A method and system for PID-based grinding speed control

Abstract

The application relates to the intelligent field of grinding processing, in particular to a grinding speed control method and system based on PID. The method comprises the following steps: collecting current and rotating speed signals of a servo motor, obtaining a pure load torque observation value through online parameter calibration, inertia-torque decoupling and selective bias compensation; determining a heterogeneous boundary event through a relative change rate sudden change variable index and a multi-cycle continuous confirmation logic, and latching an observation residual vector before and after the event; matching the residual vector with a pre-calibrated multi-hardness grade standardized residual template, identifying a disturbance amplitude grade, generating an exponential decay window-shaped nonlinear feedforward torque sequence, and converting the sequence into an equivalent speed disturbance amount to be superimposed on a PID original error to realize active compensation; monitoring a speed error peak value after the feedforward is completed, and directionally correcting a corresponding grade feedforward strength reference value. The application can solve the problem of speed fluctuation caused by heterogeneous grinding load step disturbance, and improve processing quality and system stability.

Description

Technical Field

[0001] This application relates to the field of intelligent grinding processes, and in particular to a grinding speed control method and system based on PID. Background Technology

[0002] Dissimilar grinding processes following weld repair of aero-engine blades are crucial steps in the aerospace manufacturing industry, ensuring the precision and lifespan of blade repairs. When the grinding contact area transitions instantaneously from the low-hardness base material to the high-hardness weld, the material hardness undergoes a step-like change, causing the servo motor to experience millisecond-level sudden load disturbances. Conventional PID controllers rely solely on speed error for feedback adjustment; their inherent response lag cannot match such rapid disturbances, easily leading to significant drops in grinding speed or overshoot. This, in turn, results in machining defects such as surface chatter marks, burns, and dimensional deviations, severely impacting the operational safety of aero-engines.

[0003] Existing load torque observation methods often directly use the inertia and torque constant specified on the motor nameplate for calculation, resulting in a systematic bias in torque calculation due to a mismatch between model parameters and actual operating conditions. Furthermore, traditional bias compensation mechanisms rely on continuous updates, which can easily misinterpret real load step signals as gradual biases, distorting key disturbance information. Simultaneously, traditional abrupt change detection uses absolute torque differences as the criterion, which suffers from the drawbacks of false alarms caused by noise under light load conditions and difficulty in identifying minute abrupt changes under heavy load conditions, failing to achieve reliable, low-latency detection of heterogeneous boundary events. Moreover, existing feedforward compensation schemes often use a single fixed compensation amount, which cannot adapt to the differences in disturbance amplitude caused by varying hardness, easily leading to speed overshoot due to overcompensation or residual static error due to undercompensation; and lacking online self-correction capabilities, they cannot cope with the attenuation of compensation effects caused by long-term changes such as equipment wear, grinding wheel wear, and operating condition drift. Summary of the Invention

[0004] This application provides a PID-based grinding speed control method and system, which is used to solve the speed fluctuation and compensation mismatch problems caused by millisecond-level load step disturbances in heterogeneous grinding, so as to improve speed stability, surface finish and long-term system reliability.

[0005] Firstly, this application provides a PID-based grinding speed control method, employing the following technical solution: A PID-based grinding speed control method includes: acquiring current and speed signals of a servo motor; decoupling the current and speed signals by inertia and torque to obtain the initial net load torque of the servo motor; selectively biasing the initial net load torque to obtain the current pure load torque observation value; acquiring the pure load torque observation value of the previous control cycle; calculating the mutation index of the current control cycle based on the current and previous pure load torque observation values; determining that a heterogeneous boundary event has occurred when the mutation index exceeds a preset threshold for a certain number of consecutive times; latching the pure load torque sequence before and after the event as the observation residual vector; and calculating the normalization between the observation residual vector and the standardized residual template corresponding to each hardness level. The cross-correlation coefficient is calculated; the hardness level corresponding to the template with the largest cross-correlation coefficient is selected as the current disturbance amplitude level; wherein, the standardized residual templates corresponding to multiple hardness levels are obtained by repeatedly performing heterogeneous interface experiments on standard specimens with different hardness calibrations under the same grinding process, collecting and standardizing the pure load torque observation value sequence; according to the level, the corresponding feedforward strength reference value is obtained, and a nonlinear feedforward torque sequence with exponential decay and window function smoothing is generated; the feedforward torque sequence is converted into an equivalent speed disturbance quantity through normalized gain, and superimposed on the original speed error of the PID controller to form a reconstructed speed error to drive active compensation; the peak value of the speed error is monitored; if the peak value exceeds the safety threshold, the feedforward strength reference value corresponding to the level is corrected according to the direction of the error with a preset step size.

[0006] Optionally, during the no-load acceleration phase before the grinding operation begins, the control system executes a preset constant angular acceleration command. During this phase, the cross-axis current intensity sequence of the servo motor and the encoder angular acceleration sequence are simultaneously acquired. The current intensity sequence and the angular acceleration sequence are fitted using a recursive least squares algorithm to obtain an estimated value for the system's equivalent inertia and torque constant. The acceleration coupling torque is calculated based on the estimated equivalent inertia and the angular velocity difference between adjacent cycles. The acquired servo motor current signal is subjected to a Parker transform to obtain the cross-axis current intensity, which is then converted into electromagnetic torque from the estimated torque constant. The initial net load torque is obtained by subtracting the acceleration coupling torque from the electromagnetic torque.

