Electric actuator transmission gap adaptive prediction and compensation method

Abstract

The application relates to a kind of electric actuator transmission gap adaptive prediction and compensation method, the method comprises: collecting multidimensional operation data and calculating instantaneous physical gap;Thermal expansion model containing reference parameter is constructed, the difference of the sum of measured value and theoretical thermal component and current reference parameter is calculated to generate residual sequence;Residual is separated in frequency domain, and low-frequency component representing wear trend is extracted;Accordingly, the reference parameter is revised, and compensation is carried out in combination with thermal component.The application has the advantages of effectively separating thermal deformation and mechanical wear by double time domain decoupling, preventing model reference drift, and ensuring high-precision adaptive compensation of actuator throughout its life cycle.

Description

Technical Field

[0001] This application relates to the field of electric actuators, and in particular to an adaptive prediction and compensation method for transmission backlash in electric actuators. Background Technology

[0002] Electric actuators, as the core execution unit of industrial automation control systems, typically consist of a drive motor, a mechanical transmission chain, and a control unit. During operation, the drive motor outputs rotational motion as the power source. This motion is transmitted and converted through a mechanical transmission chain composed of components such as gears, lead screws, or worm gears, ultimately driving load components such as valves or connecting rods to their designated positions. To ensure the feasibility of assembly and smooth operation of the mechanical structure, a certain physical clearance exists between the mating components within the transmission chain. This clearance causes a non-linear hysteresis between the input displacement at the motor end and the actual output displacement at the load end, thus affecting the positioning accuracy and repeatability of the actuator.

[0003] To eliminate the adverse effects of backlash on control performance, existing technologies typically employ compensation strategies based on software algorithms. Since metal components in the transmission chain expand and contract with changes in ambient temperature, causing dynamic drift in backlash values, mainstream control methods often incorporate thermal expansion models. These methods collect operating temperature data, calculate the dimensional deformation of transmission components, and then adjust the compensation parameters in the control commands in real time.

[0004] However, throughout the entire lifecycle of an electric actuator, the total clearance variation in the drivetrain is the result of multiple physical factors. Besides reversible thermoelastic deformation caused by temperature fluctuations, the mating surfaces of gears or lead screws in the drivetrain undergo irreversible mechanical wear under long-term friction, leading to a unidirectional cumulative increase in the base clearance over time. Existing compensation techniques often struggle to distinguish between these two different types of clearance variation components, frequently treating the initially calibrated reference clearance as a constant or attributing all monitored total clearance variations solely to thermal effects.

[0005] This approach ignores the low-frequency characteristic of mechanical wear, which increases slowly over time, while thermal effects exhibit high-frequency characteristics, which fluctuate rapidly with environmental changes. After prolonged operation, mechanical wear leads to a significant increase in the physical reference gap. If the reference parameters in the thermal expansion model are not updated accordingly, the calculated theoretical compensation value will deviate from the actual physical requirements. This deviation not only reduces positioning accuracy but, under certain operating conditions, may even cause overcompensation or undercompensation due to incorrect reference parameters, leading to oscillations in the control system or accelerated wear on mechanical components. Summary of the Invention

[0006] In order to effectively separate thermal deformation and mechanical wear, prevent model reference drift, and achieve high-precision adaptive compensation throughout the actuator's life cycle, this application provides an adaptive prediction and compensation method for transmission backlash in electric actuators.

[0007] This application provides an adaptive prediction and compensation method for transmission backlash in electric actuators, which adopts the following technical solution: An adaptive prediction and compensation method for transmission backlash in electric actuators includes the following steps: S1. Real-time acquisition of operating temperature data, motor drive current, position feedback signal, and vibration signal of the electric actuator; S2. Based on the motor drive current, the position feedback signal, and the vibration signal, identify the transmission clearance state of the electric actuator and calculate the current instantaneous physical clearance measurement value; S3. Call the preset thermal expansion model, obtain the current reference gap parameters, calculate the theoretical thermal gap component based on the operating temperature data, and calculate the difference between the instantaneous physical gap measurement value and the sum of the theoretical thermal gap component and the current reference gap parameters to generate a residual sequence; wherein, the thermal expansion model includes the reference gap parameters and is based on thermal deformation calculation logic operations; S4. Perform frequency domain separation processing on the residual sequence, and perform low-pass filtering on the residual sequence based on the preset cutoff frequency to filter out random fluctuation components with frequencies higher than the cutoff frequency, and extract low-frequency components that characterize the mechanical wear trend. S5. Selectively correct the reference gap parameter of the thermal expansion model according to the low-frequency component, and superimpose the corrected reference gap parameter with the theoretical thermal gap component calculated based on the current operating temperature data to generate a final compensation command, and control the electric actuator to perform position compensation.

[0008] By employing the above technical solution, the current reference gap parameters are obtained using a thermal expansion model. The difference between the instantaneous physical gap measurement and the theoretical total gap is calculated to generate a residual sequence, which is then low-pass filtered based on a preset cutoff frequency. This process utilizes the frequency domain difference between the low-frequency characteristics of mechanical wear accumulating slowly over time and the high-frequency random characteristics of thermal effects and noise to separate the low-frequency component characterizing the mechanical wear trend from the mixed residual signal. Based on this low-frequency component, the reference gap parameters of the thermal expansion model are corrected, achieving decoupling between irreversible mechanical wear and reversible thermoelastic deformation. This prevents model reference drift caused by misjudging high-frequency thermal errors as wear, allowing the model reference parameters to be dynamically updated in accordance with the physical wear trend.

