Multi-axis servo common bus energy collaborative utilization energy-saving method and system

Abstract

This invention discloses an energy-saving method and system for coordinated energy utilization on a multi-axis servo bus. By collecting power, speed, and bus voltage sampling data for each drive shaft, a multi-axis bus time sequence diagram is constructed, and regenerative energy release windows are extracted. The upper limit of mutual energy that the bus can safely absorb at each moment is quantified, forming an energy mutual constraint set. Combining the motion cycle constraints of each axis with the thermal accumulation calculation of the braking resistor, the dissipation-intensive section is determined, and the braking resistor input time set is solved in reverse. Based on this, the inter-axis margin is reverse-weighted and sorted, and an effective mutual assistance window is generated after mutual assistance time period verification. A tiered allocation strategy is formulated to form a distribution matrix. Finally, electro-mechanical coupling disturbance feedforward compensation is superimposed to generate a pre-loaded command set and solve for and output coordinated control commands. This invention achieves the orderly coordinated flow of multi-axis regenerative energy on the common bus, effectively reducing the dissipation burden of the braking resistor and improving the overall energy utilization level of the system.

Description

Technical Field

[0001] This invention relates to the field of servo drive control technology, and in particular to an energy-saving method and system for coordinated utilization of energy from a common bus in multi-axis servos. Background Technology

[0002] Multi-axis servo drive systems are widely used in CNC equipment, automated production lines, and industrial robots. To reduce system costs, multi-axis drives typically employ a common DC bus topology, with each axis's inverter unit connected in parallel to the same DC bus. During deceleration and braking, each axis motor converts the load's mechanical energy into electrical energy and feeds it back to the DC bus, forming regenerative braking energy. When multiple axes brake simultaneously or continuously, the regenerative energy rapidly accumulates on the bus, causing the bus voltage to rise continuously. Therefore, in engineering practice, braking resistor units are commonly configured to forcibly convert excess regenerative energy into heat dissipation to maintain stable bus voltage.

[0003] The braking resistor dissipation method directly converts regenerative electrical energy that could be reused between shafts into waste heat, and the problem of heat accumulation in the braking resistor is particularly prominent under frequent braking conditions. The common bus topology itself has the conditions for energy complementarity between shafts. If the regenerative energy released by the braking of one shaft can be absorbed instantly by other shafts on the same bus that are in an acceleration state, the actual amount of braking resistor input can be effectively controlled. To achieve this energy complementarity, it is necessary to accurately grasp the overlap relationship between the braking and driving behaviors of each shaft in the time domain, quantify the bus's tolerance boundary for energy flow between shafts, coordinate the constraint effect of the motion cycle of each shaft on the heat accumulation of the braking resistor, and eliminate the electromechanical coupling disturbance caused by energy flow between shafts at the scheduling execution level. Existing control schemes lack a systematic processing mechanism in the above aspects, resulting in limited inter-shaft collaborative utilization of regenerative energy. Summary of the Invention

[0004] This invention discloses a multi-axis servo common bus energy collaborative utilization energy-saving method and system. It aims to establish a precise time-domain mapping of inter-axis braking energy release and driving energy absorption behavior by analyzing the time-series data of power, speed and bus voltage sampling data of each drive shaft. Based on the quantification of bus absorption boundary and braking resistor heat accumulation constraints, the release timing and allocation priority of regenerative energy of each shaft are coordinated and scheduled. At the command execution level, feedforward compensation is superimposed to suppress the electromechanical coupling disturbance caused by energy flow. Finally, a collaborative control command is output to realize the efficient inter-axis utilization of regenerative braking energy of each drive shaft and reduce the actual dissipation burden of braking resistor.

[0005] The first aspect of this invention proposes an energy-saving method for coordinated utilization of energy from a multi-axis servo common bus, comprising the following steps: Collect power, speed and bus voltage sampling data of each drive axis of the multi-axis servo system, and construct a bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and the speed sampling data; The regenerative energy release window of each axle braking is extracted by the bus timing diagram, and the regenerative energy release window is time-aligned to generate an energy mutual assistance sequence. The upper limit of mutual assistance is calculated based on the energy mutual assistance sequence and the bus voltage sampling data to form an energy mutual assistance constraint set. Based on the energy mutual restraint set and the speed sampling data, the motion cycle constraints of each axis are fused to construct a cycle allocation matrix. The cycle allocation matrix and the power sampling data are used to calculate the heat accumulation of braking resistors to determine the dissipation dense section. The braking resistor input threshold is solved in reverse for the dissipation dense section to generate a braking input time set. The set of braking engagement times and the regenerative energy release window are weighted in reverse by the inter-axle margin to generate an energy mutual aid priority sequence. The energy mutual aid priority sequence is checked for mutual aid time periods to generate an effective mutual aid window. The effective mutual aid window is used to formulate a tiered allocation strategy to form an allocation matrix. The allocation matrix and the energy mutual restraint set are fed forward and superimposed to generate a preloaded instruction set. Based on the preloaded instruction set, power instruction calculation is performed to output cooperative control instructions.

[0006] A second aspect of this invention provides a multi-axis servo common bus energy collaborative utilization energy-saving system, comprising: The data acquisition module is used to collect power, speed and bus voltage sampling data of each drive axis of the multi-axis servo system, and to construct a bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and the speed sampling data. The energy constraint module is used to extract the regenerative energy release window of each axle braking through the bus timing diagram, perform timing alignment on the regenerative energy release window to generate an energy mutual assistance sequence, and calculate the upper limit of mutual assistance based on the energy mutual assistance sequence and the bus voltage sampling data to form an energy mutual assistance constraint set. The heat consumption assessment module is used to construct a period allocation matrix by fusing the motion period constraints of each axis based on the energy mutual restraint set and the speed sampling data, perform braking resistor heat accumulation calculation on the period allocation matrix and the power sampling data to determine the dissipation dense section, and solve the braking resistor input threshold in reverse for the dissipation dense section to generate a braking input time set. The scheduling decision module is used to generate an energy mutual assistance priority sequence by performing reverse weighting of the braking input time set and the regenerative energy release window with inter-axle margin, perform mutual assistance time period verification on the energy mutual assistance priority sequence to generate an effective mutual assistance window, and use the effective mutual assistance window to formulate a tiered allocation strategy to form a scheduling matrix. The instruction output module is used to perform feedforward compensation superposition on the allocation matrix and the energy mutual restraint set to generate a preloaded instruction set, and to execute power instruction calculation and output cooperative control instructions based on the preloaded instruction set.

[0007] The beneficial effects of this invention are reflected in the following points: 1. By aligning the power sampling data, speed sampling data, and bus voltage sampling data of each drive shaft with inter-shaft timing phase, a bus timing diagram on a unified common time axis is constructed, enabling the accurate presentation of the temporal distribution relationship of braking energy release behavior of each shaft. Based on this, the regenerative energy release window of each shaft braking is extracted, and the upper limit of energy that can safely participate in inter-shaft flow at each moment is quantified in conjunction with the real-time margin of bus voltage, forming an energy mutual assistance constraint set, providing accurate temporal and energy dual-dimensional boundary conditions for subsequent scheduling decisions. 2. By integrating the motion cycle constraints of each shaft with power sampling data, the heat accumulation distribution of braking resistors is calculated, dissipation-intensive sections are identified, and heat dissipation bottleneck periods are located. Then, the braking resistor activation trigger threshold is solved in reverse to generate a braking activation time set. This mechanism brings thermal safety constraints forward to the scheduling planning stage, reasonably determining the boundary division of inter-shaft mutual assistance and braking resistor sharing under the premise of ensuring that the braking resistor does not exceed the thermal limit, avoiding passive current limiting intervention caused by heat accumulation pressure. 3. Based on the braking engagement time set and regenerative energy release window, each axis is sorted by reverse weighting with margin. After mutual assistance period verification, an effective mutual assistance window is generated. According to the tiered allocation strategy, a dispatch matrix is ​​formed to orderly arrange the energy release sequence and allocation share of each axis. Furthermore, the dispatch matrix is ​​superimposed with electro-mechanical coupling disturbance feedforward compensation to generate a pre-loaded instruction set and solve and output coordinated control instructions. While the drive axis performs mutual assistance scheduling, the torque disturbance transmitted to other axes through the electro-mechanical coupling path by the bus voltage fluctuation is suppressed, ensuring the control stability of multi-axis coordinated operation. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating an energy-saving method for coordinated utilization of energy from a multi-axis servo common bus according to the present invention.

[0009] Figure 2 This is a structural block diagram of a multi-axis servo common bus energy collaborative utilization energy-saving system according to the present invention. Detailed Implementation

[0010] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0011] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0012] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0013] The technical solutions of the embodiments of this application will be described below.

[0014] like Figure 1 As shown, this embodiment of the invention provides an energy-saving method for multi-axis servo common bus energy collaborative utilization, including the following steps S11-S15: Step S11: Collect power, speed and bus voltage sampling data of each drive axis of the multi-axis servo system, and construct the bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and speed sampling data.

[0015] Specifically, power, speed, and bus voltage sampling data are collected for each drive axis of the multi-axis servo system. Power sampling data is independently collected for each drive axis via the driver's built-in power detection unit, with the sampling period aligned with the servo control cycle. The power sampling data covers two components: instantaneous input power and regenerative braking power. Both components are recorded with signed values; a negative sign indicates that the axis is in braking mode and feeding energy back to the common bus. In the multi-axis common bus structure, the sum of the power sampling data for each axis at the same sampling moment determines the instantaneous energy balance of the bus. When the braking feedback power of one axis and the drive power consumption of another axis highly overlap in time, the sum of the power sampling data approaches zero, indicating a direct energy complementarity between the two axes at that moment. Speed ​​sampling data is generated from the encoder feedback signals of each axis after speed estimation processing. The sampling rate of the speed sampling data for each axis is kept consistent with that of the power sampling data to ensure the time correspondence between the two signals. When the noise in the speed sampling data increases due to the decrease in encoder resolution at low speeds, a low-pass filter can be introduced in the speed estimation stage to improve this. The filter cutoff frequency must be more than three times higher than the frequency corresponding to the normal motion cycle of each axis to avoid losing effective speed information. Bus voltage sampling data is collected uniformly at the common bus node, without setting independent sampling points for each drive shaft. The bus voltage sampling data reflects the real-time voltage level of the entire common bus, with a resolution of no less than 1V to capture the rapid voltage rise during braking feedback. Insufficient resolution reduces the detection sensitivity of the voltage rise precursor. Power sampling data, speed sampling data, and bus voltage sampling data are all appended with a master control clock timestamp. The three data streams are aligned with the master control clock. Resampling is triggered when the difference between the timestamps of any two data streams exceeds one control cycle.

[0016] In some embodiments, the step of constructing a bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and the speed sampling data includes: identifying the inertia of the acceleration / deceleration transition segment of the power sampling data and the speed sampling data to generate an axis inertia weight table; identifying the axis with the highest inertia as the phase anchoring axis based on the axis inertia weight table to generate an anchoring axis; performing phase difference compensation locking alignment on the remaining axes for the anchoring axis to generate an anchoring phase-locked group; and performing timing splicing of each axis based on the anchoring phase-locked group to construct a bus timing diagram.

