A calibration method and system for inductive sensors with error compensation

Abstract

This invention discloses an error-compensated inductive sensor calibration method and system, comprising: controlling a macro-micro composite drive platform to drive a moving component on which an inductive sensor to be calibrated is mounted, causing it to continuously move relative to a fixed standard target surface; measuring the actual displacement of the moving component to obtain a standard displacement sequence; synchronously acquiring the actual output voltage of the inductive sensor to be calibrated during the movement process to form an actual measurement value sequence; calculating the measurement deviation, generating a measurement deviation sequence, and dividing the sequence into at least three compensation intervals according to the displacement range; establishing a compensation value lookup table in each compensation interval to generate calibration parameters for correcting zero-point offset, gain drift, and nonlinear characteristics. This invention combines displacement measurement with synchronous acquisition of sensor output, enabling targeted correction of zero-point offset, gain drift, and nonlinear errors, thus improving the precision and adaptability of the compensation.

Description

Technical Field

[0001] This invention relates to the field of sensor calibration technology, and specifically to an error-compensated inductive sensor calibration method and system. Background Technology

[0002] In the fields of precision measurement and high-end equipment manufacturing, inductive displacement sensors are widely used in CNC machine tools, semiconductor equipment, aerospace, and other applications requiring extremely high displacement detection accuracy due to their advantages such as non-contact operation, high resolution, and strong anti-interference capabilities. However, inductive sensors in practical applications generally suffer from systematic errors such as zero-point offset, sensitivity drift, and nonlinear response. These errors accumulate with changes in temperature, installation conditions, and usage time, severely affecting measurement accuracy and long-term stability. Traditional calibration methods often employ static point calibration or simple linear correction, which can only compensate for a portion of the errors and cannot fully reflect the dynamic response characteristics of the sensor throughout its entire measurement range, thus failing to meet the demands of high-precision applications.

[0003] To improve calibration accuracy, existing technologies have begun to introduce laser interferometers as standard displacement references, constructing error models by comparing sensor output with the actual displacement measured by the laser. For example, invention patent CN107367224B discloses a calibration device for an inductive sensor measured by a three-axis laser interferometer, using a linear motor as a macro-motion drive element for dynamic and static calibration of the inductive displacement sensor. However, such methods typically rely on manual operation or ordinary motion platforms to apply displacement, resulting in problems such as unstable motion, insufficient positioning accuracy, and asynchronous sampling. This leads to inaccurate temporal and spatial matching between the standard displacement and the sensor output, thus affecting the reliability of error modeling. Furthermore, most calibration schemes use global linear or single polynomial fitting for compensation, ignoring the non-uniformity of sensor error in different displacement ranges, especially at the edges of the measurement range or in the nonlinear region of the magnetic circuit, where the compensation effect is significantly reduced.

[0004] To address the aforementioned issues, there is an urgent need for a calibration method for inductive sensors that can achieve high repeatability, high synchronization, and full-range coverage. An ideal technical solution should possess both long stroke and high precision, enabling precise control of the relative position between the sensor and the target surface during continuous displacement, while simultaneously acquiring high-fidelity standard displacement data and sensor output signals. Based on this, a refined model of the measurement deviation is required, employing differentiated compensation strategies according to the error characteristics of different intervals to avoid local overcompensation or undercompensation problems caused by a "one-size-fits-all" approach. Simultaneously, the calibration process should include parameter writing and verification steps, forming a closed-loop calibration process to ensure the actual effectiveness of the compensation results. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an error-compensated inductive sensor calibration method and system, which solves the problem that existing calibration methods are unable to compensate for systematic errors across the entire range.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A calibration method for an inductive sensor with error compensation includes the following steps:

[0008] The macro-micro composite drive platform is controlled to drive a moving component equipped with an inductor sensor to be calibrated, causing it to perform continuous displacement relative to a fixed standard target surface. The macro-micro composite drive platform is used to achieve large-stroke motion and has high-precision positioning and motion error compensation functions. The actual displacement of the moving component is measured to obtain a standard displacement sequence.

