[0035] According to the absolute value of the sensitivity coefficient, it is divided into three levels: high sensitivity, medium sensitivity and low sensitivity.

[0036] Furthermore, the leading compensation role is assigned according to the parameter variation causal entropy, dynamic limiting instructions are generated according to the system collaborative vulnerability, and resonance suppression priorities are assigned according to the sensitivity level. These are integrated into a collaborative compensation strategy, including:

[0037] Select motors based on the parameter variation causal entropy values ​​from high to low, and assign the motor with the largest parameter variation causal entropy value as the leading compensation role;

[0038] Read the system collaborative vulnerability and generate a dynamic limit instruction based on the system collaborative vulnerability. The limit amplitude of the dynamic limit instruction is positively correlated with the system collaborative vulnerability.

[0039] Assign resonance suppression priorities according to sensitivity levels from high sensitivity level to low sensitivity level;

[0040] The compensation action instructions, dynamic limit instructions and resonance suppression priority instructions of the dominant compensation role are strategically integrated to generate a collaborative compensation strategy.

[0041] Furthermore, the leading compensation role responds to the dynamic limit instruction first when performing compensation action, and the remaining motors perform compensation actions according to the resonance suppression priority.

[0042] Furthermore, the output torque command of the speed compensator is reconstructed according to the coordinated compensation strategy and synchronously sent to the corresponding motor for execution, including:

[0043] Analyze the leading compensation role instruction in the collaborative compensation strategy and determine the compensation torque weight coefficient of the leading motor;

[0044] Convert the dynamic limit command into the torque output upper limit value, and the upper limit value serves as the amplitude constraint of all motor torque commands;

[0045] The torque response timing of each motor is allocated according to the resonance suppression priority, and the motor with the highest priority is allocated the earlier execution time slot;

[0046] reconstructing the output torque command of the speed compensator based on the compensation torque weight coefficient, the torque output upper limit value and the torque response time sequence;

[0047] Synchronously send the reconstructed output torque command to each motor controller via the real-time communication bus;

[0048] The output torque command of the dominant motor is applied with the torque weight coefficient first, and the remaining motors are applied in the order of resonance suppression priority.

[0049] In another aspect, the present invention provides a multi-motor coordinated control system based on speed compensation, comprising:

[0050] Signal acquisition module, used to collect the operating current signal and terminal voltage signal of each motor in the system in real time;

[0051] The parameter calculation module is used to calculate the real-time resistance parameters and inductance parameters of each motor online based on the operating current signal and terminal voltage signal;

[0052] The entropy network analysis module is used to calculate the causal entropy of parameter variations between motors based on real-time resistance and inductance parameters using a transfer entropy algorithm, and to determine the system's collaborative vulnerability based on Granger causal network analysis.

[0053] The oscillation sensitivity analysis module is used to extract the harmonic components of the operating current signal at the detected low-frequency oscillation frequency when low-frequency oscillation is detected in the system, and analyze the sensitivity level of each motor parameter mismatch to the current oscillation frequency;

[0054] A strategy generation module is used to assign leading compensation roles based on parameter variation causal entropy, generate dynamic limiting instructions based on system collaborative vulnerability, assign resonance suppression priorities based on sensitivity levels, and integrate them into a collaborative compensation strategy;

[0055] The instruction reconstruction module is used to reconstruct the output torque instruction of the speed compensator according to the collaborative compensation strategy, and synchronously send it to the corresponding motor for execution.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. By calculating the dynamic resistance and inductance parameters of each motor in real time, the rigid constraints of the traditional preset parameter model are broken through, the compensation benchmark inaccuracy problem caused by asynchronous parameter drift is eliminated, and a parameter variation causal entropy network is constructed based on the transfer entropy algorithm. The impact of single motor parameter drift on the overall system is accurately quantified, and the system collaborative vulnerability index is simultaneously generated to achieve penetrating perception from local anomalies to system risks. When low-frequency oscillation is detected, a device-level oscillation response classification model is established through sensitivity mapping of harmonic components and parameter mismatch, forming a direct connection between fault tracing and suppression targets.

[0058] 2. The collaborative compensation strategy integrates three complementary decision-making mechanisms: the responsibility allocation dominated by parameter variation causal entropy focuses on key disturbance sources, the dynamic limit driven by system collaborative vulnerability adapts the system stability margin in real time, the resonance suppression priority ranked by sensitivity level realizes the spatiotemporal optimization configuration of compensation resources, and the torque command reconstruction transforms the electrical compensation strategy into a mechanical control action. The weight coefficient binding and execution sequence decoupling ensure the accurate transmission of compensation energy across devices, the synchronous delivery mechanism eliminates the distributed execution sequence deviation, and the role rotation strategy avoids the risk of single-point overload, ultimately achieving the global dynamic optimization of speed compensation in multi-motor collaborative control. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart of the multi-motor coordinated control method based on speed compensation of the present invention;

[0060] Figure 2 It is a structural diagram of the multi-motor coordinated control system based on speed compensation of the present invention. DETAILED DESCRIPTION

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0062] Example 1: Figure 1 The present invention provides a multi-motor coordinated control method based on speed compensation, including:

[0063] S1, real-time acquisition of the operating current signal and terminal voltage signal of each motor in the system;

[0064] S2. Calculate the real-time resistance and inductance parameters of each motor online based on the operating current signal and terminal voltage signal;

[0065] S3. Based on the real-time resistance parameters and real-time inductance parameters, the transfer entropy algorithm is used to calculate the causal entropy of parameter changes between the motors, and the system collaborative vulnerability is determined based on Granger causal network analysis;

[0066] S4. When low-frequency oscillation is detected in the system, extract the harmonic components of the operating current signal at the detected low-frequency oscillation frequency, and analyze the sensitivity level of each motor parameter mismatch to the current oscillation frequency;

[0067] S5. Assign the leading compensation role according to the causal entropy of parameter variation, generate dynamic limiting instructions according to the system collaborative vulnerability, assign resonance suppression priority according to the sensitivity level, and integrate them into a collaborative compensation strategy;

[0068] S6. Reconstruct the output torque command of the speed compensator according to the collaborative compensation strategy and send it to the corresponding motor for execution simultaneously.

[0069] S1. Real-time acquisition of the operating current signal and terminal voltage signal of each motor in the system. The specific implementation is as follows:

[0070] Real-time acquisition of the operating current and terminal voltage signals of each motor in the system is achieved through the following method: Current sensors are used to measure the current in each motor's three-phase winding. These current sensors utilize a closed-loop Hall effect principle, with a measurement bandwidth determined by the motor's maximum operating frequency and a lower limit of twice the motor's maximum electrical frequency. For example, when the motor's maximum electrical frequency is 500 Hz, the measurement bandwidth is set to greater than 1000 Hz. The analog current signals output by the current sensors are filtered through a signal conditioning circuit for anti-aliasing. The anti-aliasing filter's cutoff frequency is set to half the motor control sampling frequency based on the Nyquist sampling theorem. The filtered signals are then digitized and sampled at fixed intervals using an analog-to-digital converter (ADC). The instantaneous current sampling for each motor's three-phase winding is synchronized by a single controller, ensuring that the time deviation between the three-phase current sampling times is less than 1% of the controller's instruction cycle, thereby generating time-aligned operating current signals.