[0009] By combining motor drive current, position feedback signal, and vibration signal, the transmission gap state of the electric actuator is identified. Utilizing multidimensional characteristics such as current change rate, velocity ripple features, and vibration energy spectral density, the critical moment when the transmission chain switches from an unloaded state to a loaded engagement state is determined. This multivariate fusion detection mechanism obtains the current instantaneous physical gap measurement value by integrating the response characteristics of different physical quantities to load changes, providing a computational basis for subsequent frequency domain separation processing and residual calculation.

[0010] The corrected reference gap parameters are superimposed with the theoretical thermal gap components calculated based on real-time operating temperature to generate the final compensation command, thus constructing a composite compensation mechanism that includes dynamic reference reconstruction and real-time thermal correction. The controller then performs position compensation accordingly, responding to thermal expansion and contraction caused by changes in ambient temperature while adaptively covering the increase in mechanical wear due to long-term component operation. This avoids positioning overshoot or system oscillation caused by fixed compensation parameters failing to adapt to wear changes.

[0011] Optionally, step S2 includes a passive measurement mode based on operational status monitoring, which includes the following sub-steps: S201. Differentiate the motor drive current to obtain the current change rate, and simultaneously differentiate the position feedback signal over time to obtain the speed signal, and extract the speed ripple characteristics of the speed signal. S202. Compare the current change rate with a preset current change rate threshold, or compare the amplitude of the speed ripple characteristic with a preset stiffness change characteristic threshold, to determine the critical moment when the transmission chain switches from an unloaded state to a loaded engagement state. S203. Accumulate and calculate the displacement change of the position feedback signal from the start of the motor commutation action to the critical moment point, and define the calculation result as the instantaneous physical gap measurement value and output it.

[0012] By employing the above technical solution, the motor drive current and position feedback signals are differentiated to obtain the current change rate reflecting load changes and the speed ripple characteristics reflecting stiffness changes. Utilizing the mechanical impact effect caused by the sudden stiffness change at the moment the transmission chain contacts the load during the gap transition, the current abrupt change point or speed fluctuation point is locked as the critical moment of load engagement, and the no-load travel of the motor is calculated accordingly. This method obtains instantaneous physical gap measurements during the normal commutation operation of the electric actuator without interrupting the business process for specialized calibration. By defining the gap boundary using physical engagement characteristics, it solves the problem of difficulty in distinguishing between no-load and load travel when relying solely on position signals.

[0013] Optionally, step S2 further includes an active measurement mode based on active excitation, which includes the following sub-steps: S211. Receive system status command. If the electric actuator is detected to be in a non-working standby state, trigger the active detection process. S212. Inject a high-frequency sinusoidal jitter signal with an amplitude less than the preset safety threshold and a frequency higher than the system cutoff frequency into the motor controller as an excitation input; S213. The vibration signal is acquired in real time as the system's frequency response output to the high-frequency sinusoidal jitter signal; S214. Analyze the frequency response output and calculate the drift of the current resonant frequency of the system relative to the preset reference frequency; S215. Call the preset frequency-gap mapping table, find the gap value corresponding to the drift amount, and output the found gap value as the instantaneous physical gap measurement value.

[0014] By employing the above technical solution, a high-frequency sinusoidal jitter signal is injected into the electric actuator in standby mode. Utilizing the influence of mechanical clearance changes on the system's equivalent stiffness and resonant frequency, the system's frequency response output is analyzed, and the resonant frequency drift is calculated. Based on the mapping relationship between frequency and clearance, the instantaneous physical clearance measurement value is derived. This method overcomes the limitation of position sensor resolution in measuring minute clearances, using frequency domain response characteristics to detect microscopic loosening or wear of the mechanical structure, achieving static non-destructive testing of transmission clearances during non-working periods.

[0015] Optionally, step S3 includes the following sub-steps: S31. Receive operating temperature data as model input; S32. Calculate the temperature difference between the operating temperature data and the preset calibration reference temperature; S33. Multiply the temperature difference by a preset comprehensive thermal expansion coefficient to calculate the dimensional deformation caused by the temperature change, and define the dimensional deformation as the theoretical thermal gap component; S34. Calculate the difference between the instantaneous physical gap measurement value and the sum of the theoretical thermal gap component and the current reference gap parameter, and generate a residual sequence.

[0016] By employing the above technical solution, the difference between the operating temperature and the calibrated reference temperature is calculated, and the dimensional deformation caused by temperature is analyzed by combining the comprehensive thermal expansion coefficient. The residual sequence is constructed by subtracting the sum of the theoretical thermal gap component and the current reference gap parameter from the instantaneous physical gap measurement value. This calculation logic separates the known thermoelastic deformation and the existing reference gap from the total measurement value, ensuring that the generated residual sequence only contains incremental information not yet covered by the current model. This eliminates the influence of the reference value itself on the residual amplitude, providing a deviation signal without DC bias for subsequent extraction of wear trends.

[0017] Optionally, step S4 includes the following sub-steps: S41. Construct a sliding time window with a length equal to the number of preset sampling points. Within the sliding time window, perform low-pass filtering on the residual sequence based on the preset cutoff frequency, and calculate the moving average of the residual sequence data within the sliding time window. S42. Calculate the variance of the residual sequence relative to the moving average within the sliding time window; S43. Compare the fluctuation variance with a preset noise variance threshold. If the fluctuation variance is less than the noise variance threshold, determine that the residual sequence is in a stable state within the sliding time window, and output the moving average as the low-frequency component.