[0009] The output voltage signal of the inductor sensor to be calibrated is acquired synchronously during the motion process to form a sequence of actual measurement values;

[0010] Based on the sensor’s nominal sensitivity and standard displacement sequence, the ideal output voltage at each corresponding displacement point is calculated, and time alignment and displacement matching are performed with the actual output voltage to obtain the measurement deviation, generate a measurement deviation sequence, and divide the sequence into no less than three compensation intervals according to the displacement range.

[0011] A lookup table for compensation values ​​is established within each compensation interval, and a local error compensation function is constructed using a polynomial fitting method.

[0012] Based on the compensation value lookup table and the local error compensation function, calibration parameters are generated to correct zero-point offset, gain drift, and nonlinear characteristics; zero-point offset describes static fixed deviation; nonlinear characteristics refer to response behavior.

[0013] The calibration parameters are written into the signal processing unit of the inductor sensor to be calibrated;

[0014] Perform a verification measurement. If the maximum residual error is less than the preset accuracy threshold, the calibration is considered complete.

[0015] This invention utilizes a macro-micro composite driving platform to continuously displace the inductor sensor to be calibrated relative to a fixed standard target surface. It measures the actual displacement of the moving parts in real time and simultaneously acquires the sensor's output voltage, obtaining a high-precision standard displacement sequence and actual measurement value sequence. Based on the nominal sensitivity, the ideal output voltage is calculated. A measurement deviation sequence is generated through time alignment and displacement matching, and this sequence is divided into multiple compensation intervals. Within each interval, a compensation value lookup table is established, and a local error compensation function is constructed using polynomial fitting, achieving refined correction of zero-point offset, gain drift, and nonlinear errors. The generated calibration parameters are written into the sensor signal processing unit and then used for verification measurements, forming a closed-loop calibration process. This invention effectively improves the calibration accuracy, repeatability, and reliability of the inductor sensor across its entire range, solving the problem of insufficient error compensation caused by unstable motion, asynchronous data, and coarse compensation models in traditional methods. It significantly enhances the measurement stability and long-term consistency of the sensor in high-precision applications.

[0016] As a preferred method, after acquiring the original displacement data using a dual-frequency laser interferometer, the method also includes a step of spatial projection correction of the standard displacement:

[0017] By detecting the pitch and yaw angles of the moving parts in real time, the original displacement data measured by the laser interferometer is cosine corrected to eliminate the projection error caused by the non-collinearity between the motion axis and the measurement axis, and the corrected standard displacement is obtained as the reference for subsequent calculations.

[0018] As a preferred embodiment, the ideal output voltage is obtained by multiplying the sensor's nominal sensitivity by the standard displacement measured by a dual-frequency laser interferometer, and is used as a theoretical reference value for calculating the measurement deviation to evaluate the sensor's static response characteristics.

[0019] As a preferred method, when establishing the compensation value lookup table, for each compensation interval, multiple repeated measurements are performed at the same location point to calculate the arithmetic mean of the deviation between the actual output voltage and the ideal output voltage within that interval. This arithmetic mean is then used as the initial compensation value for that interval and written into the corresponding entry in the lookup table to improve compensation stability.

[0020] As a preferred method, when dividing the compensation interval, the second difference of the measurement deviation sequence is first calculated to characterize the curvature characteristics of the deviation change; a preset rate of change threshold is set; when the absolute value of the second difference exceeds the threshold, it is determined to be a nonlinear significant region, and the density of the compensation interval is increased in this region; when it does not exceed the threshold, it is divided in an equal-interval manner to achieve non-uniform adaptive partitioning.

[0021] As a preferred approach, when constructing the local error compensation function, displacement is used as the input variable and measurement deviation is used as the output variable within each compensation interval. The least squares method is used to perform quadratic or cubic polynomial fitting, and the resulting fitting coefficients are used as the parameters of the local error compensation function for that interval, which are then used for real-time interpolation correction of the sensor output.