[0071] The terminal voltage signal is acquired using a differential voltage detection circuit directly connected to the power output of the motor driver, measuring the potential difference between the motor's three-phase input terminals and the negative end of the DC bus. After voltage division and attenuation, isolation and amplification, the voltage signal is input to an analog-to-digital converter for synchronous sampling. The trigger signal for voltage sampling and current sampling uses a synchronous pulse from the same controller, ensuring that the operating current signal and terminal voltage signal of the same motor have exactly the same timestamp within each sampling cycle. To eliminate switching noise interference, a second-order low-pass filter is inserted before the voltage signal enters the analog-to-digital converter. The filter's cutoff frequency must be set to both be greater than ten times the motor's fundamental frequency and less than half the switching frequency. For example, when the motor's fundamental frequency is 50 Hz and the switching frequency is 8 kHz, the cutoff frequency is set to 3 kHz.

[0072] The sampling of the operating current and terminal voltage signals maintains the same time base through the following mechanism: a high-precision timer is embedded within the controller, and the timer clock source is a temperature-compensated crystal oscillator with a frequency stability of better than 5 parts per million. At the beginning of each sampling cycle, the timer generates a global synchronization interrupt signal, which is transmitted via a hardware trigger line to the current and voltage sampling modules of all motors, triggering the analog-to-digital converters of each channel to start conversion simultaneously. When the converted data is written to the dual-port memory, the memory address pointer is uniformly updated by the timer interrupt service routine, ensuring that the operating current and terminal voltage signals of all motors have the same time stamp sequence.

[0073] The sampled data is updated and stored in a continuous cycle using a circular buffer mechanism: a fixed-length data storage area is allocated in the controller's memory and managed on a first-in, first-out basis. The depth of the storage area is set based on the system's dynamic response requirements, specifically the number of sampling points required to cover ten times the motor's electromagnetic time constant. For example, if the motor's electromagnetic time constant is 10 milliseconds and the sampling period is 100 microseconds, the storage area depth is set to 1000 data sets. During data updates, the newly sampled operating current and terminal voltage signals are written to the buffer's current pointer position in chronological order, and the pointer automatically increments to the next storage location. When the pointer reaches the end of the storage area, it automatically returns to the starting address, forming a circular overwrite.

[0074] The current sensor must meet the following technical specifications: a measurement range with a lower limit of 150% and an upper limit of 200% of the motor's rated current; a linearity error of less than 0.5% of the full scale; and a response time of less than one-fifth of the sampling period. For example, for a motor rated at 50 amperes, the current sensor measurement range is set to 0 to 100 amperes. The anti-aliasing filter in the signal conditioning circuit utilizes a Butterworth low-pass filter topology, with a passband ripple of less than 0.1 dB and a stopband attenuation greater than 60 dB. A phase compensation circuit optimizes group delay characteristics, ensuring a phase difference measurement error of less than 0.1 degrees between the phase current signals.

[0075] The parameters of the analog-to-digital converter are configured according to the following rules: the sampling resolution must be no less than 12 bits to meet control accuracy requirements; the sampling rate must be at least twenty times the motor's fundamental frequency. For example, when the motor's fundamental frequency is 100 Hz, the sampling rate should be set to no less than 2 kHz. A dedicated hardware trigger line is used for synchronous sampling, and signal transmission delay is controlled to less than 1 nanosecond using equal-length wiring. When storing data, the operating current signal at each sampling point contains the instantaneous values ​​of the three-phase currents, and the terminal voltage signal contains the instantaneous values ​​of the three-phase voltages. The storage format is 32-bit floating-point numbers, and the time stamp information uses a 64-bit microsecond timestamp.

[0076] A data protection mechanism is implemented for the continuous cycle storage area of ​​the operating current and terminal voltage signals: when the background program reads historical data, the storage unit corresponding to that cycle is locked and writes are prohibited. The storage area is managed using a dual-pointer structure: the head pointer indicates the location of the latest data, and the tail pointer indicates the location of the oldest data. If a storage area overflow is detected, a data compression algorithm is activated: linear interpolation is used to reduce the sampling rate of the earliest 50% of historical data to half the original sampling rate, and a data compression flag is set for subsequent processing.

[0077] S2. Calculate the real-time resistance and inductance parameters of each motor online based on the operating current signal and terminal voltage signal. The specific implementation is as follows:

[0078] The specific implementation process for online calculation of each motor's real-time resistance and inductance parameters based on the operating current and terminal voltage signals is as follows: The stator voltage equation of the permanent magnet synchronous motor in a rotating coordinate system is used as the basis for the parameter calculation model. This model decomposes the terminal voltage signal into d-axis and q-axis components. The d-axis component is equal to the d-axis component of the operating current signal multiplied by the real-time resistance parameter plus the derivative of the d-axis component of the operating current signal multiplied by the real-time inductance parameter minus the electrical angular velocity multiplied by the real-time inductance parameter multiplied by the q-axis component of the operating current signal. The q-axis component is equal to the q-axis component of the operating current signal multiplied by the real-time resistance parameter plus the derivative of the q-axis component of the operating current signal multiplied by the real-time inductance parameter plus the electrical angular velocity multiplied by the real-time inductance parameter multiplied by the d-axis component of the operating current signal plus the permanent magnet flux linkage multiplied by the electrical angular velocity. The electrical angular velocity is calculated by multiplying the mechanical angular velocity measured by the motor's rotor position sensor by the number of motor pole pairs. The mechanical angular velocity is acquired in real time by an incremental encoder mounted on the motor shaft.

[0079] The process for performing a central difference calculation on the operating current signal over multiple consecutive sampling cycles to obtain current rate of change data is as follows: The operating current signal for the current moment and the two adjacent sampling cycles is read from the data storage area, and a separate calculation is performed for each of the three phases. For the current rate of change calculation at the intermediate sampling point k, the instantaneous current value at the previous sampling point k-1 is subtracted from the instantaneous current value at the next sampling point k+1, and this difference is divided by twice the sampling cycle time to obtain the current rate of change. For example, when the sampling cycle is 100 microseconds, the current rate of change is equal to the instantaneous value of the operating current signal at sampling point k+1 minus the instantaneous value of the operating current signal at sampling point k-1, divided by 200 microseconds. The calculation is performed using a 32-bit floating-point unit, and the data buffer is updated after each calculation.

[0080] The steps of inputting the terminal voltage signal, operating current signal and current change rate data into the parameter solution model to construct an overdetermined equation group include: selecting data from 20 consecutive sampling points to form an overdetermined equation group, and each sampling point corresponds to two equations that describe the d-axis and q-axis relationships respectively. Each equation contains five known quantities: the instantaneous value of the d-axis component of the terminal voltage signal at the current sampling point, the instantaneous value of the q-axis component of the terminal voltage signal, the instantaneous value of the d-axis component of the operating current signal, the instantaneous value of the q-axis component of the operating current signal, and the instantaneous value of the electrical angular velocity, as well as two unknown parameters: the real-time resistance parameter and the real-time inductance parameter. When constructing the equation group, data points during periods of drastic current changes are automatically excluded. The drastic change determination condition is that the absolute value of the current change rate exceeds three times the rated current change rate of the motor.

[0081] The method for updating parameter estimates by iteratively solving an overdetermined system of equations using the recursive least squares method is as follows: The initial estimates of the real-time resistance and inductance parameters are initialized to the motor's factory nominal values, and the covariance matrix is ​​initialized to a 1000-fold identity matrix. Each time new sample data arrives, the prediction residuals between the new data vector and the current parameter estimates are calculated. A gain matrix is ​​calculated based on the current covariance matrix and the data vector. The gain matrix and residuals are used to update the parameter estimates, and finally, the covariance matrix is ​​updated. During the iteration process, the forgetting factor is set as a dynamically adjustable parameter, initially set to 0.98, and automatically adjusted based on the rate of change of the residuals.