[0007] Optionally, a preset bias update rate coefficient is used. The current bias compensation term is obtained by adding the bias compensation term from the previous moment to the product of the bias update rate coefficient and the difference between the current initial net load torque and the previous bias compensation term. The update is only performed during the period when the torque is stable without sudden changes; otherwise, the bias compensation term remains unchanged. The initial net load torque is subtracted from the bias compensation term to obtain the observed value of the pure load torque.

[0008] Optionally, the absolute value of the difference between the observed pure load torque value of the current control cycle and the observed pure load torque value of the previous control cycle is taken as the numerator; the larger of the absolute value of the current pure load torque value and a preset minimum positive number is taken as the denominator; the numerator is divided by the denominator to obtain the mutation index.

[0009] Optionally, the feedforward intensity reference value is used as the initial amplitude; the initial amplitude is multiplied by an exponential decay factor, which decreases exponentially according to the number of control cycles after feedforward injection and a preset decay time constant; then multiplied by a window function shaping coefficient, which is used to provide a smooth transition at the beginning and end of the sequence; thereby generating the nonlinear feedforward torque sequence.

[0010] Optionally, the torque value of the corresponding control cycle in the feedforward torque sequence is divided by the normalized gain factor to obtain the equivalent speed disturbance; the commanded speed is subtracted from the actual speed to obtain the original speed error; the original speed error is added to the equivalent speed disturbance to form the reconstructed speed error, wherein the physical meaning of the normalized gain factor is the coefficient that converts the torque into the speed influence.

[0011] Secondly, this application provides a PID-based grinding speed control system, which adopts the following technical solution: A PID-based grinding speed control system includes a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement the aforementioned PID-based grinding speed control method.

[0012] This application has the following technical effects: 1. By performing online calibration during the no-load acceleration phase before grinding, the equivalent inertia and torque constant of the system are accurately obtained, eliminating the torque calculation error caused by nameplate parameter mismatch from the source. A selective bias compensation mechanism with conditional gating is adopted, which slowly converges and eliminates the comprehensive friction torque and calibration residual bias during the torque stability period, and immediately freezes and updates during the torque mutation period, fully preserving the amplitude and dynamic characteristics of the load step. Combined with the mutation amount index based on the relative change rate and the multi-cycle continuous confirmation logic, the contradiction between light load noise false alarm and heavy load sensitivity reduction is effectively solved, and zero missed detection and low false alarm judgment of millisecond-level heterogeneous boundary events are achieved, providing an accurate and timely input basis for subsequent active compensation.

[0013] 2. By constructing a standardized residual template library for multiple hardness levels through offline calibration, and using a normalized cross-correlation matching algorithm to focus on waveform morphology features rather than absolute amplitude, it can robustly identify the disturbance amplitude level of the current heterogeneous boundary event, fundamentally avoiding overcompensation or undercompensation problems caused by a single fixed compensation amount; the generated nonlinear feedforward torque sequence adopts an exponential decay law to match the natural decay characteristics of grinding load disturbance, and is shaped by window functions such as the Hanning window to eliminate sharp inflection points in the time domain and suppress high-frequency components in the frequency domain, effectively avoiding speed overshoot and the inherent resonance of the grinding spindle system; the method of converting the feedforward torque into an equivalent speed disturbance and superimposing it on the original PID error does not require modification of the internal structure of the PID controller, has strong compatibility, and can be quickly integrated into various industrial servo grinding control systems.

[0014] 3. By monitoring the peak speed error within the stable window after feedforward compensation, a quantitative evaluation of the compensation effect is achieved. The directional micro-correction algorithm based on the error direction can automatically correct the compensation mismatch caused by offline calibration deviation and long-term operating condition drift, and the single correction step size is extremely small, ensuring the stability of system operation. The corrected feedforward strength reference value is automatically overwritten to the controller's non-volatile memory without interrupting the grinding operation or performing additional offline recalibration, realizing the online evolution of the feedforward compensation system, ensuring the long-term consistency of the compensation effect under different batches and different wear conditions, and further improving the processing quality and equipment operation reliability of the heterogeneous grinding process. Attached Figure Description

[0015] Figure 1 This is a flowchart of a PID-based grinding speed control method. Detailed Implementation

[0016] This application discloses a PID-based grinding speed control method, referring to... Figure 1 ,include: S1: Acquire the current signal and speed signal of the servo motor, decouple the current signal and speed signal by inertia and torque to obtain the initial net load torque of the servo motor; perform selective bias compensation on the initial net load torque to obtain the current pure load torque observation value; obtain the pure load torque observation value of the previous control cycle, calculate the mutation index of the current control cycle based on the current pure load torque observation value and the pure load torque observation value of the previous control cycle, and when the mutation index exceeds the preset threshold for a certain number of times, a heterogeneous boundary event is determined to have occurred, and the pure load torque sequence before and after the event time is latched as the observation residual vector.

[0017] In the heterogeneous grinding process following weld repair of aero-engine blades, the material hardness undergoes a step change when the grinding contact zone instantaneously enters the weld from the base material, causing the servo motor to experience sudden load disturbances on a millisecond scale. Since the rise time of this disturbance is much faster than the fluctuations in conventional grinding process parameters, the control system needs to reliably sense and determine the event within an extremely short time window. Based on this, a load torque observation link with selective bias compensation is constructed starting from the raw electrical signal of the servo motor. Real-time prediction of heterogeneous interface events is achieved on the pure load torque signal through a relative rate of change exponent and continuous confirmation logic.