[0022] As a preferred embodiment, the calibration parameters include zero-point correction parameters, gain adjustment parameters, and linearity compensation parameters. The zero-point correction parameters are used to eliminate static bias, the gain adjustment parameters are used to correct sensitivity deviation, and the linearity compensation parameters are based on a piecewise polynomial function to dynamically correct nonlinear errors, where nonlinear error refers to the specific deviation amount.

[0023] As a preferred method, during the verification measurement process, the calibrated inductor sensor is moved along the same trajectory again, and the standard displacement is synchronously acquired using a dual-frequency laser interferometer. The sensor output is processed by a compensation model consisting of a compensation value lookup table and a local error compensation function to obtain the compensated displacement. The absolute error sequence between the sensor and the standard displacement is calculated, and the maximum value is taken as the maximum residual error. If the maximum residual error is less than the preset accuracy threshold, the calibration is considered successful.

[0024] As a preferred approach, the macro-micro composite drive platform adopts a master-slave collaborative control strategy: the macro-motion module performs coarse positioning according to the preset motion trajectory, and the micro-motion module receives the real-time feedback signal from the dual-frequency laser interferometer, forming a closed-loop control system that dynamically compensates for motion fluctuations, vibrations, and positioning lags of the macro-motion module, ensuring high stability and high repeatability of the motion of the moving parts.

[0025] An error-compensated inductive sensor calibration system, comprising:

[0026] A macro-micro composite drive platform is used to drive a moving part equipped with an inductor sensor to be calibrated to move relative to a fixed standard target surface.

[0027] A dual-frequency laser interferometer is used to provide high-precision standard displacement data by measuring the displacement of the moving part;

[0028] The data synchronization acquisition module is used to synchronously acquire standard displacement data and the output voltage signal of the inductance sensor;

[0029] The ideal output calculation module is used to calculate the ideal output voltage based on nominal sensitivity and standard displacement data.

[0030] The deviation calculation module is used to align and match the ideal output voltage with the actual output voltage to generate a measurement deviation sequence;

[0031] The compensation modeling module is used to divide the measurement deviation sequence into multiple compensation intervals according to displacement, establish a compensation value lookup table in each interval and fit a local error compensation function.

[0032] The calibration parameter generation module is used to generate calibration parameters according to the lookup table and compensation function, and write them into the sensor signal processing unit;

[0033] The verification module is used to perform post-calibration verification and determine whether the accuracy requirements are met.

[0034] The present invention has at least the following beneficial effects:

[0035] This invention utilizes a macro-micro composite drive platform to continuously displace a moving component equipped with an inductor sensor to be calibrated relative to a fixed standard target surface. By combining displacement measurement with synchronous acquisition of sensor output, dynamic error acquisition across the entire measurement range is achieved. The ideal output voltage is calculated based on the nominal sensitivity and time-aligned and displacement-matched with the actual output voltage to accurately generate a measurement deviation sequence. By dividing the deviation sequence into multiple compensation intervals and establishing compensation value lookup tables and local error compensation functions for each interval, zero-point offset, gain drift, and nonlinear errors can be specifically corrected, improving the precision and adaptability of the compensation. Finally, the calibration parameters are written into the sensor signal processing unit and verification measurements are performed, ensuring the effectiveness and reliability of the error compensation. Attached Figure Description

[0036] To reveal the technical details of the embodiments of the present invention, the accompanying drawings involved in the embodiments will be briefly described below. It should be emphasized that these drawings only present several embodiments of the present invention and should not be considered as defining the scope of the invention. For those skilled in the art, other related drawings can still be derived based on these drawings without inventive effort.

[0037] Figure 1 This is a schematic diagram of a calibration method for an inductive sensor with error compensation.