[0082] When the relative change in the parameter estimate is less than the convergence threshold for a set number of consecutive times, the following logic is used: After each parameter update, the relative change between the current estimate and the previous estimate is calculated. The relative change is defined as the absolute value of the difference between the two estimates divided by the absolute value of the previous estimate. The convergence threshold is set to 0.001, and the number of consecutive times this condition is met is set to 5. For example, if the relative change in the real-time resistance parameter is less than 0.001 for five consecutive iterations, convergence is determined. After convergence, the parameter estimate is locked and output to the data bus, and the iteration counter is reset. If convergence has not occurred after 200 iterations, the median of the results of the most recent 50 iterations is used as the output value.

[0083] A data preprocessing step has been added to the current rate of change calculation process: a three-point sliding average filter is applied to the raw operating current signal, with the filter window covering the current sampling point and one sampling point before and after it. The filtered current value is used in the center difference calculation, effectively suppressing high-frequency measurement noise. When an abnormal jump in the current rate of change data is detected, the jump determination threshold is set to five times the difference in current changes between adjacent sampling points, and the current rate of change is automatically recalculated using an alternate sampling point.

[0084] The numerical stabilization measure for covariance matrix updates in the recursive least squares method is to monitor the condition number of the covariance matrix in real time. When the condition number is greater than 1,000,000, a perturbation value of 1% of the average value of the diagonal elements is added to the main diagonal elements of the covariance matrix. The adaptive adjustment rule for the forgetting factor is to calculate the rate of change of the residual root mean square value over the last 10 iterations. If the rate of change is consistently positive, the forgetting factor is reduced by 0.001 to a lower limit of 0.95; if the rate of change is consistently negative, the forgetting factor is increased by 0.001 to an upper limit of 0.99.

[0085] Parameter validity is verified before output: the real-time resistance parameter value must be within the resistance variation range corresponding to the motor's allowable operating temperature, which is 80% to 120% of the nominal value. The real-time inductance parameter value must be within the allowable range of the motor's magnetic saturation characteristics, which is 60% to 150% of the nominal value. If a parameter exceeds the allowable range, the average of the last 10 valid iterations is used as the replacement, and the parameter abnormality flag is triggered.

[0086] The overdetermined equation system is constructed using a matrix block technique: data from 20 consecutive sampling points are arranged in chronological order into a 40-row, 2-column observation matrix. The first column of the observation matrix contains the d-axis and q-axis components of the operating current signal for all sampling points, and the second column contains the corresponding current rate of change data. The terminal voltage signal vector consists of 40 elements, alternating between the instantaneous values ​​of the d-axis and q-axis components of the terminal voltage signal. Invalid data points are automatically skipped during equation construction. The criterion for invalid points is that the absolute value of the current rate of change exceeds twice the maximum allowable motor current rate of change.

[0087] The permanent magnet flux parameters in the parameter solution model use offline calibration values. The calibration method is to measure the back EMF constant with the motor in the no-load state and divide it by the electrical angular velocity. When converting to electrical angle, the mechanical angular velocity is multiplied by the number of motor pole pairs. The number of motor pole pairs is fixed to a set value based on the motor model. For example, the number of pole pairs for a 4-pole motor is 2. The permanent magnet flux values ​​required for back EMF calculations are stored in non-volatile memory and used as known constants during the parameter solution process.

[0088] S3. Based on the real-time resistance parameters and real-time inductance parameters, the transfer entropy algorithm is used to calculate the causal entropy of parameter changes between the motors, and the system collaborative vulnerability is determined based on Granger causal network analysis. The specific implementation is as follows:

[0089] The specific implementation process for extracting the real-time resistance parameters and real-time inductance parameters of each motor according to a set time window to form a parameter time series is as follows: a fixed time window is set. The time window length is determined by the motor's thermal time constant and is between one-fifth and one-tenth of the thermal time constant. For example, when the motor's thermal time constant is 30 minutes, the time window length is set to 3 minutes. The real-time resistance parameters and real-time inductance parameters of all sampling points within the time window are extracted from the data storage area in the order of the sampling period, with each sampling point corresponding to a set of parameter values. The real-time resistance parameters and real-time inductance parameters each form an independent time series, and the length of the time series is equal to the number of sampling points contained in the time window. When the sampling period is 100 milliseconds, a 3-minute time window corresponds to 1,800 sampling points. Time series data storage is managed using a circular buffer, with new data overwriting the oldest historical data.

[0090] The process for calculating transfer entropy for each pair of motor parameter time series is as follows: The target and source motors' parameter time series of the same type are selected as input data. First, the mutual information function (MIF) between the source parameter time series and its own delayed sequence is calculated, with the delay order increasing from 1 to a maximum of 50. The delay order corresponding to the first minimum of the mutual information function is used as the delay order for transfer entropy calculation. Transfer entropy calculation is performed using the histogram probability estimation method: the parameter range is dynamically divided into a set number of equal-width intervals, where the number of intervals is the integer of the square root of the time series length. For example, if the time series contains 1000 sampling points, 31 intervals are used. The joint distribution probability of the source parameter's historical state, the target parameter's current state, and its historical state is calculated. The transfer entropy value is equal to the joint entropy of the source parameter's historical state and the target parameter's current state minus the conditional entropy of the source parameter's historical state minus the conditional entropy of the target parameter's own historical state.

[0091] The process of normalizing the transfer entropy to the parameter variation causal entropy is as follows: The Shannon entropy of the source parameter time series is calculated. Shannon entropy is equal to the probability of each parameter value occurring multiplied by the negative sum of the logarithms of that probability to the base 2. The parameter variation causal entropy is equal to the transfer entropy divided by the Shannon entropy of the source parameter. The normalized parameter variation causal entropy ranges from 0 to 1, with larger values ​​indicating stronger parameter variation transmission. For example, when the transfer entropy is 0.8 bits and the source parameter Shannon entropy is 2.0 bits, the calculated parameter variation causal entropy is 0.4. The normalized result is validated. If the Shannon entropy is less than 0.01 bits, it is considered invalid and automatically replaced with the value from the previous valid window.

[0092] The steps for constructing a directed weighted network based on the causal entropy of parameter variation among all motors include: mapping each motor in the system as a network node. For any two motor nodes, if the causal entropy of parameter variation from the source motor to the target motor exceeds a set effective threshold, a directed edge is added from the source node to the target node. The weight of the directed edge is set to the causal entropy of parameter variation in the corresponding direction. The effective threshold is dynamically adjusted based on network density requirements, with an initial value of 0.15. It is automatically adjusted based on network connectivity: when the number of network edges is less than 1.5 times the number of nodes, the threshold is reduced by 0.02; when the number of edges is more than 3 times the number of nodes, the threshold is increased by 0.02. For example, in a 10-motor system, the initial effective threshold is 0.15, and when it is detected that the number of edges is less than 15, the threshold is reduced to 0.13.

[0093] The Granger causality test for the network is performed by performing a Granger causality test on the motor parameter time series corresponding to each established directed edge. An autoregressive model for the target parameter and an extended regression model containing the source parameter are established. The model order is determined using the Bayesian Information Criterion, with a search range of 1 to 10. The model coefficients are fitted using the least squares method, with an L2 regularization term added during the least squares solution, set to 1% of the residual variance. The residual sums of squares of the two models are calculated, and the F statistic is constructed. The F statistic is equal to the difference between the residual sums of squares of the two models divided by the residual sum of squares of the extended model multiplied by the degrees of freedom ratio. When the F statistic exceeds the set significance threshold, the directed edge is confirmed to be a valid causal edge. The significance threshold is the critical value of the F distribution at a 95% confidence level, for example, 2.21 for a degree of freedom of (5, 1000).