[0018] By employing the above technical solution, a sliding time window is used to perform statistical analysis on the residual sequence. Low-pass filtering is combined with this to suppress high-frequency noise interference, and the moving average and variance of the data within the window are calculated. The variance is used to measure the dispersion of the data; the data is considered stable only when the variance is less than a preset noise variance threshold, and the moving average is output as the low-frequency component. This processing introduces a statistical stability criterion, shielding against non-trend fluctuations caused by sensor transients or sudden environmental interference. This ensures that the signal used for correction reflects long-term stable mechanical characteristic changes, avoiding erroneous compensation due to signal oscillations.

[0019] Optionally, step S5 includes the following sub-steps: S51. Verify whether the low-frequency component is positive and remains positive within a preset confidence period; if so, it is determined to be an effective wear increment. S52. The low-frequency component that is determined to be an effective wear increment is added to the current reference gap parameter to obtain the corrected reference gap parameter; S53. The corrected reference gap parameter is arithmetically superimposed with the theoretical thermal gap component to obtain the total compensation amount; S54. Convert the total compensation amount into motor control steps or pulses, generate the final compensation command, and send it to the motor driver.

[0020] By adopting the above technical solution, utilizing the irreversible and unidirectional accumulation of mechanical wear, a dual logic threshold of positive value verification and confidence period is set to eliminate negative fluctuations or transient interference caused by sensor drift or calculation errors, locking only continuous positive increments as effective wear. The confirmed wear increments are accumulated into the reference clearance parameters, achieving dynamic calibration of the model's zero point. Combined with the real-time calculated theoretical thermal clearance components, a composite command including reference drift correction and thermal deformation compensation is generated, and the physical displacement is converted into a control signal recognizable by the motor actuator, enabling the control system to accurately track and actively compensate for complex clearance changes.

[0021] Optionally, after step S5, a step S6 is further included to perform closed-loop verification of the compensation effect. Step S6 includes the following sub-steps: S61. Within a preset number of motor commutation cycles after the final compensation instruction is executed, steps S1 to S3 are repeated to continuously collect new data and regenerate the updated residual sequence as verification input. S62. Calculate the absolute value of the rate of change of the moving average of the updated residual sequence; S63. Compare the absolute value of the rate of change with a preset convergence threshold; if the absolute value of the rate of change is greater than the convergence threshold, determine that the correction of the reference gap parameter is invalid, and perform a parameter rollback operation to restore the reference gap parameter to its value before correction.

[0022] By adopting the above technical solution, a posterior closed-loop verification mechanism is established after benchmark correction, using the residual sequence change trend in subsequent commutation cycles to evaluate the convergence of the compensation action. By monitoring the rate of change of the residual moving average, it is possible to identify whether the system experiences oscillations or divergences caused by erroneous compensation. When the residual change rate exceeds the convergence threshold, the benchmark update is deemed invalid and parameter rollback is forcibly executed. This prevents the solidification of erroneous parameters caused by model misjudgment or sudden disturbances, blocks the risk of positive feedback divergence that may arise from the adaptive algorithm, and maintains the stability of the control system during the parameter self-learning process.

[0023] In summary, this application includes at least one of the following beneficial technical effects: 1. This application constructs a thermal expansion model incorporating reference gap parameters and calculates the residual sequence. Utilizing frequency domain separation processing technology, it separates the low-frequency components characterizing the wear trend from the mixed signal based on the difference between the low-frequency characteristics of mechanical wear accumulating slowly over time and the high-frequency random characteristics of thermal effects and noise. This method effectively decouples irreversible mechanical wear from reversible thermoelastic deformation, preventing model reference drift caused by misjudging high-frequency thermal errors as wear. It enables the thermal expansion model to dynamically reconstruct reference parameters following the physical wear trend, ensuring consistent compensation accuracy of the actuator throughout its entire lifespan.

[0024] 2. This application integrates a passive measurement mode based on operational status monitoring and an active measurement mode based on active excitation, utilizing multi-dimensional physical characteristics such as current change rate, speed ripple characteristics, and frequency response drift of the system to high-frequency jitter signals to lock the gap boundary. This composite detection mechanism overcomes the shortcomings of insufficient signal-to-noise ratio of a single signal source under low-speed, light-load, or static conditions, breaks through the limitation of position sensor resolution for measuring minute gaps, and realizes accurate perception of transmission chain gap changes under different operating conditions.

[0025] 3. This application introduces positive verification logic based on physical monotonicity in the benchmark correction stage, and establishes a closed-loop verification mechanism based on residual convergence after correction. By eliminating negative fluctuations that violate the physical laws of wear and identifying and backing up invalid corrections that cause residual divergence, this method effectively blocks the risk of positive feedback divergence that may occur in the adaptive algorithm under sensor drift or sudden interference conditions, and maintains the stability of the control system in the parameter self-learning and dynamic compensation process. Attached Figure Description

[0026] Figure 1 A flowchart illustrating an adaptive prediction and compensation method for transmission backlash in an electric actuator according to an embodiment of the present invention is shown. Detailed Implementation

[0027] The present application will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the application and are not intended to limit the scope of the application.