[0038] Figure 2 This is a diagram illustrating the method for determining the work area in the embodiment. Detailed Implementation

[0039] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0040] In the following description, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. However, it should be understood that the present disclosure is not limited to the specific forms shown herein. Rather, it should be understood to encompass various variations, equivalents, and / or alternatives to the embodiments of the present disclosure. In illustrating the drawings, the same reference numerals will be used to denote similar components.

[0041] In this disclosure, terminology is used to describe specific embodiments and does not constitute a limitation thereof. In this context, the use of the singular form also encompasses the plural form, unless otherwise expressly stated herein. In the course of description, terms such as “comprising” or “having” are intended to indicate the presence of features, quantities, steps, operations, structural components, parts, or combinations thereof, and do not preclude the possibility or addition of one or more other features, quantities, steps, operations, structural components, parts, or combinations thereof.

[0042] It should be clarified that while the following description provides detailed specific information to aid in a comprehensive understanding of the exemplary embodiments, those skilled in the art will recognize that the exemplary embodiments can be implemented even without these specific details. For example, the system may be illustrated using block diagrams to avoid excessive detail that could obscure the clarity of the example. In other cases, to maintain the clarity of the example, unnecessary details of well-known processes, structures, and techniques may be omitted.

[0043] like Figure 1 As shown, an error-compensated inductive sensor calibration method includes the following steps:

[0044] A macro-micro composite drive platform drives a moving component equipped with an inductive sensor to be calibrated, enabling it to perform continuous displacement relative to a fixed standard target surface. This platform achieves large-stroke motion and provides high-precision positioning and motion error compensation. The platform consists of two parts: a macro-motion component responsible for large-range movement and long-stroke motion; and a micro-motion component that performs fine adjustments based on the macro-motion, correcting vibrations, offsets, or positioning inaccuracies caused by mechanical errors in real time. Position information is fed back via a laser interferometer, and the micro-motion component automatically compensates for these errors, ensuring smooth movement and accurate positioning. Therefore, this platform can complete the entire motion range while achieving high-precision positioning and motion error compensation.

[0045] The actual displacement of the moving component is measured in real time using a dual-frequency laser interferometer to obtain a standard displacement sequence.

[0046] The output voltage signal of the inductor sensor to be calibrated is acquired synchronously during the motion process to form a sequence of actual measurement values;

[0047] Based on the sensor’s nominal sensitivity and standard displacement sequence, the ideal output voltage at each corresponding displacement point is calculated, and time alignment and displacement matching are performed with the actual output voltage to obtain the measurement deviation, generate a measurement deviation sequence, and divide the sequence into no less than three compensation intervals according to the displacement range.

[0048] A lookup table for compensation values ​​is established within each compensation interval, and a local error compensation function is constructed using a polynomial fitting method.

[0049] Based on the compensation value lookup table and the local error compensation function, calibration parameters are generated to correct zero-point offset, gain drift, and nonlinear characteristics.

[0050] After constructing the compensation value lookup table and the local error compensation function, three types of key calibration parameters are generated based on these: First, by analyzing the deviation data near zero, the average offset is extracted as a zero-point correction parameter to eliminate the sensor's zero-point offset; second, by combining the overall slope difference between the ideal output and the measured output, the sensitivity deviation ratio is calculated to generate a gain adjustment parameter to correct gain drift; finally, the piecewise error values ​​in the compensation value lookup table and the polynomial coefficients of the local error compensation function are used to construct the linearity compensation parameter, achieving refined correction of nonlinear characteristics. These three types of parameters, supported by the lookup table and the compensation function, are ultimately integrated into a complete calibration parameter set.

[0051] The calibration parameters are written into the signal processing unit of the inductor sensor to be calibrated;

[0052] Perform a verification measurement. If the maximum residual error is less than the preset accuracy threshold, the calibration is considered complete.