[0017] Inertia identification is performed on power sampling data and speed sampling data during acceleration / deceleration transition periods to generate an axis inertia weight table. Inertia identification is only effective during the transition period when each axis is in an acceleration / deceleration state. When running at a constant speed, the inertial component in the power sampling data is zero, and rotational inertia information cannot be separated from it. Therefore, it is necessary to first detect the speed change interval from the speed sampling data, and mark the sampling points where the continuous speed slope exceeds a set threshold as the start and end boundaries of the acceleration / deceleration transition period. Only the power sampling data within the boundary is included in the inertia identification process. The angular acceleration α of each axis is obtained by differentiating the rotational speed sampling data with respect to time. The inertial component P_inertia is the remaining part of the power sampling data at the corresponding moment after deducting the load power component estimated based on the rated load resistance coefficient. The equivalent rotational inertia J of each axis is solved by the formula J=P_inertia / (ω×α), where J is the equivalent rotational inertia in kilograms per square meter, P_inertia is the remaining inertial component in the power sampling data after deducting the load power component in watts, ω is the angular velocity converted from the rotational speed sampling data in radians per second, and α is the angular acceleration obtained by differentiating the rotational speed sampling data with respect to time in radians per square second. During the deceleration phase, P_inertia takes a negative value, but the sign of the solution result of J remains unchanged. Each acceleration / deceleration transition segment completes one identification. The average value of the identification results of each axis after accumulating at least 3 independent transition segments is taken as the final inertia estimate of that axis. The average value of 3 times can effectively smooth the impact of short-term load fluctuations on the identification accuracy. If the number of accumulated times is insufficient, the dispersion of the identification results of the corresponding axis cannot be evaluated. The estimated inertia values ​​of each axis are normalized based on the maximum value among all axes. The normalization result is filled into the axis inertia weight table. All weight items in the axis inertia weight table are in the range of 0 to 1. The weight of the axis with the largest inertia is 1. For example, when the estimated inertia value of a certain axis is 60% of that of the largest axis, the weight item of that axis is filled with 0.6.

[0018] The highest inertia axis is identified using the axis inertia weight table and used as the phase anchoring axis. In a multi-axis system, the high inertia axis has the slowest dynamic response, is least affected by external electromagnetic disturbances or bus voltage fluctuations, and exhibits the best phase stability among all drive axes. Designating it as the reference axis maximizes the suppression of its own phase fluctuation error. The axis with the highest weight value in the axis inertia weight table is the highest inertia axis. The axis number corresponding to the largest weight item in the axis inertia weight table is used as the unique identifier for the anchoring axis. Once determined, the anchoring axis number remains fixed throughout the entire bus timing diagram construction cycle and is not re-evaluated based on changes in the operating status of each axis. If multiple axes with equal and the largest weight values ​​exist in the axis inertia weight table, the electrical transmission delay between each axis and the common bus node is compared. The axis with the shortest transmission delay is selected as the anchoring axis, as the shortest delay minimizes the transmission error of the reference signal reaching the other axes, thus improving the convergence speed of phase difference compensation. For example, if an axis has a weight of 1.0 in the axis inertia weight table and is connected to the bus node via only one drive bus, then this axis is determined as the anchor axis. All other axes must be compensated and aligned sequentially with the current phase of the anchor axis as the target value. All weight items in the axis inertia weight table are accompanied by confidence labels. Items with low confidence are excluded from the maximum value candidate range when selecting anchor axes. If there is no obvious maximum value among the remaining weight items after excluding items with low confidence, the confidence threshold is appropriately lowered and the items are re-included for comparison.

[0019] For the anchored axis, phase difference compensation and locking alignment are performed on all other axes to generate an anchored phase-locked group. Within each control cycle, the encoder feedback position of the non-anchored axis is converted to electrical phase and then subtracted from the electrical phase of the anchored axis. A positive difference indicates phase lag, and a positive increment is added to the speed command to accelerate the axis. A negative difference indicates lead, and a negative increment is added to moderately decelerate the axis. The compensation increment is proportional to the absolute value of the phase deviation. The convergence criterion is that the absolute value of the phase deviation between the axis and the anchored axis is below a preset tolerance angle threshold for five consecutive control cycles. Continuous verification over five cycles ensures that the locking conclusion is not affected by single-cycle noise. For example, if an axis's phase deviation briefly exceeds the threshold due to a load pulse in the third verification cycle, the convergence count is reset to zero and re-accumulated until the condition is met for five consecutive cycles before successful locking is confirmed. Once a lock is successfully completed, its axis number and current phase deviation residual are written into the anchored phase-locked loop (PLL) group. The phase deviation residual records the final deviation value at the moment of lock completion. This residual is directly used as the time shift basis for the power timing of each axis during the timing splicing process. The smaller the residual, the closer the offset of the corresponding axis's power timing on the common time axis is to zero. In a multi-axis structure, the difference in inertia among the axes leads to different phase convergence speeds. High-inertia axes converge more slowly, while low-inertia axes converge more quickly. The anchored PLL group does not require all axes to complete locking simultaneously. The axis that converges first is written first, and other axes are added to the anchored PLL group successively. The anchored axis itself does not participate in any compensation calculations. Its electrical phase serves as a fixed reference throughout the entire process for real-time comparison by each non-anchored axis. The phase fluctuation range of the anchored axis is directly transmitted to the residual level of each axis in the anchored PLL group.

[0020] The bus timing diagram is constructed by stitching together the timing sequences of each axis based on the anchored phase-locked loop (PLL). After phase difference compensation and locking, the power timing sequences of each axis have a unified phase reference relationship. The core operation of timing stitching is to shift the power timing sequences of each axis on the common time axis based on the residual phase deviation between them and the anchored axis. The shift amount is calculated from the residual phase deviation recorded when each axis is added to the anchored PLL, with the conversion relationship Δt = φ_residual / ω_rated, where Δt is the shift amount in seconds, φ_residual is the residual phase deviation in radians, and ω_rated is the rated angular frequency of the axis in radians per second. A positive shift indicates a backward shift of the power timing sequence, and a negative shift indicates a forward shift. The common time axis is divided into basic units based on the motion period of the anchored axis. After all axes are shifted, the power timing sequences of each axis are arranged side by side on the common time axis. The time relationship between adjacent axis power timing sequences is uniquely determined by the phase difference data recorded in the anchored PLL, without relying on an external clock synchronization mechanism. The bus timing diagram visually presents the multi-axis energy superposition relationship within the overlapping intervals of the power timing of each axis. When the power timing of one axis is in a negative value interval and the power timing of another axis is in a positive peak value interval, and they highly overlap in time, the bus timing diagram marks this overlapping segment as a potential window for energy mutual assistance between the two axes. The width of the overlapping segment is directly related to the relative phase difference between the power timing of the two axes; the smaller the difference, the wider the overlapping segment. All axes with complete phase lock flags in the anchored phase-locked loop are included in the splicing range of the bus timing diagram. Axes with incomplete locking are absent in the current bus timing diagram construction, and their power timing is left blank at the corresponding common time axis position. They will be added in the next update cycle after phase convergence, without affecting the timing of the other axes that have been spliced. The power values ​​of each axis at the same moment on the time axis of the bus timing diagram constitute the multi-axis power cross section at that moment. The difference between the absolute values ​​of the negative and positive components in the cross section is the net energy surplus or deficit of the common bus at that moment.

[0021] Step S12: Extract the regenerative energy release window of each axle brake through the bus timing diagram, perform timing alignment on the regenerative energy release window to generate an energy mutual assistance sequence, and calculate the upper limit of mutual assistance based on the energy mutual assistance sequence and the bus voltage sampling data to form an energy mutual assistance constraint set.

[0022] In some embodiments, extracting the regenerative energy release window for braking of each axle through the bus timing diagram includes: extracting the voltage rise rate of each axle bus from the bus timing diagram to generate a voltage rise rate curve; performing overvoltage threshold approximation identification based on the voltage rise rate curve to generate an overvoltage precursor segment; using the overvoltage precursor segment to back-calculate the corresponding axle braking energy release timing to generate a high-risk energy release timing; and calibrating the energy output boundary based on the high-risk energy release timing to generate a regenerative energy release window.

[0023] The voltage rise rate of each axis of the bus is extracted from the bus timing diagram to generate a voltage rise rate curve. The bus voltage sampling data in the bus timing diagram are arranged at equal time intervals. The rise rate is obtained point by point by dividing the voltage difference between adjacent sampling points by the sampling interval. The rise rate is determined by the formula R_k=(U_{k+1}-U_k) / T_s, where R_k is the bus voltage rise rate of the k-th sampling point in volts per second, U_k is the bus voltage value of the k-th sampling point in volts, U_{k+1} is the bus voltage value of the (k+1)-th sampling point in volts, and T_s is the sampling interval in seconds. When R_k is positive, the bus voltage is in the rising phase; when R_k is negative, the voltage is in the falling phase. The R_k values ​​of all sampling times are arranged sequentially to form the voltage rise rate curve. Compared to directly judging whether the absolute voltage value is approaching the threshold, analyzing the voltage rise rate curve can identify the rising trend before the voltage reaches the threshold, allowing for more lead time for window calibration. For example, in a braking event, when the bus voltage still has a 15V margin from the overvoltage threshold, the voltage rise rate curve has already shown a continuous positive value segment. Intervening at this time can gain several more control cycles of processing time than waiting for the voltage to directly reach the threshold. A segment in the voltage rise rate curve where multiple consecutive sampling points remain positive and the amplitude increases indicates that the bus voltage is in a continuous accelerating rising phase. This segment shows a sloping upward trend on the voltage rise rate curve and is the core detection target for identifying overvoltage precursors. A sudden increase in amplitude followed by an immediate drop usually originates from sampling noise and is not included in the continuous rise judgment of the voltage rise rate curve. Small jumps between adjacent sampling points in the bus timing diagram due to quantization errors are also discarded. Noise filtering requires that R_k be positive for three consecutive sampling points to confirm the start of a valid rising segment. The sampling density of the bus timing diagram determines the sensing sensitivity of the voltage rise rate curve. The shorter the sampling interval, the more accurate the identification of the overvoltage precursor segment.

[0024] Overvoltage precursor segments are generated based on the voltage rise rate curve to identify overvoltage threshold approach. The trigger condition for overvoltage threshold approach is not that the bus voltage has reached the threshold, but rather that the moment when the voltage reaches the threshold is predicted by combining the current voltage level and the trend of the voltage rise rate curve. When the interval between the predicted moment and the current moment is compressed to within a warning window, the approach state is determined. The predicted voltage increment is obtained by multiplying the average of the continuous positive segments of the voltage rise rate curve by the warning window length. When the current bus voltage plus this predicted increment exceeds the overvoltage protection threshold, the current moment is marked as the starting point of the overvoltage precursor segment. The warning window length is typically set to 3 to 5 control cycles, covering the response time required for the drive to intervene in current limiting during typical braking events. The end point of the overvoltage precursor segment is when the bus voltage stops rising or the voltage rise rate curve turns negative. The duration of the overvoltage precursor segment reflects the degree to which the braking feedback power of each axle continuously exceeds the bus's absorption capacity during this period. The longer the duration, the longer the bus is subjected to excessive feedback pressure during this period. When multiple discontinuous overvoltage precursor segments appear in the voltage rise rate curve, if the distance between the starting points of two adjacent segments is shorter than a single braking cycle, they are merged into a single process. This prevents the bus voltage from briefly dropping and artificially segmenting the same braking event. For example, if the bus voltage repeatedly approaches the threshold during continuous braking of a certain axle, the merged overvoltage precursor segment completely covers the continuous braking interval without creating artificial breaks. Each independent overvoltage precursor segment is calibrated with its own start and end times, and each segment corresponds to a different braking trigger event, without affecting each other.