[0028] In the following description, numerous specific details are set forth for purposes of explanation in order to provide a thorough understanding of the inventive concept. As part of this specification, some of the accompanying drawings of this disclosure are block diagrams illustrating structures and devices to avoid complicating the disclosed principles. For clarity, not all features of the actual embodiment need to be described. Furthermore, the language used in this disclosure has been primarily chosen for readability and instructional purposes and may not have been chosen to define or limit the subject matter of the invention, thus requiring the necessary claims to determine such inventive subject matter. References to “an embodiment” or “an embodiment” in this disclosure mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment, and multiple references to “an embodiment” or “an embodiment” should not be construed as necessarily referring to the same embodiment.

[0029] Unless explicitly defined, the terms “a,” “an,” and “the” are not intended to refer to a singular entity, but rather to include a general category whose specific examples can be used for illustration. Therefore, the use of the terms “a” or “an” can mean any number of at least one, including “a,” “one or more,” “at least one,” and “one or more.” The term “or” means any of the options and any combination of the options, including all options unless explicitly indicated that the options are mutually exclusive. The phrase “at least one of” when combined with a list of items refers to a single item in the list or any combination of items in the list. The phrase does not require all items listed unless explicitly defined as such.

[0030] like Figure 1 As shown, this embodiment provides an adaptive prediction and compensation method for transmission backlash in an electric actuator. This method is applied to the controller of an electric actuator and specifically includes the following steps S1 to S6.

[0031] S1. Real-time acquisition of operating temperature data, motor drive current, position feedback signal, and vibration signal of the electric actuator.

[0032] To acquire multi-dimensional physical signals, the electric actuator is equipped with sensing devices. Surface-mount PT100 RTDs or thermocouples are mounted close to the gearbox housing or near the motor stator windings to sense the real-time thermal balance of the transmission mechanism. A Hall current sensor or high-precision shunt is connected in series in the motor drive circuit to capture the motor armature drive current; the sampling frequency is set to no less than 1kHz to ensure the capture of microsecond-level current surges. A high-resolution absolute encoder or rotary transformer is installed on the motor output shaft or at the actuator end to provide position and speed feedback; its resolution is preferably 16 bits or higher. A piezoelectric accelerometer or MEMS vibration sensor is rigidly connected to the transmission housing bearing seat to pick up mechanical transmission vibration acceleration signals; its effective bandwidth needs to cover 1-5 times the transmission chain meshing frequency.

[0033] Operating temperature data is used as the boundary condition input for the thermal expansion model to calculate the theoretical clearance component caused by thermal effects. The geometric dimensions of the drivetrain metal material undergo thermal expansion and contraction deformation with ambient temperature and motor temperature rise. Temperature data is used to calculate the amount of thermal deformation, supporting subsequent processing in distinguishing between reversible thermal deformation errors and irreversible mechanical wear errors. The drive current is proportional to the electromagnetic torque output, reflecting the load torque state; the position feedback signal records the kinematic response. Analysis of the dynamic mapping relationship between the input torque signal and the output motion signal identifies the backlash hysteresis phenomenon caused by clearance during commutation or sudden load changes in the drivetrain.

[0034] Vibration signals capture microscopic mechanical features that are difficult to reflect using position or current signals. When transmission components wear or their fit loosens, gear meshing or lead screw operation excites mechanical waves of specific frequencies. Accelerometers pick up high-frequency vibration characteristics, revealing the microscopic contact state of the transmission pair surfaces and providing frequency domain details for frequency domain analysis. Multidimensional signal synchronous acquisition places thermal, electromagnetic, kinematic, and vibrational data on a unified time reference, utilizing the complementary and constraining relationships of different physical quantities to eliminate the ambiguity of information from a single signal source.

[0035] S2. Based on the motor drive current, the position feedback signal, and the vibration signal, identify the transmission clearance state of the electric actuator and calculate the current instantaneous physical clearance measurement value.

[0036] Instantaneous physical clearance measurements characterize the total actual mechanical backlash within the transmission chain at the current moment and under specific operating conditions. Electric actuators switch between dynamic load operation and static standby. Dynamic operation is accompanied by load disturbances and speed changes, while static operation lacks external excitation to naturally reveal the backlash. To address this differentiated requirement, a monitoring architecture incorporating both passive and active measurement modes is constructed.

[0037] Passive measurement mode is applied during the dynamic operation of the actuator. Utilizing the mechanical characteristic that the output shaft first idles to eliminate backlash before driving the load during motor commutation, the critical state from no-load to load engagement is identified by monitoring current and speed signal characteristics. The cumulative displacement during this idling process is calculated to quantify the backlash. Active measurement mode is applied during the actuator's static standby process. A high-frequency excitation signal is injected into the system, and the frequency response of the mechanical system is analyzed. Utilizing the physical law that backlash changes lead to changes in the system's equivalent stiffness, resulting in resonant frequency drift, the physical backlash value is solved.

[0038] The dual-modal mechanism works collaboratively based on the real-time status of the actuator. The passive mode captures dynamic clearance data, while the active mode supplements static clearance data. This complementary measurement method can cover the entire operating envelope of the actuator, eliminating the blind spots that exist with single measurement methods.

[0039] Specifically, step S2 includes a passive measurement mode based on operation status monitoring, which includes the following sub-steps S201-S203.

[0040] S201. Differentiate the motor drive current to obtain the current change rate, and simultaneously differentiate the position feedback signal over time to obtain the speed signal, and extract the speed ripple characteristics of the speed signal.

[0041] S202. Compare the current change rate with a preset current change rate threshold, or compare the amplitude of the speed ripple characteristic with a preset stiffness change characteristic threshold, to determine the critical moment when the transmission chain switches from an unloaded state to a loaded engagement state.