[0018] In each fixed discrete control cycle Internally, the signal acquisition unit of the servo driver first obtains the three-phase current intensity output by the Hall sensor of the servo motor. and the angular velocity signal output by the encoder Because the original signal contains electromagnetic noise and quantization errors, it needs to undergo adaptive filtering. and A second-order low-pass filter is fed in. To balance noise suppression and dynamic tracking requirements under different speed closed-loop responses—a low cutoff frequency is needed to enhance noise reduction when the speed closed-loop response is slow, and a high cutoff frequency is needed to limit phase delay when the response is fast—an adaptive cutoff frequency formula related to the system speed closed-loop bandwidth is constructed: in, This indicates the cutoff frequency of a second-order low-pass filter, expressed in radians per second. This represents the bandwidth scaling factor, empirically taken as 1.2, and is dimensionless. This represents the closed-loop bandwidth of the speed identified by the system, measured in radians per second.

[0019] Cutoff frequency With speed closed-loop bandwidth They are directly proportional. When the speed closed-loop bandwidth... When the cutoff frequency is increased (the system response becomes faster), Synchronous increase reduces filter phase delay, ensuring the ability to track rapidly changing signals; when the speed closed-loop bandwidth... When the cutoff frequency is reduced (system response slows down), Synchronization reduction enhances the filter's high-frequency noise suppression capability, effectively filtering out electromagnetic interference and quantization errors in the signal. This adaptive adjustment mechanism maintains a trade-off between denoising and dynamic tracking, matching the system's operating state.

[0020] Before using the filtered signal for inertia-torque decoupling, due to discrepancies between the nominal values ​​of the servo motor's torque constant and the system's equivalent inertia and the actual operating conditions, online calibration is required to obtain more accurate model parameters. During the no-load acceleration phase before the grinding operation officially begins, the control system executes a preset constant angular acceleration command. The unit is radians per second squared. Multiple sets of quadrature-axis current intensities are simultaneously acquired during this phase. The actual angular acceleration data obtained from the encoder angular velocity difference is used. The acquired pairwise data are fitted using a recursive least squares algorithm to obtain an estimate of the system's equivalent inertia. The unit is kg·m², and the estimated value of the torque constant is also given. The unit is Newton-meter-ampere. The recursive least squares algorithm is a well-known technique and will not be elaborated further. This online calibration process reduces the torque calculation bias caused by model parameter mismatch from the source.

[0021] After completing the online calibration, inertia-torque decoupling calculations are performed in each control cycle. Since part of the electromagnetic torque output by the servo motor is used to overcome the dynamic torque caused by the rotor and load inertia, and another part is used to overcome the external load torque and the system's combined frictional torque, the acceleration coupling torque consumed to overcome the system's own inertia under the current acceleration / deceleration state is first calculated based on the rigid body rotation dynamics equations, and the acceleration coupling torque formula is constructed: in, Indicates the first The acceleration coupling torque per control cycle, in Newton-meters; This represents the estimated equivalent inertia of the system, expressed in kilogram-meter square. Indicates the first The encoder angular velocity after filtering for each control cycle, in radians per second; Indicates the first The encoder angular velocity after filtering for each control cycle, in radians per second; This represents the discrete control period, in seconds.

[0022] Acceleration coupling torque Equivalent inertia of the system Angular velocity difference between adjacent periods They are all positively proportional to the control cycle. They are inversely proportional. When the system accelerates ( )hour, A positive value indicates that the motor needs to output additional torque to overcome inertial acceleration; when the system decelerates ( )hour, A negative value indicates that the inertial assist motor is decelerating; when the system is moving at a constant speed ( )hour, There is no inertial torque consumption.

[0023] At the same time, the filtered three-phase current intensity Performing the Park transformation yields the quadrature-axis current intensity. The Parker transformation is a well-known technical concept and will not be elaborated further. The output electromagnetic torque of the servo motor is linearly related to the quadrature-axis current. Combined with the online calibrated torque constant, the total electromagnetic torque output of the motor can be accurately calculated, providing a total torque reference for subsequent inertia-torque decoupling. The electromagnetic torque formula is then constructed as follows: in, Indicates the first The calculated electromagnetic torque for each control cycle, in Newton-meters; This represents an estimated value of the torque constant, expressed in Newton-meter-ampere. Indicates the first The quadrature-axis current intensity obtained by Parker transformation for each control cycle is expressed in amperes.

[0024] electromagnetic torque With cross-axis current intensity They exhibit a strictly proportional relationship. (Cross-axis current) The larger the value, the greater the total electromagnetic torque output by the motor. The larger the value, the stronger the driving torque it can provide; conversely, the smaller the value, the smaller the total electromagnetic torque. This linear relationship is the core foundation of servo motor torque control and is calibrated online. This ensures the consistency between the calculation results and the actual output.

[0025] because The total electromagnetic torque includes contributions from external load torque, friction torque, and inertial torque. To obtain the initial net load torque that reflects only the sum of external load and friction torque, the calculated acceleration coupling torque needs to be subtracted from the total electromagnetic torque to decouple the inertial torque, thus constructing the formula for the initial net load torque: in, Indicates the first The initial net load torque for each control cycle, in Newton-meters; Indicates the first The calculated electromagnetic torque for each control cycle, in Newton-meters; Indicates the first The acceleration coupling torque per control cycle, measured in Newton-meters.

[0026] Initial net load torque It equals the total electromagnetic torque minus the inertial torque. When the electromagnetic torque Increase and acceleration coupling torque When unchanged, A synchronous increase reflects an increase in external load or frictional torque; when acceleration coupling torque... Increase and electromagnetic torque When unchanged, The synchronous decrease reflects that more torque is being used to overcome inertia. At this point... Although the inertial torque has been removed, its value still contains the combined frictional torque and calibration residual bias, resulting in a high-noise, biased original signal.