[0025] High-risk energy release timing is generated by reverse-engineering the braking energy release timing of the corresponding axle during the overvoltage precursor period. The reverse-engineering logic starts from the time range of the overvoltage precursor period and locates all drive axes with negative power timing within this time period in the bus timing diagram. These axes continuously inject regenerative energy into the bus during the overvoltage precursor period, directly contributing to the approaching overvoltage threshold. The time overlap between the negative power timing interval of each axle and the overvoltage precursor period quantifies the contribution weight of that axle to the rise in bus voltage. The overlap ratio W_i is obtained by dividing the intersection duration of the negative power timing interval of that axle and the overvoltage precursor period by the total duration of the overvoltage precursor period, where i is the drive axle number, and W_i is the overlap ratio of the i-th axle, a dimensionless parameter ranging from 0 to 1. A higher W_i indicates a higher degree of consistency between the braking behavior of that axle and the timing of the overvoltage precursor period. Axes with W_i exceeding the identification threshold are identified as high-risk energy release axes. The setting of the W_i threshold needs to balance both false positives and false negatives: if the threshold is too high, low-contribution axes will be excluded, resulting in incomplete risk coverage for the braking resistor intervention decision; if the threshold is too low, axes with slight braking contributions will be mistakenly included in the high-risk determination, increasing unnecessary power limiting intervention. The negative power time series intervals of high-risk energy-releasing axes within the corresponding time period of the overvoltage precursor stage are extracted as the high-risk energy-releasing time series for that axis. The high-risk energy-releasing time series fully preserves the power amplitude of each sampling point. The larger the absolute value of the amplitude at a sampling point, the stronger the regenerative power injected into the bus at the corresponding time, which is the time-domain basis for prioritizing braking resistor intervention. When multiple axes trigger high-risk determination simultaneously, the high-risk energy-releasing time series of each axis are extracted independently. The power amplitude in the high-risk energy-releasing time series of each axis is summed point by point according to the sampling points to obtain the total feedback power borne by the common bus during that time period. The difference between the total feedback power and the bus absorption capacity is the minimum share that the braking resistor must bear.

[0026] The regenerative energy release window is generated based on the energy output boundary calibrated according to the high-risk energy release timing. The energy output boundary has two forms: a wide boundary and a narrow boundary. The wide boundary is applicable to the initial braking stage before the start of the high-risk energy release timing, when the bus voltage is still within the safe operating range. Each axle can freely inject regenerative energy into the bus according to actual braking and deceleration requirements. The upper limit of the wide boundary is taken as the measured peak amplitude of the negative value range of the braking power timing for each axle. After the start of the high-risk energy release timing, the narrow boundary stage begins. The upper limit of the narrow boundary power output is dynamically constrained by the current bus voltage margin. Feedback power exceeding the upper limit of the narrow boundary must be shared by the braking resistor. The higher the bus voltage, the stricter the narrow boundary and the narrower the window. The regenerative energy release window is a time-domain division combining wide and narrow boundaries. Using the upper limit of power output at each sampling moment as the vertical axis and time as the horizontal axis, it forms the complete boundary contour of the energy that can be safely released within the current braking cycle of that axis. The start and end times of the narrow boundary segment in the contour are directly inherited from the time-domain range of the high-risk energy release sequence. The difference between the power amplitude at each sampling point in the high-risk energy release sequence and the upper limit of the narrow boundary is the power share that must be shared by the braking resistor at that moment. The contour area of ​​the regenerative energy release window approximately reflects the maximum total energy that can participate in inter-axis mutual assistance during this braking cycle. The regenerative energy release window of each axis is independently calibrated according to the braking cycle. The shape of the regenerative energy release window in adjacent braking cycles may differ, depending on the residual level of the bus voltage at the end of the previous cycle. For example, if the interval between two consecutive braking cycles of an axis is short, the bus voltage may not have enough time to fully recover, and the duration of the wide boundary of the regenerative energy release window in the second braking cycle will be significantly shorter than that in the first.

[0027] Timing alignment is performed on the regenerative energy release windows to generate an energy reconciliation sequence. Timing alignment maps the regenerative energy release windows of each axis to the bus timing. Figure 1On the common time axis, the mapping process uses the residual phase deviation recorded when constructing the bus timing diagram for each axis as the time shift amount, ensuring that the relative position of the regenerative energy release window of each axis on the common time axis is completely consistent with the physical timing relationship of the actual braking behavior of each axis. After alignment, the segment where the regenerative energy release window of a certain axis overlaps with the positive power timing interval of another axis on the common time axis is the period when there is a direct mutual assistance feasibility between the two axes. The wider the overlapping segment and the higher the amplitude on both sides, the greater the mutual assistance potential of this period. The arrangement of all axis regenerative energy release windows on the common time axis constitutes the energy mutual assistance sequence. The energy mutual assistance sequence uses the start and end times of the energy release window of each axis and the upper limit of the power amplitude as the basic units. The relative positional relationship of each unit on the common time axis intuitively reflects the crossover and misalignment distribution of the braking energy release behavior of different axes in the time domain. The segment with sufficient crossover is the candidate period for priority scheduling mutual assistance, while the segment with obvious misalignment needs to rely on energy storage buffers or braking resistors to take over. The start and end times of each axis energy release unit in the energy mutual aid sequence are inherited from the calibration results of the regenerative energy release window. The boundary accuracy of the regenerative energy release window is directly transmitted to the time domain resolution of the energy mutual aid sequence. The sum of the upper limit of the power amplitude of each axis energy release unit at any time in the energy mutual aid sequence represents the maximum potential feedback power faced by the common bus at that time.

[0028] An energy mutual assistance constraint set is formed by calculating the upper limit of mutual assistance based on the energy mutual assistance sequence and bus voltage sampling data. The maximum additional power that the bus can safely withstand at each moment is the core constraint quantity. The maximum additional energy E_max that the bus can absorb at a certain moment is determined by the formula E_max = 0.5 × C_bus × (U_OV² - U_dc²), where E_max is the maximum additional energy that the bus can absorb in joules, C_bus is the equivalent filter capacity of the bus in farads, U_OV is the overvoltage protection threshold in volts, and U_dc is the measured value of the bus voltage sampling data at that moment in volts. The higher the measured value of the bus voltage sampling data, the smaller E_max, and the narrower the upper limit of the energy that can participate in mutual assistance. E_max is converted into the maximum additional power that the bus can absorb at that moment using the formula P_max = E_max / T_ctrl, where P_max is the maximum additional power absorbed by the bus in watts and T_ctrl is the servo control cycle in seconds. This unifies the dimensions of the energy quantity with the upper limit of the power amplitude of each axis energy release unit in the energy mutual assistance sequence, facilitating direct comparison. When multiple axis energy release units in the energy mutual assistance sequence are superimposed at the same moment, the sum of the upper limit of the power amplitude of each axis is compared with P_max at the current moment. When the total superposition does not exceed P_max, there is no need to restrict the energy release of each axis. When the total superposition exceeds P_max, the excess part must be guided to the braking resistor for sharing according to the priority between axes. The smaller value of P_max corresponding to each moment and the upper limit of the power amplitude of each axis in the energy mutual assistance sequence are taken moment by moment and summarized to form the energy mutual assistance constraint set. The energy mutual assistance constraint set gives the sampling point-by-sampling quantization boundary of the maximum mutual assistance energy that each axis can inject into the bus during each braking period. The most stringent period of constraint boundary is concentrated in the multi-axis superimposed braking section. In this section, the bus voltage sampling data is already at a high level and multiple axes release energy simultaneously. E_max narrows rapidly in a short period of time. The energy mutual restraint set has the highest constraint density in this section, and the amount of energy that the braking resistor must bear is also the most concentrated.

[0029] Step S13: Based on the energy mutual restraint set and speed sampling data, the motion cycle constraints of each axis are fused to construct the cycle allocation matrix. The braking resistor heat accumulation is calculated on the cycle allocation matrix and power sampling data to determine the dissipation dense section. The braking resistor input threshold is solved in reverse for the dissipation dense section to generate the braking input time set.

[0030] Specifically, a cycle allocation matrix is ​​constructed by fusing the energy mutual restraint set and speed sampling data to perform cycle constraint fusion for each axis. A complete cycle is defined as the complete change in speed from its peak value to the target speed and then back up in the speed sampling data for each axis. The start and end times of the cycle are determined by the location of the extreme points in the speed sampling data. The length of the cycle varies depending on the load characteristics. The ratio between the shortest and longest cycle axes determines the phase overlap density of the multiple axes on the common time axis. In sections with high overlap density, braking behavior is concentrated across axes, and the energy mutual restraint pressure and heat accumulation risk are simultaneously highest in these sections. The energy mutual restraint set provides a quantized boundary for the maximum mutual restraint power of each axis at each moment, sampling point by sampling point. By mapping the upper limit of the constraint in the energy mutual restraint set to the cycle periods of each axis on the common time axis, it is possible to identify which periods within each cycle are constrained in terms of braking power release and how strict the constraint is. A period in which the constraint upper limit is lower than the peak actual braking power of a certain axis indicates that the bus cannot fully absorb the feedback power of that axis at that moment. The constraint upper limit value corresponding to this period is the basis for filling the elements of the corresponding axis at the corresponding moment in the period allocation matrix. If the speed sampling data simultaneously shows that multiple axes are in a deceleration state, the constraint density of the energy mutual assistance constraint set is further tightened during this period, and the corresponding column elements of the period allocation matrix are generally low during this period. More braking resistors need to be arranged to share the excess feedback power during this period. The period allocation matrix is ​​generated by aligning and merging the motion period of each axis with the constraint boundary of the energy mutual assistance constraint set on the common time axis. The period allocation matrix has each axis as the row and each sampling moment of the common time axis as the column. Each element takes the constraint upper limit value of that axis at that moment. An element with a constraint upper limit of zero indicates that the axis has no mutual assistance energy margin at that moment.

[0031] In some embodiments, the step of performing braking resistance thermal accumulation calculation to determine the dissipation-dense section on the period allocation matrix and the power sampling data includes: extracting the braking power time sequence of each axle from the period allocation matrix and the power sampling data to generate a braking power curve; performing reverse estimation of the heat dissipation margin of the thermal resistance network on the braking power curve to generate a heat dissipation redundancy map; locating the redundancy approximation depletion segment based on the heat dissipation redundancy map to generate a heat dissipation bottleneck segment; and performing dissipation range analysis based on the heat dissipation bottleneck segment to generate a dissipation-dense section.

[0032] Braking power curves are generated by extracting the braking power timing of each axis from the periodic allocation matrix and power sampling data. The extraction range is limited by the time-domain distribution of the non-zero elements of the periodic allocation matrix. Only sampling points with negative signs in the power sampling data are extracted at sampling moments where there is a constraint upper limit value in the periodic allocation matrix. The boundary moment when the sign changes from negative to positive is the trigger moment when the axis switches from braking to driving state. Sampling points with positive signs in the power sampling data correspond to the driving state, do not generate braking feedback behavior, and are not included in the valid data range of the braking power curve. The sampling points with negative signs in the power sampling data are arranged point by point after being filtered by the periodic allocation matrix in the time domain to form the braking power curve. The larger the absolute value of the amplitude of the braking power curve, the stronger the regenerative power injected into the bus by the axis at that moment. The product of the absolute value of the amplitude and the duration approximately reflects the total amount of heat transferred to the braking resistor in a single braking event. Both affect the results of subsequent heat accumulation calculations. Sampling points where the upper limit of the periodic allocation matrix constraint is lower than the absolute value of the braking power curve amplitude are marked as over-limit points. The density of over-limit points on the braking power curve directly reflects the time-domain proportion of excess feedback power that the braking resistor must continuously bear. The denser the over-limit points, the higher the heat accumulation rate. For example, if more than 60% of the sampling points on a certain axis are marked as over-limit points in a single braking cycle, the heat accumulation pressure of the braking resistor corresponding to that axis is significantly higher than the normal level. In the overlapping sections of the multi-axis braking power curves on the common time axis, the sum of the amplitudes of each axis constitutes the total braking feedback power borne by the common bus during that time period. The total feedback power reaches its peak in the multi-axis overlapping section. The higher the multi-axis superposition amplitude of the braking power curve, the more concentrated the heat load on the braking resistor during that time period.