[0042] S203. Accumulate and calculate the displacement change of the position feedback signal from the start of the motor commutation action to the critical moment point, and define the calculation result as the instantaneous physical gap measurement value and output it.

[0043] Differential operations are performed on the motor drive current and position feedback signals to transform the steady-state time-domain signals into dynamic characteristic signals reflecting changing trends. A low-pass filter is introduced before differential processing to suppress quantization noise and electromagnetic interference in the original signal, preventing the differential operation from amplifying high-frequency noise and thus obscuring the true physical characteristics. During the commutation start-up phase, the motor is in an unloaded acceleration state when crossing mechanical gaps, with the drive current maintained at a low unload level and the output shaft speed rising smoothly. When the transmission chain eliminates the gaps and contacts the load, the motor rotor encounters a sudden change in external resistance torque, causing a step jump in the system's equivalent stiffness. The physical impact causes a sharp increase in the motor drive current, generating a significant peak in the rate of change of current; simultaneously, the rigid collision induces speed ripples or drops in the speed curve.

[0044] The current change rate threshold and stiffness change characteristic threshold are set based on the motor's rated parameters and the stiffness characteristics of the mechanical structure. The threshold levels are higher than the system background noise floor and lower than the fluctuation amplitude under normal load conditions, balancing recognition sensitivity and anti-interference capability. In a specific embodiment, the current change rate threshold is set to 3 to 5 times the standard deviation of the motor's no-load operating current, and the stiffness change characteristic threshold is set to 1.2 to 1.5 times the steady-state speed fluctuation. The controller monitors the differential signal in real time. Once it detects that the current change rate exceeds the threshold or the speed ripple amplitude breaks through the stiffness change characteristic threshold, it determines that the transmission chain has completed its idle motion and entered the load engagement state, locking this moment as the critical moment point. The controller calls the integral algorithm to accumulate and calculate the position feedback signal (or speed signal) within the time window from the start of the motor commutation action to this critical moment point. This integral result represents the total angle or total displacement swept by the motor output shaft under no-load conditions, which is the instantaneous physical clearance measurement value under the current operating condition.

[0045] In another optional embodiment, step S2 further includes an active measurement mode based on active excitation, the active measurement mode including the following sub-steps S211-S215.

[0046] S211. Receive system status command. If the electric actuator is detected to be in a non-working standby state, trigger the active detection process.

[0047] S212. Inject a high-frequency sinusoidal jitter signal with an amplitude less than the preset safety threshold and a frequency higher than the system cutoff frequency into the motor controller as an excitation input.

[0048] S213. The vibration signal is collected in real time as the frequency response output of the system to the high-frequency sinusoidal jitter signal.

[0049] S214. Analyze the frequency response output and calculate the drift of the current resonant frequency of the system relative to the preset reference frequency.

[0050] S215. Call the preset frequency-gap mapping table, find the gap value corresponding to the drift amount, and output the found gap value as the instantaneous physical gap measurement value.

[0051] Active detection is triggered when the electric actuator is in a non-operating standby state, utilizing the system's idle time window for non-destructive testing to avoid interference with normal control tasks. The high-frequency sinusoidal jitter signal injected into the motor controller must meet specific physical constraints: the amplitude must be less than a preset safety threshold to ensure that the motor rotor only generates micro-vibrations without driving the load to produce macro-displacement, ensuring system static safety; the frequency must be higher than the cutoff frequencies of the system's position and speed loops, typically set to 5 to 10 times the system's closed-loop bandwidth (e.g., between 100Hz and 500Hz). The low-pass filtering characteristics of the control system are used to allow the controller to ignore this jitter signal, measuring only the physical response of the mechanical structure, thus achieving frequency domain decoupling between the measurement signal and the control loop.

[0052] The presence of mechanical backlash alters the constraint state of the transmission chain contact surfaces, causing the system's equivalent stiffness to exhibit nonlinear characteristics. Increased backlash weakens the mechanical connection stiffness, leading to a shift in the system's natural resonant frequency. Accelerometers are used to acquire the system's vibration response to excitation signals, and the spectral structure of the vibration signals is analyzed using Fast Fourier Transform to extract the current system resonant frequency. The drift of this resonant frequency relative to a preset reference frequency under no-wear or calibration conditions is calculated. A preset frequency-backlash mapping table, constructed through prior experimental calibration or finite element dynamics simulation, stores a one-to-one correspondence between different backlash values ​​and frequency drift. The controller directly indexes the corresponding backlash value using a lookup table method, significantly reducing the computational load compared to real-time solving of complex nonlinear dynamic equations, thus meeting the real-time requirements of embedded controllers.

[0053] S3. Call the preset thermal expansion model, obtain the current reference gap parameters, calculate the theoretical thermal gap component based on the operating temperature data, and calculate the difference between the instantaneous physical gap measurement value and the sum of the theoretical thermal gap component and the current reference gap parameters to generate a residual sequence; wherein, the thermal expansion model includes the reference gap parameters and is based on thermal deformation calculation logic operations.

[0054] The thermal expansion model consists of two parts: static reference clearance parameters characterizing the system's historical state and dynamic thermal deformation logic characterizing the current environmental impact. The reference clearance parameters store the physical clearance confirmed by the actuator in the previous control cycle, reflecting steady-state characteristics including initial assembly clearance and historical accumulated wear. The dynamic thermal deformation logic is used to respond in real-time to reversible deformation caused by environmental temperature fluctuations. The theoretical thermal clearance component calculated based on temperature is superimposed with the current reference clearance parameters to synthesize the theoretical total clearance. This theoretical total clearance represents the model's theoretical estimate of the current physical clearance under the assumption of no new wear.