[0027] To extract a pure torque observation reflecting changes in external grinding load from the initial net load torque, a set of bias compensation terms with conditional gating is introduced. The combined frictional torque and calibrated residual bias mixed in the initial net load torque exhibit gradually varying characteristics, while the load torque change caused by abrupt material changes exhibits step characteristics. To eliminate the gradually varying bias without absorbing the actual load step, a bias compensation term update law with conditional gating is constructed: in, Indicates the first The bias compensation term for each control cycle, in Newton-meters; Indicates the first The bias compensation term for each control cycle, in Newton-meters; This represents the bias update rate coefficient, with a value between 0.001 and 0.01, and is a dimensionless hyperparameter. Indicates the first The initial net load torque for each control cycle, in Newton-meters.

[0028] Bias compensation term The update is performed using a first-order low-pass filter, and the update rate is... control. The larger the value, the faster the bias compensation term tracks the gradually changing bias in the initial net load torque, but it is also more likely to mistakenly absorb rapidly changing real load signals. The smaller the value, the slower the tracking speed, but the stronger the anti-interference ability.

[0029] When the system determines that it is in a period of stable torque, the update law executes normally. The system gradually converges to the sum of the combined frictional torque and the calibrated residual bias; when the system determines that a sudden torque change may occur, the update law freezes. The previous cycle value is kept unchanged to avoid misinterpreting actual load steps as bias. This update is only performed during periods of stable torque without abrupt changes, when the grinding wheel is not in a material change zone. The update is immediately frozen when the system detects a possible torque change, thus preventing the actual load step from being mistakenly absorbed as bias. To purify the pure signal reflecting only external grinding load changes from the initial net load torque, the converged bias compensation term needs to be subtracted from the initial net load torque to eliminate the influence of the combined friction torque and calibration residual bias, thus constructing a formula for the pure load torque observation value: in, Indicates the first The pure load torque observation for each control cycle, in Newton-meters; Indicates the first The initial net load torque for each control cycle, in Newton-meters; Indicates the first The bias compensation term for each control cycle, in Newton-meters.

[0030] Pure load torque observation It equals the initial net load torque minus the gradually varying offset compensation term. During the steady-state period, It has converged to the combined frictional torque and the calibrated residual bias, therefore It only reflects the actual changes in external grinding load; during transient abrupt changes, freeze, It fully preserves the entire amplitude and dynamic characteristics of the load step, without signal distortion caused by bias absorption. This selective bias compensation mechanism enables... It converges the bias only during the steady-state window, while maintaining unbiased observation of real load changes during the transient period.

[0031] After obtaining the pure load torque observations, it is necessary to extract the mutation index from them that can sensitively and robustly indicate heterogeneous boundary events. The sudden change in load torque caused by a material change manifests as an instantaneous increase in the difference between torques in adjacent cycles. However, the degree of physical impact represented by the same magnitude of torque increment differs under light and heavy load conditions. Directly using the absolute difference can lead to false alarms under light load and decreased sensitivity under heavy load. Therefore, a mutation index based on the relative rate of change is constructed to achieve reliable quantification of the mutation amount on a normalized scale. in, Indicates the first The mutation index for each control cycle, dimensionless; Indicates the first The pure load torque observation for each control cycle, in Newton-meters; Indicates the first The pure load torque observation for each control cycle, in Newton-meters; This represents a very small positive number to prevent division by zero errors; empirically, it is taken as [value missing]. The unit is Newton-meter.

[0032] Mutation index The numerator is the absolute value of the difference in pure load torque between adjacent periods, directly capturing the high-frequency variation components of the torque; the denominator is the larger of the current torque amplitude and the minimum positive number, achieving normalization. When the load torque undergoes a step change, the numerator increases sharply. Synchronization significantly increases; when only noise fluctuations exist, the molecule is smaller. It remains at a low level. Under heavy load conditions, the denominator is larger, and the corresponding absolute difference is... The smaller value avoids false alarms caused by normal torque fluctuations under heavy loads; under light load conditions, the smaller denominator corresponds to the same absolute difference. The larger capacity ensures high sensitivity for detecting minute mutations under light loads. The existence of this avoids division-to-zero errors caused by torque approaching zero under light loads.

[0033] Occasional electrical signal spikes or the shedding of grinding particles may cause... Isolated exceedances would lead to false triggering if judged directly in a single cycle; therefore, a dual-condition continuous confirmation mechanism is implemented. A preset threshold for heterogeneous boundary judgment is also included. The empirical value range is 0.3 to 0.5, a dimensionless hyperparameter that can be adjusted by the implementer according to the specific implementation scenario; number of confirmations. The number of times is set to 3 to 5, which can be adjusted by the implementer according to the specific implementation scenario. The value exceeds And this over-limit state is continuous If the condition is met continuously throughout all control cycles, the system determines that a heterogeneous boundary event has occurred and sets the heterogeneous boundary event flag. .once When the bit is set, the system synchronously latches the data before and after the event trigger time. The sequence of pure load torque observations over a period of time constitutes the observation residual vector. ,in It is a positive integer, typically ranging from 5 to 10. This vector fully records the dynamic transition process of torque from steady state to step increase during heterogeneous boundary events, and will serve as input data for subsequent disturbance amplitude level identification.