[0053] This invention utilizes a macro-micro composite driving platform to drive an inductive sensor to continuously displace relative to a fixed standard target surface. A dual-frequency laser interferometer is used to precisely measure the actual displacement of the moving component as the standard input, while the sensor's output voltage signal is simultaneously acquired, achieving high-precision time alignment between displacement and voltage data. Based on the sensor's nominal sensitivity, an ideal output voltage is calculated and compared with the actual output voltage to generate a measurement deviation sequence. This sequence is then divided into multiple compensation intervals according to displacement. Within each interval, a compensation value lookup table is established, and a local error compensation model is constructed using polynomial fitting, thereby accurately correcting zero-point offset, gain drift, and nonlinear errors. Finally, calibration parameters are written to the sensor, and verification measurements are performed, forming a closed-loop calibration. This method achieves high-precision error identification and segmented fine-grained compensation across the entire measurement range, significantly improving the measurement accuracy, stability, and repeatability of the inductive sensor.

[0054] In a preferred embodiment, such as Figure 2As shown, before officially starting standard displacement measurement and data acquisition, the system first controls the macro-micro composite drive platform to drive the moving parts to perform a low-speed pre-scan movement, covering the full range of the sensor. During this process, the output voltage signal of the inductive sensor is acquired synchronously, and the actual response slope between adjacent sampling points is calculated:

[0055] ;in, and For the first and Output voltage at the point (unit: mV), and The corresponding standard displacement value (unit: μm) This is the actual sensitivity (unit: mV / μm). Compare this value with the sensor's nominal sensitivity. The comparison must satisfy the following conditions:

[0056] ;in To determine the maximum permissible deviation between the actual and nominal sensitivity, the sensor is considered to have entered the operating range when the above conditions are met and the inequality is satisfied for N consecutive sampling points, where N is a preset minimum number of consecutive points. The corresponding displacement point at this point serves as the starting point for effective calibration. Similarly, the termination point of effective calibration is determined during reverse scanning. Subsequent standard displacement measurements, voltage acquisition, and error modeling all occurred within the specified interval. The method effectively avoids nonlinear interference at the range edges caused by incomplete magnetic circuit coupling or saturation. The aforementioned effective range identification method eliminates unreliable edge regions caused by mechanical limits or magnetic circuit saturation, thus improving the accuracy and stability of error modeling.

[0057] In a preferred embodiment, after acquiring the original displacement data using a dual-frequency laser interferometer, the method further includes a step of spatial projection correction of the standard displacement:

[0058] By detecting the pitch and yaw angles of the moving parts in real time, the original displacement data measured by the laser interferometer is cosine corrected to eliminate the projection error caused by the non-collinearity between the motion axis and the measurement axis, and the corrected standard displacement is obtained as the reference for subsequent calculations.

[0059] Real-time detection of the pitch angle of moving parts and yaw angle The original displacement data is then cosine corrected. The correction formula is as follows:

[0060] ;in, This is the corrected standard displacement, in μm (micrometers), representing the actual displacement along the axis of motion; The original displacement measured by the dual-frequency laser interferometer is expressed in μm. The pitch angle of the moving part, measured in rad (radians), is measured by an electronic level or inertial sensor mounted on the moving platform. The yaw angle of the moving part is expressed in rad.

[0061] When using a dual-frequency laser interferometer to measure the displacement of a moving part, the laser path must be strictly parallel to the actual direction of movement of the part to accurately reflect the true displacement. However, during actual movement, due to limitations in guide rail precision or mechanical deformation, the moving part may experience slight pitch or yaw changes, causing its direction of movement to no longer be perfectly aligned with the laser measurement axis. In this case, the laser interferometer only measures the projected length of the direction of movement on the laser path, not the true axial displacement, thus introducing projection error. To eliminate this effect, this method, after acquiring the original displacement data, further introduces an attitude error correction mechanism. A high-precision angle sensor is used to detect the pitch and yaw angles of the moving part in real time, and the original displacement data is spatially projected and corrected accordingly. This correction process essentially restores the "oblique displacement" measured by the laser to the "true linear displacement" along the sensor's measurement axis, effectively eliminating measurement deviations caused by skewed motion trajectories. The corrected standard displacement is closer to the true value and can serve as a reliable benchmark for subsequent calculations of the ideal output voltage and the construction of error compensation models, significantly improving the accuracy and reliability of the calibration results.