[0055] Residual calculation eliminates the influence of known physical quantities by subtracting the total model prediction, which includes the thermal component and the reference value, from the instantaneous physical gap measurement, thus extracting unknown deviations not yet covered by the current model. This deviation signal mainly consists of newly generated mechanical wear increments (low frequency) and random measurement noise (high frequency). If only the thermal component is subtracted during residual calculation without deducting the current reference parameters, the generated residual will include the absolute amplitude of the reference gap (e.g., 0.5 mm).

[0056] Specifically, step S3 includes the following sub-steps S31-S34.

[0057] S31. Receive operating temperature data as model input.

[0058] S32. Calculate the temperature difference between the operating temperature data and the preset calibration reference temperature.

[0059] S33. Multiply the temperature difference by a preset comprehensive thermal expansion coefficient to calculate the dimensional deformation caused by the temperature change, and define the dimensional deformation as the theoretical thermal gap component.

[0060] S34. Calculate the difference between the instantaneous physical gap measurement value and the sum of the theoretical thermal gap component and the current reference gap parameter, and generate a residual sequence.

[0061] The calibration reference temperature is typically selected as the constant ambient temperature during the precision assembly of the actuator at the factory (e.g., 20°C), which serves as the benchmark for thermal deformation calculations and establishes a relative reference for gap changes. Since the drivetrain of an electric actuator is usually a complex mechanical structure composed of multiple materials such as steel gears, copper turbines, and aluminum alloy housings, S33 simplifies the modeling during calculations by obtaining a preset comprehensive thermal expansion coefficient through weighted averaging or experimental fitting. This coefficient equates the complex multi-body non-uniform thermal coupling system to a single linear thermal system, and the theoretical thermal gap component caused by temperature changes is calculated based on the linear thermal expansion formula.

[0062] S34 transforms the original instantaneous physical gap measurements, acquired in an absolute physical coordinate system (unit: length, containing full information), into residual signals in a relative error coordinate system (unit: length deviation, containing only incremental information). This transformation process removes the DC reference bias and known thermal fluctuation components from the signal, making the residual sequence a zero-mean (ideally) or an error signal containing a small trend term.

[0063] S4. Perform frequency domain separation processing on the residual sequence, and perform low-pass filtering on the residual sequence based on the preset cutoff frequency to filter out random fluctuation components with frequencies higher than the cutoff frequency, and extract low-frequency components that characterize the mechanical wear trend.

[0064] The residual sequence, as a time-domain signal containing unknown biases, contains frequency components superimposed from different physical sources. Based on physical attribution analysis, high-frequency components typically correspond to random measurement noise from sensors, electromagnetic interference from circuits, or thermal disturbances caused by transient changes in ambient temperature. These disturbances are characterized by high randomness and high fluctuation frequency. Low-frequency components, on the other hand, correspond to the unidirectional gap increments that gradually accumulate due to friction and wear of mechanical components during long-term operation. This process is characterized by a long timescale and slow change. Utilizing the significant differences between the two types of signals in the frequency domain, the mixed signal can be separated into two independent channels: one rapidly changing and the other slowly changing.

[0065] The determination of the preset cutoff frequency follows the principle of optimal signal-to-noise ratio, requiring a balance between the response speed to wear trends and the ability to suppress noise: setting the frequency too high will result in residual noise, while setting it too low will cause phase lag in wear identification. Considering that mechanical wear is a long-term cumulative process, the cutoff frequency is usually set in an extremely low frequency range, such as 0.01Hz to 0.1Hz. At the algorithm implementation level, a digital low-pass filter is used to perform real-time convolution processing on the residual sequence. This processing filters out random fluctuation components above the cutoff frequency, retaining the DC or extremely low-frequency components characterizing the mechanical wear trend. The purpose of extracting low-frequency components is to provide an incremental signal with high signal-to-noise ratio, free from high-frequency noise interference, for subsequent reference parameter correction, ensuring the correctness of the parameter correction direction.

[0066] Specifically, step S4 includes the following sub-steps S41-S43.

[0067] S41. Construct a sliding time window with a length equal to the preset number of sampling points. Within the sliding time window, perform low-pass filtering on the residual sequence based on the preset cutoff frequency, and calculate the moving average of the residual sequence data within the sliding time window.

[0068] S42. Calculate the variance of the residual sequence relative to the moving average within the sliding time window.

[0069] S43. Compare the fluctuation variance with a preset noise variance threshold. If the fluctuation variance is less than the noise variance threshold, determine that the residual sequence is in a stable state within the sliding time window, and output the moving average as the low-frequency component.

[0070] Constructing a sliding time window discretizes the continuous residual signal into a series of statistically significant local observation segments, enabling the algorithm to perform feature evaluation based on neighborhood data at the current time. The moving average of the data within the window is calculated; this operation is equivalent to low-pass filtering in the time domain, smoothing out random noise using the averaging effect and extracting the main trend term of the data within the window's time scale. Simultaneously, the variance of the residual sequence within the window relative to this moving average is calculated; this variance serves as a statistical indicator quantifying the degree of data dispersion.