[0094] The process for calculating the variance of the betweenness centrality of network nodes as the system's collaborative vulnerability is as follows: First, the betweenness centrality of each node is calculated. Betweenness centrality is equal to the proportion of the shortest paths between all pairs of nodes in the network that pass through that node. The Floyd-Warshall algorithm is used to calculate the shortest paths: the path matrix is ​​initialized, and the path length between directly connected nodes is taken as the inverse of the edge weight. The path length between indirectly connected nodes is set to a maximum value, which is 100 times the sum of the inverses of all edge weights. The path matrix is ​​iteratively updated until convergence. For each node, the number of shortest paths passing through it is counted, and the betweenness centrality is calculated as this number divided by the total number of node pairs. After the betweenness centralities of all nodes are combined into a set, the variance of this set is calculated as the system's collaborative vulnerability. A larger variance indicates poorer system collaborative stability. For example, a variance of 0.25 indicates a risk of single-point failure in the system.

[0095] Parameter time series preprocessing involves performing first-order differencing on the real-time resistance and inductance parameters to eliminate nonstationary trends. The differencing formula is the current value minus the previous sampling point value. The differenced parameter values ​​are then Z-score normalized by subtracting the time series mean and dividing by the standard deviation. The normalized parameter values ​​form a new time series for subsequent calculations. If the time series length is insufficient, the time window is automatically expanded with a step size of half the original window length, and the maximum number of expansions is set to three.

[0096] The probability estimation used in the transfer entropy calculation utilizes an adaptive interval partitioning technique: the interval width is dynamically adjusted based on the parameter value distribution characteristics, ensuring that each interval contains approximately equal numbers of samples. Specifically, the parameter values ​​are sorted in ascending order and then divided equally into the target number of intervals, with each quantile serving as the interval boundary. Interval boundary smoothing uses a three-point moving average filter to eliminate abrupt changes at the boundaries. The probability density estimate is performed on the histogram using a Gaussian kernel smoothing technique, with the kernel width set to one-tenth of the interval width.

[0097] Model residual diagnostics in Granger causality testing: Calculate the residual autocorrelation function of the expanded regression model. If the absolute value of the lagged 1-order autocorrelation coefficient is greater than 0.2, autocorrelation is considered present and the model order is automatically increased. The maximum allowed order is increased to twice the initial order. If the requirements are still not met, a reliability warning is issued for that edge.

[0098] Edge validity verification mechanism during network construction: When the parameter variation causal entropy is greater than the validity threshold but less than the confidence threshold, three consecutive time windows are verified. If two of the three windows meet the conditions, the directed edge is considered valid. The confidence threshold is set to 1.5 times the validity threshold; for example, if the validity threshold is 0.15, the confidence threshold is 0.225. If conflicting results are detected during verification, statistical verification based on bootstrap resampling is initiated: 100 resampled sequences are generated and the parameter variation causal entropy is recalculated. Validity is confirmed when more than 90% of the results are greater than the validity threshold.

[0099] Path weight optimization in betweenness centrality calculation: Edge weights are converted to information transfer efficiency using the formula 1.5 minus the parameter variation causal entropy. The converted weights range from 1.0 to 1.5, with larger weights indicating higher information transfer efficiency. Shortest path calculation prioritizes efficiency, with the path length equal to the sum of the converted weights of the edges along the path.

[0100] Output calibration of system collaborative vulnerability: When the number of network nodes is less than 4, the variance of betweenness centrality is automatically replaced by the variance of node degree centrality. Degree centrality is defined as the weighted sum of a node's in-degree and out-degree, with the in-degree weight set to 0.7 and the out-degree weight set to 0.3. The variance calculation result is multiplied by a scale compensation factor, which is equal to the square root of the number of nodes divided by the baseline value of 4.

[0101] This step, S3, combines the dual analysis mechanisms of transfer entropy and Granger causality networks to more accurately capture hidden fault transmission paths in multi-motor systems than single algorithms. Specifically, transfer entropy normalization eliminates the effects of parameter dimensionality and entropy scale, making the transmission strength of parameter variations across motors comparable and avoiding the misjudgment of nonlinear relationships by traditional correlation coefficients. An initial network is constructed based on information theory, and then Granger causality tests are used to remove spurious correlations (such as those caused by common environmental interference), improving the reliability of causal edges. Compared to a single Granger test, this method reduces reliance on data stationarity and linearity assumptions. Using betweenness centrality variance (rather than conventional degree centrality) to characterize system vulnerability, it can sensitively identify cascading risks caused by failures in key hub nodes and better address the topological vulnerability characteristics of multi-motor coordination scenarios. While ensuring the algorithm's universality (e.g., transfer entropy handles nonlinearity), it effectively balances computational efficiency and diagnostic accuracy through statistical validation and physical properties (e.g., the thermal time constant setting window).

[0102] S4. When low-frequency oscillation is detected in the system, the harmonic components of the operating current signal at the detected low-frequency oscillation frequency are extracted, and the sensitivity level of each motor parameter mismatch to the current oscillation frequency is analyzed. The specific implementation is as follows:

[0103] Spectral analysis identifies low-frequency components in the running current signal whose amplitude exceeds a set ratio of the fundamental amplitude. Low-frequency oscillation is determined when the frequency of a low-frequency component falls within the set low-frequency range. The specific implementation process involves performing a windowed Fourier transform on the running current signal. A Hanning window is selected as the window function to reduce spectral leakage, and the window length is set to an integer multiple of the fundamental period to ensure complete sampling. The amplitude of each frequency component in the spectrum is calculated, where the fundamental amplitude specifically refers to the power frequency component. The set ratio is determined based on power system stability requirements and ranges from 20% to 40% of the fundamental amplitude. This range is obtained through statistical analysis of historical fault data. The set low-frequency range is determined by the motor type and is typically 0.5Hz to 5Hz for synchronous motors, covering the typical low-frequency oscillation frequency range. When a low-frequency component's amplitude exceeds the set ratio and its frequency falls within the set low-frequency range, the system is determined to be in a low-frequency oscillation state. For example, if the fundamental amplitude is 100 amperes and the set ratio is 30%, a low-frequency component exceeding 30 amperes triggers a detection.

[0104] When low-frequency oscillation occurs, the process for extracting harmonic components within a set percentage bandwidth, centered around the oscillation frequency, is as follows: the set percentage bandwidth is dynamically adjusted based on the characteristics of the oscillation pattern, typically between 10% and 20% of the oscillation frequency. A smaller bandwidth is used for high-frequency oscillations, while a larger bandwidth is used for low-frequency oscillations. A bandpass digital filter is constructed to extract harmonics, with the filter's center frequency set to the oscillation frequency and a bandwidth equal to the oscillation frequency multiplied by twice the set percentage bandwidth. The operating current signal is filtered in real time to extract a sequence of harmonic components within the target frequency band. The filtered signal's instantaneous amplitude is calculated using a Hilbert transform, forming a time series of harmonic component amplitudes. The sampling interval is consistent with the original current signal. For example, when the oscillation frequency is 2 Hz and the set percentage bandwidth is 15%, harmonic components within the frequency range of 1.7 Hz to 2.3 Hz are extracted.