[0033] A thermal redundancy diagram is generated by performing inverse estimation of the thermal resistance network's heat dissipation margin on the braking power curve. The physical meaning of the heat dissipation margin is the difference between the maximum allowable junction temperature of the braking resistor and the currently estimated junction temperature. When the difference approaches zero, the braking resistor must be forcibly taken out of operation. The thermal redundancy diagram uses the common time axis of the braking power curve as the horizontal axis and the estimated heat dissipation margin value of each axis as the vertical axis, presenting the remaining distribution of the braking resistor's heat dissipation capacity across the entire time domain. The absolute value of the amplitude at each sampling point of the braking power curve directly determines the power dissipated by the braking resistor at that moment. As the dissipated power is continuously applied to the thermal resistance network, the junction temperature gradually accumulates according to the formula T_j = T_amb + P_brk × R_th, where T_j is the junction temperature of the braking resistor in degrees Celsius, T_amb is the ambient temperature in degrees Celsius, P_brk is the absolute value of the amplitude at the current sampling point of the braking power curve in watts, and R_th is the equivalent thermal resistance from the braking resistor junction to the environment in degrees Celsius per watt. T_j increases linearly with increasing P_brk. The heat dissipation margin is determined by M_th = T_max - T_j, where M_th is the heat dissipation margin in degrees Celsius, T_max is the rated maximum allowable junction temperature of the braking resistor in degrees Celsius, and T_j continues the meaning of the previous formula. When M_th drops to the protection threshold, the braking resistor input must be reduced in advance. When M_th drops to zero, the current braking resistor operation must be forcibly stopped. The continuous high-amplitude segment in the braking power curve corresponds to the period when the heat dissipation margin drops rapidly in the heat dissipation redundancy diagram. The steeper the slope of the drop, the higher the heat accumulation rate. The recovery rate after the margin drops depends on the cooling rate of the braking resistor to the environment after the braking event ends. The cooling rate is determined by the equivalent thermal resistance R_th and the heat capacity. The larger the R_th estimation error, the higher the offset of the margin curve in the heat dissipation redundancy diagram. The heat dissipation margin M_th corresponding to the braking power curve of each axle is estimated at each sampling point and then filled into the heat dissipation redundancy diagram.

[0034] For example, the step of locating the redundant approximation depletion segment and generating the heat dissipation bottleneck segment based on the heat dissipation redundancy map includes: performing multi-axis redundancy synchronization analysis on the heat dissipation redundancy map to generate redundancy synchronization degree; using the redundancy synchronization degree to identify the multi-axis synchronous approximation depletion segment and generate a set of cooperative failure segments; performing overall bottleneck weighting on the set of cooperative failure segments to generate a bottleneck weight table; and performing bottleneck segment calibration based on the bottleneck weight table to generate the heat dissipation bottleneck segment.

[0035] Multi-axis redundancy synchronization analysis is performed on the thermal redundancy diagram to generate redundancy synchronization degree. The core metric for multi-axis redundancy synchronization is the degree of coordination in the decreasing behavior of the thermal margin curves of each axis in the thermal redundancy diagram at the same time. The more sampling times where the margin curves of each axis slope downward and the closer the decrease in margin of each axis, the more synchronized the heat accumulation behavior of the braking resistors of each axis is during that period. The synchronization analysis performs a horizontal comparison of the thermal margin curves of each axis in the thermal redundancy diagram at each sampling point. The number of axes that meet the margin decrease condition at the same sampling time is divided by the total number of axes participating in the analysis to obtain the normalized redundancy synchronization degree value. This value is in the range of 0 to 1. When it is 1, it means that all axes are synchronously approaching the thermal limit at that time, and when it is 0, no axis is in the state of decreasing thermal margin. When the absolute values ​​of the margin curves of each axis in the thermal redundancy diagram are different, only axes whose margin is below the safety warning line are included in the redundancy synchronization degree statistics. Axis axes whose margin is still above the safety range are not included in this round of statistics. For example, if at a certain time in a 5-axis system only 2 axes have thermal margins below the warning line and decrease synchronously, the redundancy synchronization degree value for that time is 0.4, which does not trigger the high coordination risk judgment. The redundancy synchronization degree is continuously recorded at each sampling time of the common time axis to form a numerical sequence. The continuous high value period in the sequence is the concentrated area where the multi-axis redundancy synchronization is about to be exhausted. The redundancy synchronization degree value always remains high in this section. The heat dissipation redundancy diagram shows a collective rapid decline of multiple margin curves in this section, forming a one-to-one time domain relationship with the redundancy synchronization degree sequence.

[0036] Redundancy synchronization is used to identify multi-axis synchronous approach depletion segments and generate a set of cooperative failure segments. Continuous sampling intervals where the redundancy synchronization value exceeds the cooperative trigger threshold are identified as multi-axis synchronous approach depletion segments. The cooperative trigger threshold is typically set between 0.6 and 0.8. A higher threshold results in a more conservative coverage of the cooperative failure segment set, capturing only a high proportion of multi-axis synchronous failure events; a lower threshold provides broader coverage but may misclassify localized overheating of individual axes as cooperative failures. The threshold selection is based on a comprehensive consideration of the total number of drive axes and the heat dissipation redundancy design objective. Segments where the redundancy synchronization value briefly drops below the cooperative trigger threshold and then immediately recovers are not segmented into independent segments. If the duration of the drop is shorter than the shortest single braking cycle, the two segments are merged into a single unit to prevent the brief drop in redundancy synchronization during braking intervals from artificially truncating the same continuous heat accumulation event. For example, if a single axis briefly recovers cooling during multi-axis synchronous braking, causing the redundancy synchronization to momentarily fall below the threshold, and the interval duration is shorter than the shortest braking cycle, the entire segment is still treated as a single cooperative failure segment. Each independent multi-axis synchronous approach exhaustion segment extracts the start and end times and the peak value of redundancy synchronization within the time period and then merges them into the collaborative failure segment set. The higher the peak value of redundancy synchronization, the more axes approach the thermal limit at the same time period, and the higher the collaborative risk level of thermal accumulation in the corresponding time period. The difference in risk level of each segment in the collaborative failure segment set is transformed into different weight contributions in the bottleneck weighting process.

[0037] A bottleneck weight table is generated by performing an overall bottleneck weighting on the set of collaborative failure segments. The weighting criteria cover the peak redundancy synchronization of each collaborative failure segment, the lowest absolute value of the heat dissipation margin within each segment, and the duration of each segment. After normalization of the three indicators, they are summed and combined according to weight. The comprehensive weight is determined by the formula W_bn=k_s×S_peak_norm+k_m×(1-M_min_norm)+k_d×D_norm, where W_bn is the comprehensive weight of the collaborative failure segment, which is a dimensionless parameter; S_peak_norm is the normalized value of the peak redundancy synchronization, ranging from 0 to 1; M_min_norm is the normalized value of the lowest point of the heat dissipation margin, ranging from 0 to 1, and the lower the value, the higher the risk, so 1 is taken as the risk contribution item minus this value; D_norm is the normalized value of the duration, ranging from 0 to 1; and k_s, k_m, and k_d are the corresponding weighting coefficients, usually set to 0.5, 0.3, and 0.2 respectively. The sum of the three coefficients is 1, and the proportion of each coefficient can be adjusted according to the redundancy target of the heat dissipation design. The redundancy synchronization peak coefficient has the highest weight because the more shafts in the coordinated failure segment set that simultaneously approach the thermal limit, the more uncontrollable the impact on overall thermal safety becomes. The duration coefficient has the lowest weight because as the duration increases, the cooling mechanism of the braking resistor also accumulates heat; simply increasing the duration does not necessarily mean a proportional increase in risk. Each coordinated failure segment in the coordinated failure segment set receives a comprehensive weight value according to the above weighting rules and is written to the corresponding row of the bottleneck weight table. Segments in the bottleneck weight table whose comprehensive weight exceeds the bottleneck identification threshold are included as candidate bottleneck segments; segments that do not exceed the threshold are considered localized minor heat accumulation events and are not included in the heat dissipation bottleneck segment calibration range. The comprehensive weight values ​​of all coordinated failure segments are summarized and arranged to form the bottleneck weight table. Segments with higher comprehensive weights in the bottleneck weight table are given priority in heat dissipation bottleneck segment calibration. Candidate segments with higher comprehensive weights pose a more significant threat to overall thermal safety, and priority must be given to ensuring that their corresponding time domain is completely included in the heat dissipation bottleneck segment.

[0038] Bottleneck segments are generated based on a bottleneck weight table. Cooperative failure segments with a comprehensive weight exceeding the bottleneck identification threshold in the bottleneck weight table have their start and end times directly inherited from the corresponding time domain range in the cooperative failure segment set. The calibration process combines the comprehensive weight with the time domain range to determine whether the coverage area needs to be extended to both sides. The extension criterion is whether the heat dissipation margin of several sampling points outside the start and end times is still below the warning line. If it is still below the warning line, the extended range is included in the heat dissipation bottleneck segment; if it exceeds the warning line, it ends at the current boundary. Two candidate segments with high comprehensive weights but adjacent start and end times are merged. When the interval between the two segments is shorter than the shortest braking cycle, they are considered different stages of the same heat accumulation event. The merged time domain range is the outer envelope of the start and end times of the two segments, and the comprehensive weight of the merged segment is the higher of the two segments to prevent fragmentation of heat dissipation bottleneck segment identification caused by the boundary cutting of adjacent heat accumulation events. After the heat dissipation bottleneck segments are calibrated, the corresponding bottleneck weight values ​​are output along with the bottleneck segments. Bottleneck segments with higher weights are prioritized in the dissipation range analysis. For example, if a segment's overall weight reaches 1.5 times the bottleneck identification threshold and spans two adjacent braking cycles, this segment is calibrated as a high-priority heat dissipation bottleneck segment and is included in the dissipation range analysis first. Collaborative failure segments with an overall weight below the bottleneck identification threshold in the bottleneck weight table do not participate in the current heat dissipation bottleneck segment calibration. These segments are retained as mild heat accumulation events and will be re-calibrated if their weight exceeds the threshold due to historical data correction after the accumulation of operating cycles. The range of heat dissipation bottleneck segments tends to stabilize as the sample size increases. In the initial operating phase, when the sample size is limited, the weight estimation deviation is large, and the confidence level of the calibration conclusions for each segment is relatively low.

[0039] Dissipation range analysis is performed based on the heat dissipation bottleneck segment to generate dissipation-dense regions. The dissipation range analysis starts from the time-domain boundary of the heat dissipation bottleneck segment and extends to both sides to explore continuous intervals in the braking power curve where the amplitude exceeds a set dissipation intensity threshold. If the amplitude of the braking power curve continuously exceeds the dissipation intensity threshold in the extension direction, the interval is identified as a dissipation-dense region; intervals below the threshold are excluded from the extension. The weight value of the heat dissipation bottleneck segment determines the maximum exploration distance in both directions. Higher weights result in longer exploration distances for the heat dissipation bottleneck segment, ensuring that high-dissipation intervals around high-risk heat accumulation events are not overlooked. Lower weights result in shorter exploration distances for the heat dissipation bottleneck segment, avoiding misclassifying distant low-intensity braking events into dissipation-dense regions. Time-domain intervals in the braking power curve where the amplitude continuously exceeds the dissipation intensity threshold may exist both inside and outside the heat dissipation bottleneck segment. Only the time-domain range of the heat dissipation bottleneck segment and its extended exploration distance are considered for the exceeding-threshold intervals to exclude distant braking events that are not causally related to the heat dissipation bottleneck segment. The dissipation range analysis results corresponding to each heat dissipation bottleneck section are performed independently. After integrating the obtained over-threshold intervals, the overlapping parts are removed. The time domain width of the dissipation-intensive section is directly related to the weight distribution of the heat dissipation bottleneck section. The more concentrated the weight, the wider the dissipation-intensive section. The selection of the dissipation intensity threshold has a significant impact on the range of the dissipation-intensive section. If the threshold is too high, it only covers the short-term peak interval of the braking power curve with extremely high amplitude, and the continuous medium-amplitude heat accumulation section may be missed. If the threshold is too low, the dissipation-intensive section is too wide, including low-intensity braking events and increasing unnecessary braking resistor intervention. The threshold is usually set to 70% to 80% of the rated continuous dissipation power of the braking resistor.