[0071] A preset noise variance threshold serves as a logic threshold, effectively shielding against non-steady-state interference. When a sensor experiences a sudden change due to poor contact, or when the actuator is subjected to external mechanical shock or vibration, the variance of the residual sequence will significantly increase and exceed this threshold. In this case, the algorithm determines the data is in a non-steady state and rejects the output, thus avoiding misinterpreting occasional transient fluctuations as valid wear increments. Only when the fluctuation variance is less than the noise variance threshold is the residual sequence considered to be in a steady state, at which point the output moving average has high confidence.

[0072] S5. Selectively correct the reference gap parameter of the thermal expansion model according to the low-frequency component, and superimpose the corrected reference gap parameter with the theoretical thermal gap component calculated based on the current operating temperature data to generate a final compensation command, and control the electric actuator to perform position compensation.

[0073] Selective correction avoids control oscillations caused by updating the baseline for every tiny residual fluctuation. This strategy acts as a logical gateway for model parameter updates, ensuring that only significant changes consistent with physical characteristics are used to correct the model, maintaining the steady-state performance of the control loop. The signal recombination logic re-integrates two previously separate physical processes in the frequency domain: a low-frequency reference signal characterizing accumulated mechanical wear is used to update the model's static zero point, while a real-time calculated high-frequency thermal signal characterizes reversible deformation caused by ambient temperature. The combination of these two signals constructs a complete physical clearance model, covering the full-frequency error characteristics from long-term wear trends to transient thermal fluctuations. The final compensation command aims to eliminate positioning errors caused by both temperature fluctuations and mechanical wear, enabling the electric actuator to maintain consistent positioning accuracy throughout its entire lifespan, whether in the break-in period or the aging phase, through dynamic compensation, achieving full-time-domain closed-loop position control.

[0074] Specifically, step S5 includes the following sub-steps S51-S54.

[0075] S51. Verify whether the low-frequency component is positive and remains positive within a preset confidence period. If so, it is determined to be an effective wear increment.

[0076] S52. The low-frequency component that is determined to be an effective wear increment is added to the current reference gap parameter to obtain the corrected reference gap parameter.

[0077] S53. The corrected reference gap parameter is arithmetically superimposed with the theoretical thermal gap component to obtain the total compensation amount.

[0078] S54. Convert the total compensation amount into motor control steps or pulses, generate the final compensation command, and send it to the motor driver.

[0079] The monotonicity verification based on physical laws leverages the inherent characteristics of irreversible and unidirectionally increasing mechanical wear. Through positive value judgment logic, the system automatically eliminates negative values ​​generated by sensor temperature drift, calculation truncation errors, or the elastic recovery of the mechanical structure, preventing non-physical factors from interfering with the model baseline. A confidence period is introduced as a time-domain filtering method, requiring the wear increment signal to persist within a preset time window. This confirms that the change belongs to permanent structural wear, rather than occasional mechanical jamming, changes in lubricating oil film thickness, or transient displacement caused by external impacts.

[0080] The cumulative update mechanism of the reference parameters clarifies the iterative logic of the reference gap parameter as the zero point of model evolution. That is, the new reference gap equals the old reference gap plus the confirmed effective wear increment, realizing the model parameters following the state of the physical object. S53 merges the corrected reference parameters representing the static historical accumulation with the theoretical thermal gap component representing the current dynamic environment to calculate the total compensation required at the current moment. S54 completes the dimension conversion, mapping the physical length compensation amount in millimeters or micrometers to the number of control steps or pulses that the motor driver can execute, based on the motor transmission ratio and encoder resolution.

[0081] Optionally, after step S5, a step S6 is included to perform closed-loop verification of the compensation effect. Step S6 includes the following sub-steps S61-S63.

[0082] S61. Within a preset number of motor commutation cycles after the final compensation command is executed, steps S1 to S3 are repeated to continuously collect new data and regenerate the updated residual sequence as verification input.

[0083] S62. Calculate the absolute value of the rate of change of the moving average of the updated residual sequence.

[0084] S63. Compare the absolute value of the rate of change with a preset convergence threshold; if the absolute value of the rate of change is greater than the convergence threshold, determine that the correction of the reference gap parameter is invalid, and perform a parameter rollback operation to restore the reference gap parameter to its value before correction.

[0085] When abnormal data is generated at the input due to strong external interference or occasional sensor malfunctions, the algorithm may misjudge it as actual wear and perform incorrect compensation, resulting in the actual error of the physical system not only not decreasing but increasing. S61 sets a verification window after compensation execution, the length of which is preferably 3 to 10 complete motor commutation cycles. Observing within a certain number of motor commutation cycles is to skip the mechanical transient response at the moment of compensation execution and ensure that the collected residual sequence reflects the steady-state system performance after compensation takes effect.

[0086] S62 calculates the absolute value of the rate of change of the moving average of the updated residual sequence. This indicator is mathematically equivalent to the magnitude of the first derivative of the error trend. Under ideal convergence conditions, the compensated residuals should remain stable or tend towards zero, and their rate of change should be extremely low. If the calculated absolute value of the rate of change exceeds the preset convergence threshold, it indicates that the residuals have experienced drastic fluctuations or rapid divergence after compensation, suggesting that the previous benchmark correction did not achieve the expected effect or caused system oscillations.

[0087] Once the system is detected to be trending towards an unstable state through the aforementioned indicators, the controller immediately determines that the latest reference clearance parameter correction is invalid and forcibly executes a rollback command to restore the model parameters to their safe values ​​before the correction. This mechanism prevents the cumulative effect of erroneous parameters over time, prevents model failure due to a single misjudgment, and ensures that the control system can maintain basic operational safety and stability when facing uncertain disturbances.