[0105] The parameter mismatch is calculated based on the relative deviation between the measured parameters of each motor and the benchmark parameters based on the real-time resistance and inductance parameters. The benchmark parameters are either the rated motor parameters or the average of the parameters over the last ten sampling periods when the system is in a stable state. The real-time resistance and inductance parameters are retrieved from the parameter storage area, with the sampling timestamps strictly aligned with the time series of the harmonic component amplitudes. The parameter mismatch is calculated as the measured parameter minus the benchmark parameter, divided by the benchmark parameter, and multiplied by 100%. The result is a dimensionless percentage. The absolute values ​​of the resistance and inductance parameter mismatch are calculated separately and then weighted together to form a comprehensive parameter mismatch. The resistance weight ranges from 0.5 to 0.7, and the inductance weight ranges from 0.3 to 0.5. The specific weights are determined based on the motor type through sensitivity analysis. For example, if the measured resistance value is 10.0 ohms and the benchmark value is 9.5 ohms, the resistance mismatch is calculated to be 5.26%.

[0106] Establishing a linear mapping between parameter mismatch and harmonic component amplitude and obtaining the sensitivity coefficient through least squares fitting involves: Collecting parameter mismatch and harmonic component amplitude data pairs for all sampling points within the current time window to form a sample set. Constructing a linear regression model with parameter mismatch as the independent variable and harmonic component amplitude as the dependent variable. Using the least squares method, the regression coefficient is calculated; this regression coefficient serves as the sensitivity coefficient. The fitting process employs an outlier rejection mechanism. Residuals exceeding three times the sample standard deviation are identified as outliers and discarded. The fitting process is repeated until the residual change rate between two consecutive iterations is less than 5%. The sensitivity coefficient is expressed in amperes per percentage, representing the change in harmonic amplitude for every 1% change in parameter mismatch. For example, a sensitivity coefficient of 1.2 amperes per percentage indicates that for every 1% increase in parameter mismatch, the harmonic amplitude increases by an average of 1.2 amperes.

[0107] The implementation method for classifying the sensitivity coefficient into three levels of high, medium, and low sensitivity is as follows: two grading thresholds are set: the first threshold ranges from 0.4 to 0.6 amperes per percentage, and the second threshold ranges from 0.15 to 0.25 amperes per percentage. The specific thresholds are dynamically adjusted based on the system's operating status, with a lower threshold used when the system is in a critically stable state to improve detection sensitivity. When the absolute value of the sensitivity coefficient is greater than the first threshold, the sensitivity level is high; when the absolute value of the sensitivity coefficient is less than the first threshold but greater than the second threshold, the sensitivity level is medium; and when the absolute value of the sensitivity coefficient is less than the second threshold, the sensitivity level is low. The sensitivity coefficient corresponding to the degree of mismatch in the comprehensive parameters of each motor is classified into different levels to generate a sensitivity level list. For example, if a motor has a sensitivity coefficient of 0.6 amperes per percentage, it is classified as high sensitivity when the first threshold is 0.5.

[0108] Parameter alignment and time synchronization: The time series of harmonic component amplitudes and the time series of parameter mismatches are precisely time-stamped, with a maximum allowable time deviation of half the sampling period. If the time deviation exceeds this limit, data resampling is performed using cubic spline interpolation to align the time points. Interpolated data points are assigned a lower weight in the least-squares fit, with a weight coefficient of 0.5 times the weight of the measured data, determined through error propagation analysis.

[0109] Sensitivity Coefficient Verification Mechanism: The fitted sensitivity coefficient is statistically tested for significance. The t-statistic is calculated and compared to the critical value at the set significance level. The t-statistic is equal to the sensitivity coefficient divided by the standard error, which is calculated using the residual sum of squares and the sample size. If the absolute value of the t-statistic is less than the critical value, the sensitivity coefficient is considered insignificant, and the corresponding sensitivity level is marked as pending. The significance level is typically 5%, and the critical value is determined by consulting the t-distribution table using the degrees of freedom, which is equal to the sample size minus 2. For example, a sample size of 50 has 48 degrees of freedom, corresponding to a critical value of 2.01.

[0110] Sensitivity Level Output Format: Each motor's sensitivity level is output in combination with its sensitivity coefficient, including three levels corresponding to the resistance parameter mismatch sensitivity coefficient, the inductance parameter mismatch sensitivity coefficient, and the combined sensitivity coefficient. The output is sorted in descending order by combined sensitivity level, with motors with higher sensitivity levels prioritized. For sensitivity coefficients whose status is pending, a Boolean reliability flag is appended to the output.

[0111] Abnormal Condition Handling: When multiple oscillation frequencies are detected, the dominant frequency is selected based on oscillation energy. Oscillation energy is calculated as the square of the amplitude multiplied by the bandwidth. A sensitivity analysis is performed on each of the three oscillation frequencies with the highest energy. The analysis results for each oscillation frequency are output independently and labeled with a frequency identifier. If the energy difference between two oscillation frequencies is less than 10%, both dominant frequencies are labeled.

[0112] Parameter mismatch recalculation mechanism: Parameter mismatch recalculation is triggered when a sudden change in harmonic component amplitude occurs. This is determined when the difference between the current amplitude and the mean of the previous 10 sampling points exceeds three standard deviations. During recalculation, a sliding window is used to update the baseline parameters, shortening the window length to half the original window length.

[0113] S5. Assign the leading compensation role based on the parameter variation causal entropy, generate dynamic limit instructions based on the system collaborative vulnerability, assign resonance suppression priorities based on the sensitivity level, and integrate them into a collaborative compensation strategy. The specific implementation is as follows:

[0114] Motors are selected based on the parameter variation causal entropy values, ranked from high to low. The motor with the largest parameter variation causal entropy value is assigned the leading compensation role. The specific implementation process is as follows: The calculated parameter variation causal entropy values ​​for each motor are directly read from the system parameter storage area. This value was obtained in the previous step through a time-varying correlation analysis of parameter mismatch and harmonic component amplitude. The parameter variation causal entropy values ​​for all motors are sorted in descending order, and the motor with the largest value in the sorted results is selected as the leading compensation role. If the difference in the parameter variation causal entropy values ​​of two or more motors is less than the set tolerance of 5%, the motor with the greater comprehensive parameter mismatch is selected as the leading compensation role. The leading compensation role is assigned the core compensation responsibility, with a lower limit of 60% of the total system compensation it assumes. For example, if the parameter variation causal entropy of motor A is 0.85 and that of motor B is 0.83, and the set tolerance is 5%, the motor with the greater comprehensive parameter mismatch is selected because the difference of 2.4% is less than 5%.

[0115] The specific operational process for reading the system collaborative vulnerability and generating a dynamic limit command based on the system collaborative vulnerability is as follows: The quantified system collaborative vulnerability value is obtained from the system status database in real time. This value has been calculated in the previous step through the multi-motor impedance coupling characteristic analysis. A dynamic limit mapping rule table is constructed to map the system collaborative vulnerability value range to the limit amplitude ratio. The mapping relationship is a monotonically increasing function. The limit amplitude ratio is defined as the percentage of the maximum allowable output current to the reference current value, and its value increases linearly with the increase of the system collaborative vulnerability. The dynamic limit command output is the maximum allowable compensation current value, which is calculated by multiplying the reference compensation current by the limit amplitude ratio. For example, a system collaborative vulnerability of 0.7 corresponds to a limit amplitude ratio of 80%. When the reference compensation current is 100 amperes, an 80 ampere limit command is generated.