[0040] In some embodiments, the step of reversely solving the braking resistor engagement threshold in the dissipation-dense section to generate a braking engagement time set includes: extracting the synchronous bus absorption margin in the dissipation-dense section to generate a bus absorption margin curve; performing saturation inflection point location on the bus absorption margin curve to generate an absorption saturation inflection point set; back-calculating the corresponding braking resistor engagement triggering condition based on the absorption saturation inflection point set to generate a back-calculated threshold set; and calibrating the engagement triggering time based on the back-calculated threshold set to generate a braking engagement time set.

[0041] In the dissipation-intensive section, the synchronous bus absorption margin is extracted to generate the bus absorption margin curve. The bus absorption margin is determined by the formula M_bus=U_OV-U_dc, where M_bus is the bus absorption margin in volts, U_OV is the overvoltage protection threshold in volts, and U_dc is the current bus voltage in volts. The smaller the value of M_bus, the more limited the voltage rise space of the bus at that moment, and the more constrained the additional feedback power it can withstand. The bus voltage sampling data at each sampling moment in the dissipation-intensive section is subtracted from the overvoltage protection threshold point by point, and the difference sequence constitutes the original numerical source of the bus absorption margin curve. The dissipation-intensive section is the period when the heat accumulation of the braking resistor is most concentrated. During this period, the bus voltage is usually at a high level due to the influence of simultaneous braking feedback from multiple shafts. The value of the bus absorption margin curve is generally low during this period. The low value section indicates that the bus has extremely limited space to absorb additional feedback energy, and the proportion of energy that the braking resistor must bear is relatively higher. The shape of the bus absorption margin curve in the dissipation-intensive section is affected by the superposition relationship of braking time of each axle. When multiple axles brake simultaneously, the bus voltage rises rapidly and the absorption margin curve declines rapidly. When only one axle brakes, the bus voltage rises relatively slowly and the absorption margin curve declines more slowly. Therefore, the decline rate of the bus absorption margin curve fluctuates with the superposition density of braking of each axle. Bus voltage sampling data outside the dissipation-intensive section is not included in the construction of the bus absorption margin curve for this section. Focusing on the dissipation-intensive section can improve the analytical relevance of the margin curve for high-risk periods. The lower limit of the bus absorption margin curve is the core criterion input for saturation inflection point location.

[0042] A saturation inflection point set is generated by locating the saturation inflection point on the bus absorption margin curve. The saturation inflection point is determined by the inflection sampling point where the bus absorption margin curve changes from a continuous downward trend to a flat or brief upward trend. The inflection point represents the moment when the bus voltage temporarily stops rising, the absorption capacity no longer shrinks further, and it is a signal moment when the braking resistor input can be appropriately reduced. The inflection point identification uses the slope sign change criterion. The first sampling point where the slope changes from negative to positive is identified as an upward inflection point, and the first sampling point where the slope changes from negative to close to zero is identified as a flat inflection point. The upward inflection point corresponds to a significant recovery in the bus absorption capacity, while the flat inflection point only corresponds to temporary stability and no recovery. The two types of inflection points constitute the absorption saturation inflection point set. If there is an abnormal jump in amplitude exceeding 5% of the average margin within 3 sampling points before and after the inflection point, it is considered a noise point and not identified as an inflection point. The analysis must be extended to the next inflection point that meets the smoothing condition to avoid noise interference causing misjudgments in the absorption saturation inflection point set. The bus absorption margin curve may have multiple inflection points in the dissipation-intensive section. Each inflection point corresponds to the stage saturation time of different braking events. The absorption saturation inflection point set summarizes the time information of all inflection points. The steeper the slope of the preceding margin decrease at each inflection point, the more severe the compression of the bus absorption capacity before reaching that inflection point. The absorption saturation inflection point set corresponds to the higher degree of urgency of the braking resistor being put into operation. The inflection point with the steepest slope will obtain the lowest threshold when back-deriving the triggering conditions.

[0043] The back-calculation threshold set is generated by reverse-engineering the corresponding braking resistor activation trigger conditions based on the absorption saturation inflection point set. The back-calculation logic starts from the moment of each absorption saturation inflection point and traces backward to find the continuous decline process that the bus absorption margin curve experienced before reaching that inflection point. The starting moment of the continuous decline process is the corresponding braking event trigger point. The bus voltage value at this trigger point and the amplitude of the braking power curve of each axle at that time together constitute the initial state condition that the braking resistor must intervene in advance. The core quantitative content of the triggering condition is that the braking resistor must be activated when the amplitude of the braking power curve exceeds a certain threshold. The reverse threshold is equal to the maximum feedback power that the bus can withstand at the absorption saturation inflection point. The conversion relationship is P_th=0.5×C_bus×(U_OV²-U_dc²) / T_ctrl, where P_th is the reverse threshold in watts, C_bus is the bus equivalent filter capacitance in farads, U_OV is the overvoltage protection threshold in volts, U_dc is the bus voltage at the inflection point in volts (i.e., the difference between U_OV and the residual margin), and T_ctrl is the servo control cycle in seconds. Each inflection point in the absorption saturation inflection point set is independently back-calculated to obtain a trigger threshold. The trigger thresholds corresponding to multiple inflection points in the absorption saturation inflection point set may differ, stemming from the variations in bus voltage levels and the degree of braking superposition at each inflection point. The inflection point with the steepest slope of the preceding margin decrease usually corresponds to the lowest back-calculated threshold, meaning the braking resistor must be triggered at a lower braking power level. For example, if the preceding margin in the absorption saturation inflection point set drops from 50% to 10% within two control cycles at a certain inflection point, the corresponding back-calculated threshold is much lower than the inflection point threshold corresponding to the period of slow preceding margin decrease. The trigger thresholds obtained from back-calculation at each inflection point are summarized to form a back-calculated threshold set. Each threshold in the back-calculated threshold set corresponds one-to-one with its corresponding inflection point. The difference between different thresholds in the back-calculated threshold set reflects the distribution differences in the intensity of phased heat accumulation in each braking event within the dissipation-intensive section. The larger the difference, the more significant the difference in the urgency of braking resistor intervention at different stages.

[0044] A braking engagement time set is generated based on the calibration of the back-calculated threshold set. Each threshold in the back-calculated threshold set corresponds to a specific braking event stage. The absolute value of the power amplitude at each sampling point in the braking power curve corresponding to that stage is scanned from front to back. The sampling time at which the power amplitude first exceeds the threshold corresponding to that stage in the back-calculated threshold set is the braking resistor engagement trigger time. Exceeding this threshold indicates that the bus will not be able to fully absorb the feedback energy of the shaft in the following control cycles, and the braking resistor must be immediately deployed to absorb the excess. If the absolute value of the braking power curve at a certain moment is exactly equal to the corresponding threshold in the back-calculated threshold set, it is treated as exceeding the threshold to avoid boundary ambiguity leading to engagement time delays. If the braking power curve amplitude crosses the threshold multiple times within the same braking event stage, only the first crossing time is taken as the engagement trigger time to prevent redundant terms from being triggered repeatedly in the braking engagement time set. Even if the braking power curve amplitude briefly drops and then rises again after the first crossing, a new trigger time is not recalibrated to maintain the consistency of the braking resistor engagement behavior. After the activation trigger times for each stage are calibrated, a braking activation time set is formed. The time interval between each trigger time in the braking activation time set reflects the frequency density of the braking resistor's continuous intervention within the dissipation-intensive section. The more frequent the trigger times, the higher the proportion of the braking power curve that is consistently higher than the threshold of the back-calculated threshold set within the dissipation-intensive section, indicating that the braking resistor must maintain a high activation state for a long period. If the interval between trigger times in the braking activation time set is shorter than a single braking cycle, it indicates that the braking resistor must be re-activated before the previous activation has completed its heat dissipation recovery. During continuous high-density triggering, the thermal margin of the braking resistor must be reassessed to ensure that it can maintain a safe operating state throughout all trigger events planned in the braking activation time set.

[0045] Step S14: Implement reverse weighting of the braking engagement time set and the regenerative energy release window with inter-axle margin to generate an energy mutual assistance priority sequence; perform mutual assistance time period verification on the energy mutual assistance priority sequence to generate an effective mutual assistance window; and use the effective mutual assistance window to formulate a tiered allocation strategy to form an allocation matrix.

[0046] In some embodiments, the step of generating an energy mutual aid priority sequence by performing inverse weighting of the inter-axis margin on the braking engagement time set and the regenerative energy release window includes: performing time-period margin difference calculation on the braking engagement time set and the regenerative energy release window to generate an inter-axis margin map; performing output volatility analysis on the inter-axis margin map to generate output stability; distinguishing between stable output axes and intermittent output axes based on the output stability to generate a stable output axis set; and performing priority scheduling weighting on the stable output axis set to generate an energy mutual aid priority sequence.

[0047] The inter-axis margin diagram is generated by calculating the time-domain margin difference between the braking engagement time set and the regenerative energy release window. The time-domain margin difference calculation is based on the time-domain width of the regenerative energy release window for each axis, subtracting the number of control cycles occupied by the triggering moments of the coaxial braking engagement time set within that regenerative energy release window. The difference represents the net margin duration that each axis can actually use for inter-axis mutual assistance within the current braking cycle. The longer the net margin duration, the more ample the mutual assistance time available for that axis. Under typical operating conditions, feed axes, due to their small load inertia and frequent changes in direction, have concentrated braking engagement times and densely distributed triggering moments. The width of the regenerative energy release window is frequently compressed by the braking resistor, resulting in a significantly lower net margin duration. Main shafts or high-inertia shafts have long braking cycles and short single-event durations, resulting in sparse braking engagement time sets and wider net margin durations for the regenerative energy release window, making them the preferred source of mutual assistance supply. When the trigger time of the braking engagement time set falls within the regenerative energy release window, the mutual aid qualification of the control cycle in which the trigger time occurs is marked as restricted. The period marked as restricted is deducted from the available margin in the inter-axis margin diagram. The deduction ratio is proportional to the duration of braking resistor engagement during the trigger time; the longer the engagement duration, the more mutual aid margin is deducted. The net margin duration of each axis is arranged along the common time axis. The inter-axis margin diagram is arranged with each axis as a row and the common time axis as a column. Each element is filled with the estimated net margin value of the corresponding axis at that moment. The position with a lower net margin value indicates that the mutual aid capability of that axis is most severely compressed by the braking engagement time set during that period. The greater the difference in net margin between two axes at the same moment, the more significant the difference in the allocation of mutual aid scheduling priority between the two axes must be. The column direction difference distribution of the inter-axis margin diagram is a direct data source for output volatility analysis.