[0034] Adaptive filtering achieves a dynamic balance between signal denoising and dynamic tracking. Online parameter calibration reduces torque calculation bias caused by model parameter mismatch at the source. Inertia-torque decoupling eliminates interference from inertial torque. Selective bias compensation eliminates slowly varying biases while preserving the true load step. The relative rate of change mutation exponent and continuous confirmation logic effectively overcome the contradiction between false alarms under light load noise and decreased sensitivity under heavy load. A high-fidelity, low-latency load torque observation link is constructed, achieving zero missed detections and low false alarms for millisecond-level material mutation disturbances during heterogeneous grinding of aero-engine blades, providing a reliable input foundation for subsequent disturbance amplitude identification and feedforward compensation.

[0035] Thus, we obtain the observed values ​​of the pure load torque, the determination results of the mutation index, and the observed residual vector of the heterogeneous boundary event.

[0036] S2: Calculate the normalized cross-correlation coefficient between the observed residual vector and the standardized residual template corresponding to each hardness level; select the hardness level corresponding to the template with the largest cross-correlation coefficient as the current disturbance amplitude level; wherein, the standardized residual templates corresponding to multiple hardness levels are obtained by repeatedly performing heterogeneous interface experiments on standard specimens with different hardness calibrations under the same grinding process, collecting and standardizing the pure load torque observation value sequence; obtain the corresponding feedforward strength reference value according to the level, and generate a nonlinear feedforward torque sequence with exponential decay and window function smoothing; convert the feedforward torque sequence into an equivalent velocity disturbance quantity through normalized gain, and superimpose it on the original velocity error of the PID controller to form a reconstructed velocity error to drive active compensation.

[0037] When the heterogeneous boundary event flag Set, system synchronous latch observation residual vector Subsequently, the disturbance amplitude level identification process is initiated. Because the load torque step amplitude differences caused by heterogeneous interfaces with varying hardness are significant, using a single fixed compensation amount for all events would lead to overcompensation causing velocity overshoot or undercompensation leaving residual steady-state error. Therefore, the disturbance intensity of each event must be independently classified. Based on an offline-built multi-hardness-level standardized residual template library, normalized cross-correlation matching is used to classify the currently observed transient torque transition waveform to the closest hardness level, thereby transforming the unmeasurable disturbance amplitude into a quantifiable discrete level label.

[0038] In the offline phase, a series of standard specimens calibrated by the Rockwell hardness standard were used to repeatedly perform heterogeneous interface triggering experiments, cutting from the low-hardness base material region into the high-hardness weld region, under the same grinding process parameters and on the same equipment. During each experiment, samples were collected from... Before and after the set time Pure load torque observations within each control cycle The sequence has a total length of 1 sampling point. For each hardness grade The obtained sequences were subjected to zero-mean and variance normalization processes to eliminate the influence of differences in absolute torque amplitude between different experiments, while retaining the unique transient rising edge waveform characteristics of each level, thus obtaining the standardized residual template corresponding to that level. ,in , This represents the total number of hardness grades.

[0039] During the online matching phase, retrieve the currently latched observation residual vector. Its length is also Each sampling point, and each template in the template library The normalized cross-correlation coefficients are calculated one by one. The offline-constructed multi-hardness-level normalized residual templates retain the unique transient rising edge waveform characteristics of each level. In order to accurately classify the currently observed transient torque transition waveforms to the closest hardness level, a normalized cross-correlation coefficient formula is constructed. Robust identification of the disturbance amplitude level is achieved by measuring the morphological similarity between the observed waveform and the template waveform. in, Represents the relationship between the observed residual vector and the first... The normalized cross-correlation coefficient of the standardized residual template for each hardness grade is dimensionless and its value ranges from [value missing]. ; Represents the first element in the observation residual vector. The pure load torque observations at each sampling point are expressed in Newton-meters. Represents the observation residual vector The mean of the sequence, in Newton-meters; Indicates the first In the first hardness grade template The standardized torque value at each sampling point is dimensionless. Indicates the first Standardized residual template for each hardness level The mean of a sequence, dimensionless; This represents the number of control cycles latched before and after the triggering time of the heterogeneous boundary event; it is a positive integer, typically ranging from 5 to 10. This represents the total number of sampling points between the observed residual vector and the standardized residual template.

[0040] Normalized cross-correlation coefficient The numerator measures the covariance trend between the observed waveform and the template waveform after removing their respective DC components, while the denominator is the product of their standard deviations. The similarity measure is then normalized to... Interval. The closer it is to 1, the better the observed waveform is to the first... The more similar the transient rising edge morphology of the templates, the closer the hardness level of the current heterojunction event is to the level corresponding to that template; The closer the value is to -1, the more negatively correlated the two waveforms are. A value close to 0 indicates that there is no significant correlation between the two. This calculation method focuses on comparing waveform shape rather than absolute amplitude, and is naturally robust to changes in signal gain, capable of reliably distinguishing hardness levels of waveforms with similar profiles but different amplitudes.

[0041] The system traverses all Given a template, obtain the corresponding cross-relationship number. Then, select to make The hardness level associated with the template that achieves the maximum value is used as the disturbance amplitude level label for the current event. Then, from a pre-calibrated gain mapping table stored in the controller's non-volatile memory, the corresponding... The only corresponding feedforward strength reference value The unit of this value is Newton-meter. The process of establishing the gain mapping table is completed simultaneously with the template library calibration. It records the initial amplitude required by the feedforward torque sequence to completely cancel the additional load torque increment introduced by the step change of this hardness level in steady state.