[0116] The specific process for assigning resonance suppression priorities from high to low sensitivity levels is as follows: The sensitivity classification results for each motor are obtained, which have already been classified into three levels based on the absolute values ​​of the sensitivity coefficients in the previous step. The priority assignment rule is as follows: high-sensitivity motors are assigned to the first priority sequence, medium-sensitivity motors are assigned to the second priority sequence, and low-sensitivity motors are assigned to the third priority sequence. Motors within the same priority sequence are reordered by parameter variation causal entropy values, with those with larger values ​​receiving higher sub-priority numbers. Each priority level corresponds to a compensation response time window and a resource allocation coefficient, with the first priority response time window being 5 milliseconds. For example, for two highly sensitive motors, motor A with a parameter variation causal entropy of 0.8 is assigned a sub-priority of 1.1, while motor B with a value of 0.7 is assigned a sub-priority of 1.2.

[0117] The technical implementation for generating a coordinated compensation strategy by strategically fusing the compensation action instructions, dynamic limit instructions, and resonance suppression priority instructions of the leading compensation role involves constructing a three-dimensional instruction fusion structure, with the motor identifier as the first dimension, the instruction type as the second dimension, and the time series as the third dimension. The compensation action instructions of the leading compensation role are written into the leading instruction field of the corresponding motor identifier and contain the compensation current amplitude, phase angle, and waveform generation parameters. Dynamic limit instructions are written into the limit constraint field of all motor identifiers, serving as a hard upper limit on the current output. The resonance suppression priority instructions are converted into time weight coefficients and written into the priority field. The weight coefficient is calculated by dividing the base weight by the priority number. Cross-domain parsing generates an executable compensation parameter set for each motor. For example, the time weight coefficient for a motor with sub-priority 1.1 is 0.91 (base weight 1.0 / 1.1), and the response time window is set to 5 milliseconds.

[0118] When the leading compensation role performs compensation, it prioritizes responding to dynamic limit commands. The remaining motors then perform compensation according to their resonance suppression priority. The control logic is as follows: At the start of the compensation cycle, the calculated compensation current of the leading compensation role is first verified to see if it exceeds the dynamic limit command value. If so, the leading compensation role's output current is limited to the limit value, and the excess compensation amount is defined as the pending compensation difference. The pending compensation difference is then distributed to the remaining motors in proportion to the resonance suppression priority weight coefficients. The higher-priority motor receives priority, and the allocation ratio is positively correlated with the weight coefficient. This allocation process is repeated until the compensation difference is fully distributed. For example, if the leading motor is required to output 90 amperes but is limited to 80 amperes, resulting in a 10 ampere difference, the motor with sub-priority 1.1, with a weight coefficient of 0.91, will receive 5.5 amperes, while the motor with sub-priority 1.2, with a weight coefficient of 0.83, will receive 4.5 amperes.

[0119] Strategy execution timing control: A fixed compensation cycle of 10 milliseconds is set, divided into three sequential execution phases. In the first phase (0-3 milliseconds), the leading compensation role performs basic compensation. In the second phase (3-6 milliseconds), the high-sensitivity motor performs priority compensation. In the third phase (6-10 milliseconds), the medium- and low-sensitivity motors perform supplementary compensation. A 1 millisecond overlap buffer is set between phases for command synchronization.

[0120] Command conflict resolution mechanism: When dynamic limiting constraints conflict with priority allocation requirements, a two-stage adjustment strategy is activated. The first stage adjusts the limiting value based on bus voltage deviation, relaxing the limiting amplitude by 5% when the voltage deviation exceeds 5%. The second stage compresses the response time based on the resonant energy growth rate, shortening the time window by 30% when the growth rate exceeds 10%.

[0121] Compensation Effect Feedback Calibration: After each compensation cycle, the system's total harmonic distortion (THD) is collected as a feedback indicator. If the THD exceeds the preset safety threshold, the compensation intensity is increased by 5% of the baseline compensation, with a maximum of three levels at a time. Once the THD reaches the safety threshold, the baseline compensation parameters are restored.

[0122] Multi-ringing condition handling: When the system has multiple dominant oscillation frequencies, a separate coordinated compensation strategy is generated for each. This strategy is executed using a time-slicing round-robin mechanism, processing compensation tasks for up to three oscillation frequencies within each 10-millisecond cycle. Time resources are allocated based on oscillation energy, from highest to lowest.

[0123] Strategy Persistence Storage: The resulting collaborative compensation strategy is encoded as a structured data message containing four fields: motor address code, compensation type code, action parameter set, and timing control code. This data message is stored in a circular strategy buffer with a capacity of 100 records, which are overwritten and updated in chronological order.

[0124] S6. Reconstruct the output torque command of the speed compensator according to the coordinated compensation strategy and send it to the corresponding motor for execution. The specific implementation is as follows:

[0125] The specific implementation process of parsing the dominant compensation role instruction in the collaborative compensation strategy and determining the compensation torque weight coefficient of the dominant motor is as follows: extracting the dominant compensation role instruction set from the instruction storage area of ​​the collaborative compensation strategy data structure, which contains the compensation current amplitude, phase angle and role identification code. The compensation torque weight coefficient is defined as the proportion of the total system compensation torque borne by the motor, which is calculated by dividing the compensation current amplitude of the dominant motor by the system baseline compensation current value. The value range of the compensation torque weight coefficient is 60% to 80%. The specific value is determined by linear interpolation based on the parameter variation causal entropy value of the dominant motor. The higher the parameter variation causal entropy value, the larger the compensation torque weight coefficient. For example, when the parameter variation causal entropy value of the dominant motor is 0.8, the compensation torque weight coefficient obtained by interpolation calculation is 75%.

[0126] The technology for converting dynamic limit commands into a torque output upper limit, which acts as a magnitude constraint for all motor torque commands, is implemented by reading the maximum allowable compensation current value recorded in the dynamic limit command and multiplying it by the motor's real-time torque constant to obtain the torque output upper limit. The real-time torque constant is obtained from a motor parameter database, which updates the torque constant calibration value in real time based on motor temperature and speed. The torque output upper limit acts as a rigid constraint on the generation of output torque commands for all motors. If the calculated output torque of any motor exceeds this upper limit, the system automatically corrects it to the upper limit. For example, when the maximum allowable compensation current is 80 amperes and the real-time torque constant is 0.8 Newton-meters per ampere, the torque output upper limit is 64 Newton-meters.

[0127] The torque response timing of each motor is assigned based on the resonance suppression priority, with motors with higher priorities being assigned earlier execution time slots. The following process is used: Obtain a resonance suppression priority list, which contains the priority number and sub-priority number for each motor. Establish a time slot allocation mapping rule: The motor sequence with priority number 1 is assigned to execute between 0 and 3 milliseconds after the start of the compensation cycle, the sequence with priority number 2 is assigned to execute between 3 and 6 milliseconds, and the sequence with priority number 3 is assigned to execute between 6 and 10 milliseconds. Motors within the same priority sequence are arranged in ascending order of sub-priority number, and each motor is assigned a separate micro-time slot. The length of the micro-time slot is evenly distributed based on the total number of motors in the priority sequence. For example, if there are two motors in the priority 1 sequence, sub-priority 1.1 is assigned to execute between 0.0 and 1.5 milliseconds, and sub-priority 1.2 is assigned to execute between 1.5 and 3.0 milliseconds.