[0048] Output volatility analysis is performed on the inter-axis margin diagram to generate output stability. Volatility describes the cross-cycle variation of the net margin duration for each axis across multiple braking cycles. Axis with large volatility contributes significantly different periods of mutual assistance across different braking cycles, making it difficult to include them in a stable mutual assistance arrangement. Axis with small volatility contributes relatively consistently across cycles, and the scheduling scheme can directly refer to historical averages for prediction. When the machine tool executes repetitive machining programs, the motion trajectory of each axis is highly periodic, and the cross-cycle volatility of the net margin duration is usually small. When switching machining parts or executing non-standard program segments, the motion planning of each axis changes significantly, and the standard deviation of the net margin sequence for that period in the inter-axis margin diagram increases accordingly, and the volatility increases accordingly. The inter-axis margin diagram extracts the net margin sequence of each axis over the entire braking cycle along the axis direction. The volatility C_v is determined by the formula C_v=σ_L / μ_L, where C_v is the dimensionless normalized dispersion index of the volatility of the net margin duration sequence, σ_L is the standard deviation of the net margin duration sequence in milliseconds, and μ_L is the mean of the net margin duration sequence in milliseconds. When μ_L is zero, there is no available mutual assistance margin for that axis throughout the entire process, and it is not included in the volatility analysis and is directly ranked at the bottom. The volatility C_v of each axis is normalized across the entire axis range after taking its reciprocal. The normalized result serves as the output stability value. Higher output stability indicates a higher predictability of the cross-cycle mutual assistance contribution of that axis. For example, if an axis in the inter-axis margin diagram has a net margin sequence mean of 75ms and a standard deviation of only 4ms over 12 consecutive braking cycles, then C_v is 0.053, corresponding to an output stability close to 1. This represents a high-stability mutual assistance source, and the scheduling scheme can rely with high confidence on the historical mean of that axis in the inter-axis margin diagram to arrange mutual assistance. The accuracy of the output stability value is positively correlated with the number of braking cycle samples. When the cumulative number of cycles is insufficient, the confidence level is low, and an insufficient confidence label must be added. Insufficient confidence items are handled according to conservative rules in subsequent differentiation stages.

[0049] A stable output axis set is generated by distinguishing between stable and intermittent output axes based on output stability. Axes with output stability values ​​exceeding the stability threshold are classified as stable output axes, while those below the threshold are classified as intermittent output axes. The stability threshold is set according to the reliability design goals of multi-axis mutual assistance scheduling; the higher the threshold, the stricter the threshold for inclusion in the stable output axis set. In actual machining, when the spindle performs constant speed cutting deceleration braking, the braking pattern is stable and the net margin fluctuates little across cycles, so it is usually classified into the stable output axis set. Workpiece transport axes, due to frequent switching of motion rhythm according to process requirements, have a high standard deviation of the net margin sequence, and the volatility C_v exceeds the threshold, so they are classified as intermittent output axes and are not included in the core scheduling arrangement of the stable output axis set. Boundary axes with output stability values ​​close to the stability threshold are sensitive to the sample size of historical braking cycles. If the confidence is insufficient, they are treated as intermittent output axes to avoid unexpected gaps in mutual assistance scheduling after unstable axes are included in the stable output axis set. The stable output axis set includes the axis number and corresponding output stability value of all stable output axes. The relative output stability values ​​of each axis in the stable output axis set determine their weight in priority scheduling. Axes with higher output stability are prioritized at the front of the energy mutual aid priority sequence. The larger the size of the stable output axis set, the more axes can serve as sources of stable mutual aid among multiple axes, and the stronger the overall mutual aid scheduling immunity. Intermittent output axes are not included in the stable output axis set, but their regenerative energy release window is still tested during the effective mutual aid window verification phase, and they are used as supplementary scheduling objects when the stable output axis set cannot cover the demand gap.

[0050] Based on the stable output axis set, priority scheduling weighting is performed to generate an energy mutual aid priority sequence. Axes in the stable output axis set are arranged from highest to lowest output stability value. This arrangement determines the initial scheduling priority of each axis, with the axis with the highest stability receiving the largest available window first in the mutual aid time allocation. For axes with similar output stability values ​​in the stable output axis set, the mean of the net margin sequence in the inter-axis margin diagram is further compared. Axes with a higher mean have higher priority. The mean net margin reflects the absolute amount of mutual aid time that axis can contribute; the more abundant the absolute amount, the greater the scheduling flexibility. For example, when the output stability of the main axis and the large inertia feed axis are similar, the large inertia feed axis will have a higher priority if its mean net margin is higher. Intermittent output axes outside the stable output axis set are arranged from highest to lowest according to the mean net margin value after all stable output axes have been weighted. Therefore, the energy mutual aid priority sequence covers all drive axes participating in mutual aid scheduling, with the first segment being stable output axes and the second segment being intermittent output axes. These two segments together constitute a complete mutual aid scheduling order framework. After priority weighting is completed, it is necessary to check whether the last axis in the energy mutual aid priority sequence can still be allocated to at least one available mutual aid time period. If there is no available time period at all, the axis is marked. The tiered allocation strategy adopts a gap filling strategy for the marked axis rather than forced allocation. The energy released by the marked axis is temporarily taken by the braking resistor. The arrangement of the energy mutual aid priority sequence is continuously optimized as the operation cycle accumulates. The larger the cross-cycle sample size, the more accurate the output stability estimation and the more stable the sequence arrangement.

[0051] In some embodiments, the step of performing mutual aid time period verification on the energy mutual aid priority sequence to generate an effective mutual aid window includes: extracting the start and end times of energy release and the start and end times of energy absorption for each axis from the energy mutual aid priority sequence to generate an energy release and absorption pairing table; identifying energy release and absorption misalignment blind zones in the energy release and absorption pairing table to generate a mutual aid blind zone set; reverse-calculating connectable time periods based on the mutual aid blind zone set to generate a bridgeable time period set; and calibrating the time-domain mutual aid boundary through the bridgeable time period set to generate an effective mutual aid window.

[0052] The energy release start and end times and energy absorption start and end times of each axis are extracted from the energy mutual aid priority sequence to generate an energy release and absorption pairing table. The energy release start and end times correspond to the time domain boundaries of the regenerative energy release window of each axis, and the energy absorption start and end times correspond to the start and end boundaries of the positive value interval of the power sampling data of each axis. The positive value interval represents that the axis is in an accelerated drive state and continuously absorbs energy from the common bus. For example, the positive power peak is the highest when the Z-axis is rapidly rising, while the positive value interval is frequent but the single amplitude is low when the X-axis is interpolating and feeding. The difference in the energy absorption timing of the two types of axes directly affects the distribution of effective pairing time periods in the energy release and absorption pairing table. The order of each axis in the energy mutual aid priority sequence determines the filling priority of the energy release and absorption pairing table. The energy release start and end times of axes with higher priority are paired with the energy absorption start and end times of other axes first. Pairing resources are tilted towards stable output axes to ensure that the time periods of high-reliability mutual aid sources are occupied first. The energy release and absorption pairing table lists the time overlap intervals between the energy release window of each axis and the energy absorption periods of all other axes, arranged sequentially by axis number according to the energy mutual assistance priority sequence. Pairing records with a non-zero time domain width of the overlap interval are considered valid pairings. The time domain width of a valid pairing reflects the maximum length of the feasible mutual assistance period between the two axes. When multiple axes absorb and release energy simultaneously during the same period, the energy release and absorption pairing table generates multiple valid pairing records for that period. The overlapping portion of multiple records on the time axis is marked as a competition period. The sum of energy released by each axis during the competition period must be strictly controlled by the upper limit of the constraint corresponding to the energy mutual assistance constraint set. Resource allocation within the competition period is still determined according to the order of the energy mutual assistance priority sequence. The more valid pairing records in the energy release and absorption pairing table, the more sufficient the intersection of the braking energy release sequence of that axis with the driving energy absorption sequence of other axes on the common time axis, and the higher the utilization rate of direct energy flow between axes on the common bus.

[0053] To identify energy release and absorption misalignment blind zones in the energy release and absorption pairing table, a mutual assistance blind zone set is generated. An energy release and absorption misalignment blind zone is a time-domain interval in the energy release and absorption pairing table where the energy release window of a certain axis does not overlap with the energy absorption periods of all other axes. Within this interval, the regenerative energy injected along the common busbar of that axis cannot be immediately absorbed by any driving axis; all injected energy must be received by the braking resistor or temporarily stored in the busbar capacitor. The mutual assistance blind zone set summarizes the start and end times and duration of all such non-effective pairing periods. In terms of formation mechanism, the causes of misalignment blind zones can be divided into two categories: one is that all other axes are in a constant speed or braking state during this period, with no axis accelerating to consume busbar energy. This type of blind zone cannot be eliminated by timing adjustments and must rely entirely on the braking resistor or energy storage buffer to absorb it; the other is that although the energy-absorbing axis exists, its energy absorption start and end times are completely offset from the energy release window of the energy-releasing axis on the time axis, differing by several control cycles. Appropriate adjustment of the motion phase can bring their timings closer. Pairing records in the energy release and absorption pairing table with an effective pairing time domain width insufficient for a single control cycle are also included in the mutual aid blind zone set annotation scope. Effective pairing in extremely short time domains is difficult to implement in actual execution due to command response delays, and is equivalent to a true blind zone in terms of processing strategy. The mutual aid blind zone set annotates the two types of blind zones separately. The two types of annotation information are processed separately during the calculation stage of the bridging time period set. The first type of blind zone is directly included in the mandatory acceptance range of the braking resistor, while the second type of blind zone enters the phase adjustment feasibility assessment. The corresponding position of the second type of blind zone in the energy release and absorption pairing table will be converted into a newly added effective pairing record after phase adjustment. The higher the proportion of the total duration of the second type of blind zone in the mutual aid blind zone set to the total duration of the regenerative energy release window, the greater the mutual aid potential that can be released through the timing optimization of the energy release and absorption pairing table.

[0054] A bridgeable time period set is generated by reverse calculation of the connectable time periods based on the mutual aid blind zone set. The bridgeable time period targets the second type of blind zone in the mutual aid blind zone set. Its calculation logic starts from the start and end times of the blind zone and extends forward and backward by a phase adjustment tolerance range. If there are energy absorption start and end times within the tolerance range, the interval is confirmed as a bridgeable time period, indicating that the motion phase of the corresponding axis can overlap with the energy release axis after limited adjustment. The adjustment of the feed axis motion phase must be performed within the interpolation error range allowed by the CNC program. The phase adjustment amount must not cause the workpiece dimensions to exceed tolerance. The upper limit of the tolerance usually corresponds to no more than 2 to 3 times the servo control cycle. Phase adjustments exceeding this range may have an unacceptable impact on machining accuracy. The phase adjustment tolerance δ_t is positively correlated with the size of the bridging time period set, determined by the formula δ_t = Δφ_max / ω_ref, where δ_t is the phase adjustment tolerance in seconds, Δφ_max is the maximum allowable phase offset for the axis motion control in radians, and ω_ref is the reference angular velocity for the corresponding axis in radians per second. A larger δ_t indicates more identifiable bridging time periods and a greater potential for mutual assistance, but this must be done without exceeding motion accuracy constraints. The bridging time period set summarizes all connectable time domain intervals corresponding to the second type of blind zone that can be eliminated through phase adjustment. Each record contains corresponding axis pairing information and a suggested phase adjustment direction. The adjustment direction is determined by the sign of the timing misalignment between the two axes. When the energy-releasing axis phase leads the energy-absorbing axis phase, it is recommended to moderately delay the energy release start; conversely, it is recommended to advance it. The temporal width of each record in the bridging time set represents the newly added effective mutual assistance time after the phase adjustment is implemented. The larger the temporal width, the higher the mutual assistance benefit of the bridging adjustment. The total benefit duration of the bridging time set is a direct quantitative indicator for measuring the multi-axis temporal coordination optimization space.