[0088] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0089] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for adaptive prediction and compensation of transmission backlash in an electric actuator, characterized in that, Includes the following steps: S1. Real-time acquisition of operating temperature data, motor drive current, position feedback signal, and vibration signal of the electric actuator; S2. Based on the motor drive current, the position feedback signal, and the vibration signal, identify the transmission clearance state of the electric actuator and calculate the current instantaneous physical clearance measurement value; S3. Call the preset thermal expansion model, obtain the current reference gap parameters, calculate the theoretical thermal gap component based on the operating temperature data, and calculate the difference between the instantaneous physical gap measurement value and the sum of the theoretical thermal gap component and the current reference gap parameters to generate a residual sequence; wherein, the thermal expansion model includes the reference gap parameters and is based on thermal deformation calculation logic operations; S4. Perform frequency domain separation processing on the residual sequence, and perform low-pass filtering on the residual sequence based on the preset cutoff frequency to filter out random fluctuation components with frequencies higher than the cutoff frequency, and extract low-frequency components that characterize the mechanical wear trend. S5. Selectively correct the reference gap parameter of the thermal expansion model according to the low-frequency component, and superimpose the corrected reference gap parameter with the theoretical thermal gap component calculated based on the current operating temperature data to generate a final compensation command, and control the electric actuator to perform position compensation.

2. The adaptive prediction and compensation method for transmission backlash in electric actuators according to claim 1, characterized in that, Step S2 includes a passive measurement mode based on operational status monitoring, which includes the following sub-steps: S201. Differentiate the motor drive current to obtain the current change rate, and simultaneously differentiate the position feedback signal over time to obtain the speed signal, and extract the speed ripple characteristics of the speed signal. S202. Compare the current change rate with a preset current change rate threshold, or compare the amplitude of the speed ripple characteristic with a preset stiffness change characteristic threshold, to determine the critical moment when the transmission chain switches from an unloaded state to a loaded engagement state. S203. Accumulate and calculate the displacement change of the position feedback signal from the start of the motor commutation action to the critical moment point, and define the calculation result as the instantaneous physical gap measurement value and output it.

3. The adaptive prediction and compensation method for transmission backlash in electric actuators according to claim 1, characterized in that, Step S2 further includes an active measurement mode based on active excitation, which includes the following sub-steps: S211. Receive system status command. If the electric actuator is detected to be in a non-working standby state, trigger the active detection process. S212. Inject a high-frequency sinusoidal jitter signal with an amplitude less than the preset safety threshold and a frequency higher than the system cutoff frequency into the motor controller as an excitation input; S213. The vibration signal is acquired in real time as the system's frequency response output to the high-frequency sinusoidal jitter signal; S214. Analyze the frequency response output and calculate the drift of the current resonant frequency of the system relative to the preset reference frequency; S215. Call the preset frequency-gap mapping table, find the gap value corresponding to the drift amount, and output the found gap value as the instantaneous physical gap measurement value.

4. The adaptive prediction and compensation method for transmission backlash in electric actuators according to claim 1, characterized in that, Step S3 includes the following sub-steps: S31. Receive operating temperature data as model input; S32. Calculate the temperature difference between the operating temperature data and the preset calibration reference temperature; S33. Multiply the temperature difference by a preset comprehensive thermal expansion coefficient to calculate the dimensional deformation caused by the temperature change, and define the dimensional deformation as the theoretical thermal gap component; S34. Calculate the difference between the instantaneous physical gap measurement value and the sum of the theoretical thermal gap component and the current reference gap parameter, and generate a residual sequence.

5. The adaptive prediction and compensation method for transmission backlash in electric actuators according to claim 1, characterized in that, Step S4 includes the following sub-steps: S41. Construct a sliding time window with a length equal to the number of preset sampling points. Within the sliding time window, perform low-pass filtering on the residual sequence based on the preset cutoff frequency, and calculate the moving average of the residual sequence data within the sliding time window. S42. Calculate the variance of the residual sequence relative to the moving average within the sliding time window; S43. Compare the fluctuation variance with a preset noise variance threshold. If the fluctuation variance is less than the noise variance threshold, determine that the residual sequence is in a stable state within the sliding time window, and output the moving average as the low-frequency component.

6. The adaptive prediction and compensation method for transmission backlash in electric actuators according to claim 1, characterized in that, Step S5 includes the following sub-steps: S51. Verify whether the low-frequency component is positive and remains positive within a preset confidence period; if so, it is determined to be an effective wear increment. S52. The low-frequency component that is determined to be an effective wear increment is added to the current reference gap parameter to obtain the corrected reference gap parameter; S53. The corrected reference gap parameter is arithmetically superimposed with the theoretical thermal gap component to obtain the total compensation amount; S54. Convert the total compensation amount into motor control steps or pulses, generate the final compensation command, and send it to the motor driver.

7. The method according to claim 1, characterized in that, Following step S5, a step S6 is included to perform closed-loop verification of the compensation effect. Step S6 includes the following sub-steps: S61. Within a preset number of motor commutation cycles after the final compensation instruction is executed, steps S1 to S3 are repeated to continuously collect new data and regenerate the updated residual sequence as verification input. S62. Calculate the absolute value of the rate of change of the moving average of the updated residual sequence; S63. Compare the absolute value of the rate of change with a preset convergence threshold; if the absolute value of the rate of change is greater than the convergence threshold, determine that the correction of the reference gap parameter is invalid, and perform a parameter rollback operation to restore the reference gap parameter to its value before correction.

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