[0042] get Then, the system generates a segment with Nonlinear feedforward torque sequence for control period , Directly injecting feedforward torque in a step manner will cause severe overshoot and mechanical resonance in the speed response. In order to achieve smooth active hedging against sudden load increases, a nonlinear feedforward torque sequence formula is constructed. The decay process of the compensation torque is controlled by an exponential decay factor, and sharp inflection points in the time domain are eliminated by a window function shaping coefficient to suppress high-frequency components and avoid exciting the inherent resonance mode of the grinding spindle system. in, Indicates the first The nonlinear feedforward torque value for each control cycle, in Newton-meters; This represents the feedforward strength reference value corresponding to the current disturbance amplitude level, in Newton-meters. This indicates the control period of the feedforward torque sequence. ; This represents the total length of the feedforward torque sequence, expressed in control cycles. This represents the decay time constant, which determines the rate at which the compensation torque decreases from its initial amplitude to its... The required number of control cycles is empirically taken to be between 3 and 10, which is a dimensionless hyperparameter. This represents the shaping coefficients of the window function, such as the initial segment of a Hanning or Hamming window. It is dimensionless, and its empirical values ​​are generated based on the standard formula of the selected window function.

[0043] For example, a Hanning window is used as... Its standard generation formula is: in: Indicates the first Window function coefficient values ​​for each counting cycle; Pi is a constant, approximately equal to ; This represents the total length of the feedforward torque sequence, expressed in control cycles.

[0044] Nonlinear feedforward torque It is obtained by multiplying the feedforward strength reference value, the exponential decay factor, and the window function shaping coefficient. Feedforward strength reference value This determines the initial maximum amplitude of the compensation torque. The larger the value, the stronger the initial compensation torque; exponential decay factor With counting period The increase in decreases exponentially. The larger the value, the slower the decay rate and the longer the duration of the compensation torque; the window function shaping coefficient exist Nearby, the torque rises smoothly from zero. near The torque decays smoothly to zero, eliminating sharp inflection points in the time domain and suppressing high-frequency components in the frequency domain, thus preventing the excitation of mechanical resonance. The combination of these three factors enables the smooth injection and withdrawal of the compensating torque, ensuring the stability of the speed response. The generation of this sequence follows the principle of causal construction; the introduction of the window function shaping coefficient eliminates sharp inflection points in the time domain, thereby suppressing high-frequency components in the frequency domain and preventing the excitation of the inherent resonant modes of the grinding spindle system.

[0045] Feedforward torque sequence After generation, it needs to be converted into an equivalent disturbance in the speed domain to change the response of the PID controller. The feedforward torque sequence needs to be converted into an equivalent disturbance in the speed domain before it can be sensed by the PID controller and output a corresponding drive torque command. By reconstructing the speed error, the feedforward torque is converted into an equivalent speed deviation and superimposed on the original speed error, enabling the PID controller to sense load disturbances in advance and actively increase the output torque, achieving unidirectional active hedging against sudden load increases. The formula for reconstructing the speed error is as follows: in, Indicates the first The reconstruction speed error per control cycle, in radians per second; This indicates the commanded rotational speed of the servo motor, expressed in radians per second. Indicates the first The encoder angular velocity after filtering for each control cycle, in radians per second; Indicates the first The torque values ​​in the feedforward torque sequence corresponding to each control cycle are expressed in Newton-meters. Indicates heterogeneous boundary event marker The control cycle number corresponding to the set time; This represents the normalized gain factor, which physically represents the coefficient that converts torque into the equivalent rotational speed effect. The unit is Newton-meter-second per radian, and its value is determined by the low-frequency gain of the speed loop identified by the system.

[0046] Reconstruction speed error equal to the original speed error Adding the equivalent speed disturbance calculated from the feedforward torque. When a heterogeneous interface event causes a sudden increase in the grinding wheel load and the actual rotational speed... When a downward trend occurs, When the value is positive, the reconstructed speed error is amplified on the basis of the original error. After the PID controller senses the larger speed deviation, its proportional and integral terms synchronously output stronger driving torque commands, which precisely counteract the grinding load resistance caused by the increased conflict. As the feedforward torque sequence decays exponentially and the window function is shaped, the additional equivalent speed disturbance smoothly returns to zero, and the control loop returns to the pure feedback regulation state without disturbance, thus completing the one-way active countermeasure against the sudden disturbance.

[0047] By constructing a standardized residual template library for multiple hardness levels offline and combining it with normalized cross-correlation matching, robust identification of disturbance amplitude levels was achieved, solving the overcompensation or undercompensation problems caused by a single fixed compensation amount. The nonlinear feedforward torque sequence, through exponential decay and window function shaping, achieved smooth injection and withdrawal of compensation torque, effectively avoiding speed overshoot and mechanical resonance. Converting the feedforward torque into a method for reconstructing speed error requires no modification to the internal structure of the PID controller, exhibiting strong compatibility and enabling rapid integration into existing servo control systems. Overall, hierarchical and precise feedforward compensation for heterogeneous interface disturbances was achieved, significantly improving the speed stability and machining quality of the grinding process.

[0048] Thus, the identification of the disturbance amplitude level of heterogeneous boundary events and the generation and injection of nonlinear feedforward torque sequences have been completed.

[0049] S3: Monitor the peak value of the speed error; if the peak value exceeds the safety threshold, then correct the feedforward intensity reference value corresponding to the level with a preset step size according to the direction of the error.