[0055] An effective mutual aid window is generated by calibrating the time-domain mutual aid boundary using a bridging time period set. The effective mutual aid window is based on existing overlapping effective pairing time periods in the energy release and absorption pairing table, superimposed with newly added mutual aid intervals achievable through phase adjustment within the bridging time period set. After merging the two parts, the first type of blind period that cannot be eliminated from the mutual aid blind zone set is removed, and the remaining continuous time-domain range constitutes the effective mutual aid window. For example, when a tool's rapid descent phase involves a large Z-axis braking that coincides with X-axis interpolation acceleration in time, a generous effective pairing time period is formed at the corresponding position in the energy release and absorption pairing table. This time period is fully incorporated into the effective mutual aid window, allowing the Z-axis braking feedback energy to be directly injected into the X-axis drive end through the common bus without dissipation via the braking resistor, achieving zero-loss energy flow between axes. Effective mutual aid windows are marked separately for each axis on the common time axis. When effective mutual aid windows of different axes overlap, it indicates that these axes can participate in mutual aid simultaneously during that time period. The overlapping section is a candidate period for prioritizing multi-axis coordinated energy release in the tiered allocation strategy. However, the total power released by multiple axes simultaneously must be strictly controlled by the upper limit of the energy mutual aid constraint set and must not exceed the maximum absorption capacity of the common bus at the current moment. Internal discontinuities caused by the first type of mutual aid blind zone within the effective mutual aid window will be merged if the discontinuity width is shorter than the shortest control period. If the discontinuity width is larger, the discontinuity will be retained, and the corresponding time period will be marked as the forced braking resistor interval. The tiered allocation strategy will skip this interval and directly enter the next effective mutual aid window segment. The complete coverage of the effective mutual aid window determines the maximum time domain space that the subsequent tiered allocation strategy can utilize.

[0056] A tiered allocation strategy is formulated using an effective mutual aid window to form an allocation matrix. The effective mutual aid window serves as the time-slot search space, the energy mutual aid priority sequence as the axis allocation order, and the energy mutual aid constraint set as the boundary of the total power for each time slot. Energy release slots are allocated sequentially to the effective mutual aid window according to priority. The highest priority axis occupies the widest and most concentrated energy release slot in the effective mutual aid window first, and the remaining slots are filled sequentially according to the next lower priority axis, until all allocable slots within the effective mutual aid window are covered or all axes are allocated. The constraints of the tiered allocation come from the energy mutual aid constraint set. The sum of the energy release power of each axis within each allocation slot must not exceed the constraint upper limit corresponding to that slot. Any excess must be transferred to the next priority axis or delayed to an adjacent slot with a more lenient constraint upper limit. The final allowed power release value is written to the corresponding position in the allocation matrix hourly. The constraint upper limit is most tightened in the multi-axis superimposed braking section, where the corresponding column elements of the allocation matrix must be strictly compressed within the constraint range. The intervals marked as requiring phase adjustment within the effective mutual assistance window are from the bridging time period set. The allocation matrix adds phase adjustment annotations to the allocation schemes for these intervals, including the axis number and adjustment direction to be adjusted. Before implementation, it must be confirmed that the phase adjustment does not exceed the motion control tolerance of the corresponding axis. After the time period allocation of all axes is completed within the effective mutual assistance window, the upper limit of the allowable energy release power allocated to each axis at each time is arranged by axis as rows and by the sampling time of each common time axis as columns. The constraint content of the allocation matrix is ​​refined from the total boundary on the bus side of the energy mutual assistance constraint set to the independent energy release allocation scheme of each axis after tiered scheduling. The distribution density of non-zero elements in the allocation matrix reflects the time domain proportion of each axis that can participate in mutual assistance scheduling. The higher the proportion, the more fully the regenerative braking energy of that axis is incorporated into the inter-axis mutual assistance system within the corresponding braking cycle.

[0057] Step S15: The allocation matrix and the energy mutual restraint set are fed forward compensation superimposed to generate a preloaded instruction set, and the power instruction is calculated and output based on the preloaded instruction set to generate a cooperative control instruction.

[0058] In some embodiments, the step of superimposing the allocation matrix and the energy mutual restraint set with feedforward compensation to generate a preloaded instruction set includes: performing electromechanical coupling disturbance path tracing on the allocation matrix and the energy mutual restraint set to generate a disturbance propagation graph; performing reaction disturbance amount prediction on the disturbance propagation graph to generate reaction disturbance; performing pre-suppression compensation amount calculation based on the reaction disturbance to generate a suppression compensation table; and performing compensation injection on the allocation matrix based on the suppression compensation table to generate a preloaded instruction set.

[0059] Electromechanical coupling disturbance path tracing is performed on the allocation matrix and energy mutual restraint set to generate a disturbance propagation diagram. The physical starting point of the disturbance is the moment when a certain axis in the allocation matrix injects braking feedback power into the common bus as planned. The injection behavior causes the common bus voltage to rise. The higher the upper limit of the constraint in the energy mutual restraint set, the greater the allowed feedback power injection, and the higher the corresponding common bus voltage fluctuation amplitude. The voltage fluctuation is then propagated along the common bus electrical topology to each disturbed axis. There is an attenuation coefficient on the propagation path, which is jointly determined by the bus impedance and the input impedance of each axis inverter. The disturbed axis with a physical location closer to the injection source axis has a smaller attenuation and a stronger torque disturbance. In terms of the influence of topology layout, the X-axis and Y-axis connected in parallel via short busbars have the largest disturbance amplitude when the main shaft brakes, while the Z-axis, connected via a longer cable, has a slightly larger attenuation. The propagation coefficients of each injection source-disturbed axis path are calibrated one by one and then summarized and filled into the disturbance propagation diagram. The level of the propagation coefficient reflects the spatial distribution difference of the disturbance amplitude. Each planned energy injection event in the allocation matrix corresponds to an independent disturbance propagation process. When multiple axes inject energy simultaneously according to the allocation matrix, the bus voltage fluctuations caused by each injection source are superimposed on the common bus. The combined torque disturbance experienced by the disturbed bearing is the algebraic sum of the contributions from all sources. The superposition period is usually concentrated in the high-density section of the multi-axis synchronous energy release in the allocation matrix. This section corresponds to the period when the upper limit of the energy mutual restraint set is the tightest. When the dense constraints of the energy mutual restraint set in this section fail to completely suppress the superposition amplitude of the disturbance, the combined disturbance amplitude of each disturbed axis in the disturbance propagation diagram reaches its peak value. This is the core period that feedforward compensation must focus on covering.

[0060] The reaction disturbance is generated by predicting the reaction disturbance amount for each axis on the disturbance propagation diagram. The prediction must be completed before the disturbance actually reaches the torque loop of the target axis. The lead time is equal to the complete propagation delay of the electro-mechanical coupled disturbance from the injection source axis to the target axis. The typical propagation delay is usually 2 to 4 control cycles. The prediction work must be completed within this time window and the results must be written into the reaction disturbance sequence. Prediction results outside the window cannot be effectively implemented as feedforward compensation due to insufficient timeliness. The planned energy release power sequence in the future control cycles in the allocation matrix is ​​multiplied by the conduction coefficient of the corresponding path in the disturbance propagation diagram time by time to obtain the predicted value of the torque disturbance that the target axis will experience at the corresponding time. The conduction coefficient drifts slowly with temperature and load changes due to the common bus impedance. It needs to be corrected periodically based on measured data. When the correction period is too long, the deviation of the prediction value accumulates, and the feedforward compensation effect decreases accordingly. When a machine tool performs precision hole machining, the X and Y axes interpolate simultaneously. The common bus voltage fluctuation caused by the spindle tool change deceleration generates a reaction disturbance on the X and Y axes precisely during the stage with the highest interpolation accuracy requirements. In the disturbance propagation diagram, the transmission coefficient from the spindle to the X and Y axes directly determines the magnitude of the predicted amplitude during this stage. The predicted amplitudes of the X and Y axes are the highest in the reaction disturbance sequence during this stage. The suppression compensation table must cover the maximum compensation amount in the corresponding time period. If the prediction deviation of any axis is too large, the contour error of the interpolation trajectory will exceed the allowable range. The predicted amounts of the reaction disturbances of each axis are summarized by axis number and prediction time to form a reaction disturbance sequence. Elements with larger amplitudes in the sequence are concentrated in the period when the allocation matrix plans for multi-axis synchronous energy release. During these periods, the common bus voltage fluctuation and the combined disturbance intensity reach their peak synchronously.

[0061] The suppression compensation table is generated based on the pre-suppression compensation amount calculated according to the reaction disturbance. The polarity of the compensation amount is strictly opposite to that of the reaction disturbance amount. When the reaction disturbance sequence predicts that the torque of a certain axis will be too large, the compensation amount is in the negative direction to pre-reduce the corresponding axis command; when the predicted torque will be too small, it is in the positive direction to pre-addition, so that the two cancel each other out at the driver execution level. The compensation amount ΔP_comp is determined by the formula ΔP_comp=-K_ff×ΔT_dist×ω_ref, where ΔP_comp is the compensation amount in watts, K_ff is the feedforward gain coefficient, which is a dimensionless parameter, ΔT_dist is the predicted torque disturbance amount of the corresponding axis at the corresponding time in the reaction disturbance in Newton-meters, and ω_ref is the current reference angular velocity of the axis in radians per second. The formula converts the disturbance amount in the torque domain into the compensation amount in the power command domain through the current angular velocity. The ΔP_comp of each axis at each time is written into the suppression compensation table row by row and column by column, and can be directly superimposed with the allocation matrix, which has the same dimensions. When K_ff is set to 1, it represents full feedforward compensation, suitable for conditions where the estimation accuracy of the disturbance propagation coefficient is high and the prediction deviation of the reaction disturbance is small. In engineering practice, K_ff is usually set between 0.7 and 0.9, reserving a certain margin to deal with nonlinear components that are difficult to model in the reaction disturbance prediction and to provide a safety net for feedback control, preventing secondary oscillations introduced by over-compensation in the torque loop. The time domain coverage of the suppression compensation table must be completely aligned with the coverage of the non-zero elements of the adjustment matrix. Missing alignment means that there is no feedforward protection at the corresponding moment, and the disturbance must be handled independently by the feedback control. The lag in feedback adjustment during the high-speed interpolation stage of the feed axis is sufficient to cause the profile error to exceed the tolerance band.

[0062] The pre-loaded instruction set is generated by injecting compensation into the allocation matrix based on the suppression compensation table. The timing accuracy of the compensation injection is the core constraint for the pre-loaded instruction set to effectively suppress disturbances. The ΔP_comp of each axis at each time in the suppression compensation table must be issued with a propagation delay time earlier than the corresponding energy release power command in the allocation matrix, so that the compensation amount takes effect precisely when the disturbance actually reaches the torque loop of the target axis. When the advance error exceeds half a control cycle, the time domain overlap between the compensation and the disturbance decreases, and the residual disturbance amplitude increases with the increase of the timing deviation. In the precision interpolation stage, the X-axis and Y-axis have the lowest tolerance for torque fluctuations, and the injection advance amount of the corresponding suppression compensation table components must be calibrated by actual measurement. The motion stability requirements of the Z-axis are relatively relaxed, and the advance amount can be implemented based on theoretical estimation. Each non-zero element in the allocation matrix is ​​algebraically added to the ΔP_comp at the same instant on the same axis in the suppression compensation table. The superposition result is written to the corresponding position in the preload instruction set. When ΔP_comp is negative and has a large amplitude, the superposition result is lower than the original value of the allocation matrix, which means that the axis must actively reduce the actual released energy in exchange for sufficient suppression of the target axis torque fluctuation. The larger the reduction, the stronger the disturbance of the energy injection event on the disturbed axis and the higher the cost of feedforward protection. The positions with zero values ​​in the allocation matrix are not modified, and the instructions at these times in the preload instruction set retain their original values ​​to avoid unnecessary modifications that introduce additional control noise. The preload instruction set fully covers the time-by-time power instructions of all drive axes in the entire braking mutual assistance scheduling time domain, and encodes energy release allocation information and disturbance suppression information. It is a unified execution carrier after the allocation matrix and suppression compensation table are superimposed in time sequence alignment.