[0128] The method for reconstructing the speed compensator's output torque command based on the compensation torque weight coefficient, torque output upper limit, and torque response timing is as follows: a torque command reconstruction matrix is ​​constructed, with the row index corresponding to the motor identifier and the column attributes including the compensation torque weight coefficient, torque output upper limit, execution start time, and duration. The output torque command of the dominant motor is calculated by multiplying the base torque command by the compensation torque weight coefficient. The result is then compared with the torque output upper limit and the minimum value is taken. The output torque command of the non-dominant motor is calculated by multiplying the base torque command by the priority weight coefficient. The priority weight coefficient is equal to the base weight coefficient divided by the sub-priority number of the motor. The output torque command of each motor must be bound to its timing parameters, including the command's effective start time and duration. For example, the priority weight coefficient of a motor with sub-priority 1.1 is 0.91 (base weight coefficient 1.0 divided by 1.1). If the base torque command is 50 N·m, the output torque command is 45.5 N·m.

[0129] The technology for synchronously sending reconstructed output torque commands to each motor controller via a real-time communication bus is implemented as follows: a time-triggered Ethernet protocol is used as the real-time communication bus, and the bus communication cycle is synchronized with the system compensation cycle to 10 milliseconds. Two milliseconds before the start of the compensation cycle, all reconstructed motor output torque commands are encapsulated in a standard data frame format. The standard data frame contains four fields: the target motor address code field, the torque command value field, the command effective timestamp field, and the command duration field. The data frame is broadcasted by the bus controller to ensure that the transmission delay does not exceed 100 microseconds, and all motor controllers complete command reception and parsing before the start of the compensation cycle. For example, command encapsulation is completed at 8.0 milliseconds, and successful reception by all nodes is ensured before 9.9 milliseconds.

[0130] The output torque command of the dominant motor is given priority in applying the torque weight coefficient, while the control logic for the other motors is applied in the order of resonance suppression priority: at the start of the compensation cycle, the dominant motor immediately executes the output torque command adjusted by the compensation torque weight coefficient. The output torque command of the non-dominant motor is stored in the controller's command buffer register. When the system time reaches the starting time point specified by the motor timing parameters, the buffer register automatically releases the command to the execution unit. During the execution process, the actual output torque value is monitored in real time. If it is detected that the actual value exceeds the torque output upper limit, the limiter is immediately activated to clamp the output value to the upper limit. For example, the dominant motor executes the torque command at 0.0 milliseconds, the sub-priority 1.1 motor executes it at 0.0 milliseconds, and the sub-priority 1.2 motor executes it at 1.5 milliseconds.

[0131] Timing synchronization and calibration mechanism: The IEEE 1588 precision time protocol is used to synchronize the local clocks of each motor controller, limiting the maximum clock deviation to less than 50 microseconds. If the deviation between the actual execution start time and the instruction timestamp exceeds 100 microseconds, a time compensation offset equal to the deviation is automatically inserted at the beginning of the next compensation cycle.

[0132] Command pre-verification process: The motor controller performs three verifications before executing a command: verifying that the torque command value is less than the motor's safe torque limit, verifying that the command's effective timestamp is within the current compensation cycle, and verifying that the target address code is consistent with the local address. If any of these verifications fail, the command is discarded and the valid command from the previous cycle is used. The fault type is also reported through an error code.

[0133] Dynamic weight adjustment strategy: During the compensation cycle, the rate of change of the system's resonant energy is monitored in real time. When the rate of change exceeds a threshold of 10% per second, the compensation torque weight coefficient of the dominant motor is increased by 5%, while the priority weight coefficients of the non-dominant motors are proportionally reduced by 5%. The adjustment takes effect in the next compensation cycle.

[0134] Multi-cycle role rotation: A mechanism for rotating the dominant and compensating motors is established. The dominant motor in the current cycle cannot assume the dominant role again in the next two cycles. During role switching, the weight coefficients are redistributed using a compensation conservation algorithm. This switching process is completed within 2 milliseconds of the cycle interval. For example, if the dominant motor's weight coefficient is 70% in the current cycle, it will drop to 40% after the switch, and the difference will be transferred to the new dominant motor.

[0135] Communication Fault Tolerance: If bus communication is interrupted for more than 200 microseconds, each motor controller switches to local compensation mode. This mode uses fixed parameters: a compensation torque weighting factor of 50%, an upper limit for torque output of 80% of the rated value, and default execution priorities. The system continuously monitors communication status and automatically switches back to coordinated compensation mode upon recovery.

[0136] The entire compensation control process of this embodiment establishes a quantitative causal relationship between parameter mismatch and harmonic disturbances through parameter variation causal entropy. Unlike conventional threshold judgment mechanisms, this approach dynamically assigns leading compensation roles based on causal strength to achieve focused responsibility. System collaborative vulnerability quantifies the risk of multi-motor coupled oscillation. Its real-time positive correlation with dynamic limiting commands replaces the fixed limiting mode, synchronously adapting to changes in system stability. Resonance suppression priorities are hierarchically ranked based on device sensitivity levels, forming a spatiotemporal gradient response sequence for fault suppression. These three decision-making elements establish a complementary constraint relationship in strategy fusion. When the leading role performs the core limiting task, the priority sequence dynamically allocates residual compensation, forming a complete compensation demand transmission chain. The torque command reconstruction process converts electrical compensation into mechanical torque control, achieving precise spatiotemporal decoupling of energy distribution through weight coefficient and timing binding. A synchronous command issuance mechanism ensures temporal consistency across device control, and a role rotation strategy mitigates the risk of single-point overload.

[0137] Example 2: Figure 2 The structural diagram of the multi-motor coordinated control system based on speed compensation of the present invention is given. The multi-motor coordinated control system based on speed compensation includes:

[0138] Signal acquisition module, used to collect the operating current signal and terminal voltage signal of each motor in the system in real time;

[0139] The parameter calculation module is used to calculate the real-time resistance parameters and inductance parameters of each motor online based on the operating current signal and terminal voltage signal;

[0140] The entropy network analysis module is used to calculate the causal entropy of parameter variations between motors based on real-time resistance and inductance parameters using a transfer entropy algorithm, and to determine the system's collaborative vulnerability based on Granger causal network analysis.

[0141] The oscillation sensitivity analysis module is used to extract the harmonic components of the operating current signal at the detected low-frequency oscillation frequency when low-frequency oscillation is detected in the system, and analyze the sensitivity level of each motor parameter mismatch to the current oscillation frequency;

[0142] A strategy generation module is used to assign leading compensation roles based on parameter variation causal entropy, generate dynamic limiting instructions based on system collaborative vulnerability, assign resonance suppression priorities based on sensitivity levels, and integrate them into a collaborative compensation strategy;

[0143] The instruction reconstruction module is used to reconstruct the output torque instruction of the speed compensator according to the collaborative compensation strategy, and synchronously send it to the corresponding motor for execution.

[0144] The calculations involved in the embodiments are all dimensionless numerical calculations, and the preset parameters and thresholds in the calculations are set by those skilled in the art according to actual conditions.

[0145] It should be noted that the present invention can be deployed on the device itself to implement embedded applications, and can also be run on a PC or other terminal with a user interface, thereby meeting various hardware environments and usage requirements.

[0146] The above embodiments can be implemented in whole or in part via software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When loaded or executed on a computer, the processes or functions described in the embodiments of this application are fully or partially performed. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, tapes), optical media (e.g., DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0147] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and modules described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0148] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the modules is only a logical function division. In actual implementation, there may be other division methods, such as multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0149] The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, and may be located in one place or distributed across multiple network modules. Some or all of the modules may be selected to achieve the purpose of this embodiment according to actual needs.