[0050] When the nonlinear feedforward torque sequence exist After the injection of the last control cycle is completed, this sequence affects the reconstruction speed error. The active superposition effect terminates synchronously, and the PID controller reverts to being controlled solely by the original speed error. The drive operates under pure feedback regulation. This is due to the offline calibrated feedforward strength reference value. There may be a deviation between the actual load torque step amplitude and the actual current heterogeneous interface event, and the recovery process of the speed loop after the feedforward compensation is withdrawn will show residual speed fluctuations. Therefore, immediately after the current feedforward injection phase is officially completed, the system initiates a post-event monitoring and evaluation process for the speed error peak value.

[0051] A stability discrimination window is defined, whose initial control period corresponds to the moment when the last element of the feedforward torque sequence is injected, and the window length is [value missing]. One control cycle, The empirical value is 15 to 30, which is an overparameter and can be adjusted by the implementer according to the specific implementation scenario. Within each control cycle covered by this window, the monitoring module continuously collects the raw speed error. The instantaneous value of the original speed error is the commanded rotational speed. Compared with the actual filtered encoder angular velocity The difference, expressed in radians per second. For all [areas] within the window. The absolute values ​​are compared periodically, and the maximum value is extracted and recorded as the error peak value of this feedforward compensation event. The unit is radians per second. The amplitude directly reflects the degree of mismatch between the compensation amplitude and the actual disturbance amplitude: the larger the amplitude, the stronger the residual speed oscillation after the feedforward action is withdrawn, and the lower the accuracy of the compensation.

[0052] Obtain the peak error Then, the system compares it with a preset safety error threshold. Comparison, The value is determined based on the tolerance requirements for surface integrity in the grinding process. An empirical range of 10 to 30 radians per second is considered an overparameter and can be adjusted by the implementer according to the specific implementation scenario. This indicates that the deviation of the feedforward compensation is still within the safety margin allowed by the process, and the speed fluctuation will not cause quality defects such as surface cracks or burns. Therefore, the feedforward strength reference value corresponding to this hardness grade is [value missing]. Keep the original value unchanged and do not trigger the correction action.

[0053] when When this occurs, it indicates that the compensation effect has exceeded the safety margin, and further action must be taken. Directional micro-correction is performed. There may be a deviation between the offline calibrated feedforward strength benchmark value and the actual load torque step amplitude value of the current heterogeneous interface event, and the operating parameters will slowly drift over time, causing the feedforward compensation effect to gradually decrease. To achieve online adaptive evolution of the feedforward strength benchmark value, a directional micro-correction formula is constructed based on the peak velocity error after feedforward compensation withdrawal. The benchmark value is adjusted according to the error direction to ensure the compensation effect continuously converges to the optimal state. in, This represents the corrected feedforward strength reference value, in Newton-meters. This represents the feedforward strength reference value before correction, in Newton-meters. This represents the preset step size, which is a preset fixed positive decimal value. The empirical range of this value is 0.01 to 0.1 Newton-meters. It is a dimensionless hyperparameter. The sign function for the peak value of the speed error is +1 when the original peak value is positive and -1 when it is negative. This represents the peak velocity error within the stability discrimination window after feedforward compensation, expressed in radians per second.

[0054] Corrected feedforward strength reference value It equals the original reference value minus the product of the preset step size and the sign of the peak speed error. When the peak speed error is positive, that is... When the actual rotational speed is lower than the commanded rotational speed, the system is in an undercompensated state. Decrease the original value by a preset step size This is equivalent to reducing the feedforward injection amount in subsequent events of the same magnitude; when the peak velocity error is negative, i.e. When the actual rotational speed is higher than the commanded rotational speed, the system is in an overcompensated state. Increase the value by a preset step size from the original value. This is equivalent to increasing the feedforward injection amount in subsequent events of the same magnitude. Adaptive adjustment of step size. The value is much smaller than the typical order of magnitude of the feedforward strength reference value. Each correction applies only a conservative, minute offset, avoiding drastic jumps in the reference value due to a single, occasional anomaly, thus ensuring the stability of the system. The direction of this correction is always consistent with the goal of reducing the error.

[0055] Corrected feedforward strength reference value Then, the gain mapping table stored in the controller's non-volatile memory is overwritten, overwriting... The original baseline value corresponding to the grade completes one iteration of online parameter evolution. The next time the system determines that the same hardness grade has occurred... During heterogeneous boundary events, due to the read and used to generate nonlinear feedforward torque sequences of The updated values ​​will be used. Therefore, this monitoring-evaluation-correction closed loop enables the feedforward strength reference value to automatically converge with the slow drift of the operating parameters during long-term operation, without interrupting the grinding operation or performing additional offline recalibration.

[0056] By monitoring the peak speed error after feedforward compensation, a quantitative assessment of the compensation effect is achieved. A directional micro-correction mechanism based on the error direction automatically corrects compensation mismatch issues caused by offline calibration deviations and operating condition drift. The corrected reference value is automatically overwritten to the controller's non-volatile memory without interrupting the grinding operation or performing additional offline recalibration, enabling the online adaptive evolution of the feedforward compensation system. Overall, this ensures the long-term stability and consistency of the feedforward compensation effect, further improving the machining quality and equipment reliability in heterogeneous grinding processes.

[0057] This completes the post-hoc evaluation of the feedforward compensation effect and the online adaptive correction of the feedforward strength benchmark value.

[0058] This application also provides a PID-based grinding speed control system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the computer program is executed by the processor, it implements the steps of a PID-based grinding speed control method of any of the above embodiments.