[0063] Based on the preloaded instruction set, the power command is calculated and output as a coordinated control command. The commands for each axis at each moment in the preloaded instruction set are expressed in power units. They must be converted into torque increments that the driver can directly execute, according to the formula ΔT_cmd=P_cmd / ω_act, combined with the real-time angular velocity of each axis. Here, ΔT_cmd is the calculated torque increment in Newton-meters, P_cmd is the power command value at the corresponding moment in the preloaded instruction set in watts, and ω_act is the measured angular velocity at the corresponding moment in radians per second. The lower the angular velocity, the larger the torque increment corresponding to the same power. It must be confirmed that the rated torque reserve of the drive axis is not exceeded. If it is exceeded, the power value is reduced to the power equivalent corresponding to the rated torque and then recalculated. During low-speed intensive interpolation, the calculated torque increment of the feed axis may be too large. It is necessary to verify after calculation whether the rated torque constraint has been reached. For example, if a feed axis undertakes energy release during a low-speed intensive interpolation segment and the torque increment has reached 85% of the rated value, the maximum energy release power that the axis can handle must be corrected downwards to the power equivalent of the corresponding rated torque. The correction amount is written back to that position in the pre-load command set to avoid over-torque protection action interrupting the current mutual aid execution. If the measured speed of a certain axis in the pre-load command set is zero at a certain moment, the axis is in a stationary state, and the calculation skips that position, not participating in the mutual aid execution in that session. The calculation of other axes continues unaffected. After the torque increment calculation of each axis is completed, it is superimposed with the current speed loop command. The superposition result constitutes a collaborative control command in the standard torque command format. The collaborative control command uses the master clock as a unified time reference and is consistent with the previous steps. After being sent to each axis driver, each axis performs normal interpolation while releasing or absorbing regenerative energy according to the collaborative control command. The execution result is fed back to the power sampling data of the next control cycle to form a closed-loop adjustment.

[0064] To implement the above-described method embodiment, a multi-axis servo common bus energy collaborative utilization energy-saving method is proposed to achieve the corresponding functions and technical effects. See also... Figure 2 , Figure 2 This diagram illustrates a structural block diagram of a multi-axis servo common bus energy-coordinated utilization energy-saving system 200 provided in an embodiment of this application. For ease of explanation, only the parts relevant to this embodiment are shown. The multi-axis servo common bus energy-coordinated utilization energy-saving system 200 provided in this embodiment includes: Data acquisition module 201 is used to acquire power, speed and bus voltage sampling data of each drive axis of the multi-axis servo system, and to construct a bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and the speed sampling data; Energy constraint module 202 is used to extract the regenerative energy release window of each axle braking through the bus timing diagram, perform timing alignment on the regenerative energy release window to generate an energy mutual assistance sequence, and calculate the upper limit of mutual assistance based on the energy mutual assistance sequence and the bus voltage sampling data to form an energy mutual assistance constraint set. The heat consumption assessment module 203 is used to construct a period allocation matrix by fusing the motion period constraints of each axis based on the energy mutual restraint set and the speed sampling data, perform braking resistor heat accumulation calculation on the period allocation matrix and the power sampling data to determine the dissipation dense section, and solve the braking resistor input threshold in reverse for the dissipation dense section to generate a braking input time set. The scheduling decision module 204 is used to perform reverse weighting of the braking input time set and the regenerative energy release window with inter-axle margin to generate an energy mutual assistance priority sequence, perform mutual assistance time period verification on the energy mutual assistance priority sequence to generate an effective mutual assistance window, and use the effective mutual assistance window to formulate a tiered allocation strategy to form a scheduling matrix. The instruction output module 205 is used to perform feedforward compensation superposition on the allocation matrix and the energy mutual restraint set to generate a preloaded instruction set, and to execute power instruction calculation and output cooperative control instructions based on the preloaded instruction set.

[0065] The multi-axis servo common bus energy-coordinated utilization energy-saving system 200 described above can implement the multi-axis servo common bus energy-coordinated utilization energy-saving method of the above method embodiments. The options in the above method embodiments are also applicable to this embodiment, and will not be detailed here. The remaining contents of this application embodiment can be referred to the contents of the above method embodiments, and will not be repeated in this embodiment.

[0066] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

[0067] The above embodiments are not an exhaustive list based on the present invention, and there may be many other embodiments not listed. Any substitutions and improvements made without departing from the concept of the present invention are within the protection scope of the present invention.

Claims

1. A multi-axis servo common bus energy collaborative utilization energy-saving method, characterized in that, include: Collect power, speed and bus voltage sampling data of each drive axis of the multi-axis servo system, and construct a bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and the speed sampling data; The regenerative energy release window of each axle braking is extracted by the bus timing diagram, and the regenerative energy release window is time-aligned to generate an energy mutual assistance sequence. The upper limit of mutual assistance is calculated based on the energy mutual assistance sequence and the bus voltage sampling data to form an energy mutual assistance constraint set. Based on the energy mutual restraint set and the speed sampling data, the motion cycle constraints of each axis are fused to construct a cycle allocation matrix. The cycle allocation matrix and the power sampling data are used to calculate the heat accumulation of braking resistors to determine the dissipation dense section. The braking resistor input threshold is solved in reverse for the dissipation dense section to generate a braking input time set. The set of braking engagement times and the regenerative energy release window are weighted in reverse by the inter-axle margin to generate an energy mutual aid priority sequence. The energy mutual aid priority sequence is checked for mutual aid time periods to generate an effective mutual aid window. The effective mutual aid window is used to formulate a tiered allocation strategy to form an allocation matrix. The allocation matrix and the energy mutual restraint set are fed forward and superimposed to generate a preloaded instruction set. Based on the preloaded instruction set, power instruction calculation is performed to output cooperative control instructions.

2. The method according to claim 1, characterized in that, The step of constructing a bus timing diagram by performing inter-shaft timing phase differential mapping on the power sampling data and the speed sampling data includes: The power sampling data and the rotational speed sampling data are used to identify the inertia of the acceleration / deceleration transition segment and generate an axis inertia weight table. Based on the axis inertia weight table, the axis with the highest inertia is identified as the phase anchoring axis and an anchoring axis is generated. For the anchoring axis, perform phase difference compensation, locking, and alignment on the remaining axes to generate an anchoring phase lock group; Based on the anchored phase-locked group, the timing sequence of each axis is spliced ​​to construct the bus timing diagram.

3. The method according to claim 1, characterized in that, The step of extracting the regenerative energy release window for each axle brake through the bus timing diagram includes: The voltage rise rate of each axis bus is extracted from the bus timing diagram to generate a voltage rise rate curve; Based on the voltage rise rate curve, an overvoltage threshold approximation identification is performed to generate an overvoltage precursor segment. The high-risk energy release timing is generated by reverse-engineering the corresponding axle braking energy release timing using the overpressure precursor segment; Based on the high-risk energy release timing, the energy output boundary is calibrated to generate a regenerative energy release window.

4. The method according to claim 1, characterized in that, The step of performing braking resistor heat accumulation calculation to determine the dissipation-dense section on the period allocation matrix and the power sampling data includes: Braking power curves are generated by extracting the braking power timing of each axle from the period allocation matrix and the power sampling data; A heat dissipation redundancy diagram is generated by performing a reverse estimation of the heat dissipation margin of the thermal resistance network for the braking power curve. Based on the aforementioned heat dissipation redundancy diagram, a heat dissipation bottleneck segment is generated by locating the redundancy approximation depletion segment. Based on the heat dissipation bottleneck section, a dissipation range analysis is performed to generate a dissipation-dense section.

5. The method according to claim 1, characterized in that, The step of inversely solving the braking resistor engagement threshold in the dissipation-dense section to generate a braking engagement time set includes: Extract the synchronous bus absorption margin in the dissipation-intensive section to generate the bus absorption margin curve; Perform saturation inflection point location on the bus absorption margin curve to generate an absorption saturation inflection point set; A back-calculated threshold set is generated by reverse-calculating the corresponding braking resistor activation trigger condition based on the absorption saturation inflection point set. Based on the back-calculated threshold set, the activation trigger time is calibrated to generate the braking activation time set.

6. The method according to claim 1, characterized in that, The step of generating an energy mutual assistance priority sequence by applying an inter-axle margin inverse weighting to the braking engagement time set and the regenerative energy release window includes: The inter-axis margin map is generated by performing time-period margin difference calculation between the braking engagement time set and the regenerative energy release window. Perform output volatility analysis on the inter-axis margin diagram to generate output stability; Based on the output stability, a set of stable output axes is generated by distinguishing between stable output axes and intermittent output axes. Based on the stable output axis set, priority scheduling and weighting are performed to generate an energy mutual aid priority sequence.

7. The method according to claim 1, characterized in that, The step of performing mutual aid time period verification on the energy mutual aid priority sequence to generate a valid mutual aid window includes: The start and end times of energy release and energy absorption of each axis are extracted from the energy mutual assistance priority sequence to generate an energy release and absorption pairing table. For the energy release and absorption pairing table, identify energy release and absorption misalignment blind zones and generate a mutual assistance blind zone set; Based on the aforementioned mutual assistance blind zone set, a bridgeable time period set is generated by reverse calculation of connectable time periods; An effective mutual assistance window is generated by calibrating the time-domain mutual assistance boundary using the bridgeable time-segment set.

8. The method according to claim 1, characterized in that, The step of generating a preloaded instruction set by superimposing the allocation matrix and the energy mutual restraint set through feedforward compensation includes: Electromechanical coupling perturbation path tracing is performed on the allocation matrix and the energy mutual restraint set to generate a perturbation propagation graph; Perform reaction disturbance prediction on each axis of the disturbance propagation diagram to generate reaction disturbance; Based on the aforementioned reaction disturbance, a pre-suppression compensation amount is calculated to generate a suppression compensation table; Based on the suppression compensation table, the allocation matrix is ​​compensated and injected to generate a preloaded instruction set.

9. The method according to claim 4, characterized in that, The step of locating the redundant approximation depletion segment based on the heat dissipation redundancy map to generate the heat dissipation bottleneck segment includes: Perform multi-axis redundancy synchronization analysis on the aforementioned heat dissipation redundancy diagram to generate redundancy synchronization degree; The redundant synchronization degree is used to identify multi-axis synchronous approximation depletion segments and generate a set of cooperative failure segments; For the aforementioned set of collaborative failure segments, perform an overall bottleneck weighting to generate a bottleneck weight table; Based on the bottleneck weight table, the bottleneck segment is calibrated to generate a heat dissipation bottleneck segment.

10. A multi-axis servo common bus energy collaborative utilization energy-saving system, characterized in that, include: The data acquisition module is used to collect power, speed and bus voltage sampling data of each drive axis of the multi-axis servo system, and to construct a bus timing diagram by performing inter-axis timing phase differential mapping on the power sampling data and the speed sampling data. The energy constraint module is used to extract the regenerative energy release window of each axle braking through the bus timing diagram, perform timing alignment on the regenerative energy release window to generate an energy mutual assistance sequence, and calculate the upper limit of mutual assistance based on the energy mutual assistance sequence and the bus voltage sampling data to form an energy mutual assistance constraint set. The heat consumption assessment module is used to construct a period allocation matrix by fusing the motion period constraints of each axis based on the energy mutual restraint set and the speed sampling data, perform braking resistor heat accumulation calculation on the period allocation matrix and the power sampling data to determine the dissipation dense section, and solve the braking resistor input threshold in reverse for the dissipation dense section to generate a braking input time set. The scheduling decision module is used to generate an energy mutual assistance priority sequence by performing reverse weighting of the braking input time set and the regenerative energy release window with inter-axle margin, perform mutual assistance time period verification on the energy mutual assistance priority sequence to generate an effective mutual assistance window, and use the effective mutual assistance window to formulate a tiered allocation strategy to form a scheduling matrix. The instruction output module is used to perform feedforward compensation superposition on the allocation matrix and the energy mutual restraint set to generate a preloaded instruction set, and to execute power instruction calculation and output cooperative control instructions based on the preloaded instruction set.

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