[0150] In addition, each functional module in each embodiment of the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0151] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0152] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

[0153] Finally: The above description is only 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 in the scope of protection of the present invention.

Claims

1. A multi-motor coordinated control method based on speed compensation, characterized in that: include: S1, real-time acquisition of the operating current signal and terminal voltage signal of each motor in the system; S2. Calculate the real-time resistance and inductance parameters of each motor online based on the operating current signal and terminal voltage signal; S3. Based on the real-time resistance and inductance parameters, the transfer entropy algorithm is used to calculate the causal entropy of parameter variations among the motors. The system collaborative vulnerability is determined based on Granger causal network analysis, including: Extract the real-time resistance parameters and real-time inductance parameters of each motor according to the set time window to form a parameter time series; The transfer entropy is calculated for the parameter time series of each two motors, and the delay order of the transfer entropy is determined according to the minimum point of the mutual information; The transfer entropy value is normalized to the parameter variation causal entropy, which represents the parameter variation transmission intensity. A directed weighted network is constructed based on the causal entropy of parameter variation among all motors, where nodes represent motors and edge weights represent the causal entropy of parameter variation; Perform Granger causality test on the network and add causal edges when the test statistic exceeds the set significance threshold; The variance of the betweenness centrality of network nodes is calculated as the system collaborative vulnerability; S4. When low-frequency oscillation is detected in the system, extract the harmonic components of the operating current signal at the detected low-frequency oscillation frequency, and analyze the sensitivity level of each motor parameter mismatch to the current oscillation frequency; S5. Assign the leading compensation role based on the parameter variation causal entropy, generate dynamic limit instructions based on the system collaborative vulnerability, assign resonance suppression priorities based on the sensitivity level, and integrate them into a collaborative compensation strategy, including: Select motors based on the parameter variation causal entropy values ​​from high to low, and assign the motor with the largest parameter variation causal entropy value as the leading compensation role; Read the system collaborative vulnerability and generate a dynamic limit instruction based on the system collaborative vulnerability. The limit amplitude of the dynamic limit instruction is positively correlated with the system collaborative vulnerability. Assign resonance suppression priorities according to sensitivity levels from high sensitivity level to low sensitivity level; The compensation action instructions, dynamic limit instructions and resonance suppression priority instructions of the leading compensation role are strategically integrated to generate a collaborative compensation strategy; S6. Reconstruct the output torque command of the speed compensator according to the collaborative compensation strategy and send it to the corresponding motor for execution simultaneously.

2. The multi-motor coordinated control method based on speed compensation according to claim 1, characterized in that: Real-time acquisition of the operating current signal and terminal voltage signal of each motor in the system, including: Synchronously sample the instantaneous current value of each motor's three-phase winding to generate a running current signal; The instantaneous value of the input voltage of each motor drive terminal is synchronously sampled to generate a terminal voltage signal.

3. The multi-motor coordinated control method based on speed compensation according to claim 2, characterized in that: The sampling of the operating current signal and the terminal voltage signal maintains the same time reference and is updated and stored in a continuous cycle.

4. The multi-motor coordinated control method based on speed compensation according to claim 1, characterized in that: Based on the operating current signal and terminal voltage signal, the real-time resistance parameters and real-time inductance parameters of each motor are calculated online, including: A parameter calculation model is established based on the motor stator voltage equation. The parameter calculation model expresses the terminal voltage signal as a function of the operating current signal and its derivative. Perform central difference calculation on the operating current signal of multiple consecutive sampling periods to obtain current change rate data; Input the terminal voltage signal, operating current signal and current change rate data into the parameter solution model to construct an overdetermined equation group; Iteratively solving the overdetermined equations by using the recursive least squares method to update the estimated values ​​of the real-time resistance parameters and the real-time inductance parameters; When the relative change of the estimated value is less than the convergence threshold for a set number of consecutive times, the real-time resistance parameter and the real-time inductance parameter are output.

5. The multi-motor coordinated control method based on speed compensation according to claim 1, characterized in that: When low-frequency oscillation is detected in the system, the harmonic components of the operating current signal at the detected low-frequency oscillation frequency are extracted, and the sensitivity level of each motor parameter mismatch to the current oscillation frequency is analyzed, including: Identify low-frequency components in the operating current signal whose amplitude exceeds the set ratio of the fundamental amplitude through spectrum analysis. If the low-frequency component frequency is within the set low-frequency range, determine that low-frequency oscillation exists. When there is low-frequency oscillation, the harmonic components of the positive and negative set percentage bandwidth are extracted with the oscillation frequency as the center; Based on the real-time resistance parameters and real-time inductance parameters, the relative deviation between the measured parameters of each motor and the reference parameters is calculated as the parameter mismatch; A linear mapping relationship between parameter mismatch and harmonic component amplitude is established, and the sensitivity coefficient is obtained through least square fitting; According to the absolute value of the sensitivity coefficient, it is divided into three levels: high sensitivity, medium sensitivity and low sensitivity.

6. The multi-motor coordinated control method based on speed compensation according to claim 1, characterized in that: When the leading compensation role performs compensation action, it responds to the dynamic limit instruction first, and the other motors perform compensation actions according to the resonance suppression priority.

7. The multi-motor coordinated control method based on speed compensation according to claim 1, characterized in that: Reconstruct the output torque command of the speed compensator based on the coordinated compensation strategy and send it to the corresponding motor for execution simultaneously, including: Analyze the leading compensation role instruction in the collaborative compensation strategy and determine the compensation torque weight coefficient of the leading motor; Convert the dynamic limit command into the torque output upper limit value, and the upper limit value serves as the amplitude constraint of all motor torque commands; The torque response timing of each motor is allocated according to the resonance suppression priority, and the motor with the highest priority is allocated the earlier execution time slot; reconstructing the output torque command of the speed compensator based on the compensation torque weight coefficient, the torque output upper limit value and the torque response time sequence; Synchronously send the reconstructed output torque command to each motor controller via the real-time communication bus; The output torque command of the dominant motor is applied with the torque weight coefficient first, and the remaining motors are applied in the order of resonance suppression priority.

8. A multi-motor coordinated control system based on speed compensation, used to implement the multi-motor coordinated control method based on speed compensation according to any one of claims 1 to 7, characterized in that: include: Signal acquisition module, used to collect the operating current signal and terminal voltage signal of each motor in the system in real time; The parameter calculation module is used to calculate the real-time resistance parameters and inductance parameters of each motor online based on the operating current signal and terminal voltage signal; The entropy network analysis module is used to calculate the causal entropy of parameter variations between motors based on real-time resistance and inductance parameters using a transfer entropy algorithm, and to determine the system's collaborative vulnerability based on Granger causal network analysis. The oscillation sensitivity analysis module is used to extract the harmonic components of the operating current signal at the detected low-frequency oscillation frequency when low-frequency oscillation is detected in the system, and analyze the sensitivity level of each motor parameter mismatch to the current oscillation frequency; A strategy generation module is used to assign leading compensation roles based on parameter variation causal entropy, generate dynamic limiting instructions based on system collaborative vulnerability, assign resonance suppression priorities based on sensitivity levels, and integrate them into a collaborative compensation strategy; The instruction reconstruction module is used to reconstruct the output torque instruction of the speed compensator according to the collaborative compensation strategy, and synchronously send it to the corresponding motor for execution.

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