[0059] The computer program used to perform the operations of this application may be assembly instructions, Instruction Set Architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, integrated circuit configuration data, or source code or object code written in any combination of one or more programming languages ​​and procedural programming languages. The computer program may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer via any type of network, including a Local Area Network (LAN) or Wide Area Network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, to perform aspects of this application, electronic circuits, including, for example, programmable logic circuits, Field-Programmable Gate Arrays (FPGAs), or Programmable Logic Arrays (PLAs), may execute computer-readable program instructions using status information from computer-readable program instructions to personalize the electronic circuits.

[0060] Therefore, those skilled in the art should recognize that although many exemplary embodiments of this application have been shown and described in detail herein, many other variations or modifications conforming to the principles of this application can be directly determined or derived from the disclosure of this application without departing from the spirit and scope of this application. Thus, the scope of this application should be understood and construed as covering all such other variations or modifications.

Claims

1. A grinding speed control method based on PID, characterized in that, Including the following steps: Acquire the current and speed signals of the servo motor, and decouple the current and speed signals by inertia and torque to obtain the initial net load torque of the servo motor, including: During the no-load acceleration phase before the grinding operation begins, the control system executes a preset constant angular acceleration command. During this phase, the cross-axis current intensity sequence of the servo motor and the angular acceleration sequence of the encoder are acquired synchronously. The current intensity sequence and the angular acceleration sequence are fitted using a recursive least squares algorithm to obtain the system's equivalent inertia estimate and torque constant estimate. The acceleration coupling torque is calculated based on the estimated equivalent inertia and the difference in angular velocity between adjacent periods; the Parker transform is performed on the acquired servo motor current signal to obtain the quadrature-axis current intensity, and the electromagnetic torque is converted from the estimated torque constant; the initial net load torque is obtained by subtracting the acceleration coupling torque from the electromagnetic torque. Selective bias compensation is applied to the initial net load torque to obtain the current pure load torque observation value; the pure load torque observation value of the previous control cycle is obtained; based on the current pure load torque observation value and the pure load torque observation value of the previous control cycle, the mutation index of the current control cycle is calculated; when the mutation index exceeds the preset threshold for a certain number of times, the heterogeneous boundary event is determined to have occurred, and the pure load torque sequence before and after the event time is latched as the observation residual vector. Calculate the normalized cross-correlation coefficient between the observed residual vector and the standardized residual template corresponding to each hardness level; select the hardness level corresponding to the template with the largest cross-correlation coefficient as the current disturbance amplitude level; wherein, the standardized residual templates corresponding to multiple hardness levels are obtained by repeatedly performing heterogeneous interface experiments on standard specimens with different hardness calibrations under the same grinding process, collecting and standardizing the pure load torque observation value sequence; obtain the corresponding feedforward strength benchmark value according to the level, and generate a nonlinear feedforward torque sequence with exponential decay and window function smoothing; convert the feedforward torque sequence into an equivalent velocity disturbance quantity through normalized gain, and superimpose it on the original velocity error of the PID controller to form a reconstructed velocity error to drive active compensation. The peak value of the speed error is monitored; if the peak value exceeds the safety threshold, the feedforward intensity reference value corresponding to the level is corrected according to the direction of the error with a preset step size.

2. The grinding speed control method based on PID according to claim 1, characterized in that, The selective bias compensation of the initial net load torque to obtain the pure load torque observation includes: A preset bias update rate coefficient is used to obtain the current bias compensation term by adding the bias compensation term of the previous moment to the product of the bias update rate coefficient and the difference between the current initial net load torque and the previous bias compensation term; and the update is only performed during the period when the torque is stable without sudden changes, otherwise the bias compensation term remains unchanged; the initial net load torque is subtracted from the bias compensation term to obtain the observed value of the pure load torque.

3. The grinding speed control method based on PID according to claim 1, characterized in that, The step of obtaining the observed pure load torque value from the previous control cycle, and calculating the mutation index for the current control cycle based on the current and previous pure load torque observation values, includes: Take the absolute value of the difference between the observed pure load torque value of the current control cycle and the observed pure load torque value of the previous control cycle as the numerator; take the larger of the absolute value of the current pure load torque value and a preset minimum positive number as the denominator; divide the numerator by the denominator to obtain the mutation index.

4. The grinding speed control method based on PID according to claim 1, characterized in that, The generation of the nonlinear feedforward torque sequence with exponential decay and window function smoothing includes: The initial amplitude is taken as the feedforward intensity benchmark value; the initial amplitude is multiplied by an exponential decay factor, which decreases exponentially according to the number of control cycles after feedforward injection and a preset decay time constant; then multiplied by a window function shaping coefficient, which is used to provide a smooth transition at the beginning and end of the sequence; thereby generating the nonlinear feedforward torque sequence.

5. The grinding speed control method based on PID according to claim 1, characterized in that, The step of converting the feedforward torque sequence into an equivalent speed disturbance through normalized gain and then adding it to the original speed error of the PID controller to form a reconstructed speed error includes: Divide the torque value of the corresponding control cycle in the feedforward torque sequence by the normalized gain factor to obtain the equivalent speed disturbance; subtract the actual speed from the commanded speed to obtain the original speed error; add the original speed error to the equivalent speed disturbance to form the reconstructed speed error, wherein the physical meaning of the normalized gain factor is the coefficient that converts the torque into the speed influence.

6. A PID-based grinding speed control system, characterized in that, include: A processor and a memory, the memory storing computer program instructions that, when executed by the processor, implement a PID-based grinding speed control method according to any one of claims 1-5.

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