[0062] In a preferred embodiment, the ideal output voltage is obtained by multiplying the sensor's nominal sensitivity by the standard displacement measured by a dual-frequency laser interferometer, and is used as a theoretical reference value for calculating the measurement deviation to evaluate the sensor's static response characteristics.

[0063] ;in, The ideal output voltage, measured in mV (millivolts), represents the voltage value that the sensor should output under error-free conditions. The nominal sensitivity of the sensor is expressed in mV / μm (millivolts per micrometer), provided by the manufacturer, and represents the voltage output corresponding to a unit displacement change. The standard displacement after projection correction is expressed in μm (micrometers) and is precisely measured by a dual-frequency laser interferometer.

[0064] The working principle of an inductive sensor is to convert displacement changes into a voltage signal output. Its output characteristics are typically defined by a nominal sensitivity provided by the manufacturer, representing the voltage change corresponding to a unit displacement change. During calibration, the actual displacement of the moving part is precisely measured using a dual-frequency laser interferometer. This data has extremely high accuracy and can be used as a standard input value. Multiplying this standard displacement by the sensor's nominal sensitivity yields the voltage value the sensor should output under ideal linear conditions, i.e., the ideal output voltage. This ideal value represents the sensor's theoretical response under error-free conditions and serves as a benchmark for evaluating its actual performance. By comparing the sensor's actual output voltage with this ideal value, the difference between the two can be clearly identified, thus accurately calculating the measurement deviation. This deviation reflects errors in the sensor's zero point, gain, and linearity, providing a crucial basis for subsequent compensation model construction. Therefore, the calculation of the ideal output voltage is a fundamental step in the entire calibration process, used to quantify the sensor's static response characteristics and ensure the scientific validity of error analysis and the accuracy of compensation parameters.

[0065] In a preferred embodiment, when establishing the compensation value lookup table, for each compensation interval, multiple repeated measurements are performed at the same location point to calculate the arithmetic mean of the deviation between the actual output voltage and the ideal output voltage within that interval. This arithmetic mean is then used as the initial compensation value for that interval and written into the corresponding entry in the lookup table to improve compensation stability.

[0066] A displacement range of [2.0mm, 2.2mm] is defined as a compensation range. To determine how much error should be compensated for in this range, the system performs five repeated measurements at the midpoint of this range (e.g., 2.1mm). In each measurement, the actual output voltage of the sensor is recorded, and the ideal output voltage is calculated based on the nominal sensitivity and standard displacement. The difference between the two is the deviation of this measurement. The arithmetic mean of these five deviations is the representative error of this compensation range.

[0067] To improve the stability and reliability of compensation when establishing the compensation value lookup table, the system performs multiple repeated measurements at the same location point within each defined displacement compensation interval. Since sensor output may be affected by electrical noise, environmental fluctuations, or minor mechanical vibrations, the deviation value obtained from a single measurement may exhibit random fluctuations, which could easily introduce instability if used directly. By repeatedly measuring and calculating the arithmetic mean of the deviation between the actual output voltage and the ideal output voltage, the influence of random errors can be effectively suppressed, making the acquired deviation data smoother and more reliable. This average deviation value, as the representative error at that location point, is written into the corresponding entry in the compensation value lookup table as the initial compensation value for that interval. This statistical averaging-based processing method enhances data repeatability and consistency, avoids compensation inaccuracies caused by accidental factors, and thus significantly improves the stability and long-term reliability of subsequent error compensation, providing a solid data foundation for achieving high-precision calibration.

[0068] In a preferred embodiment, the calibration process further includes a step of obtaining temperature compensation parameters: placing the inductor sensor to be calibrated in a temperature-controlled environment, and calibrating it at two different temperature points (e.g., ...). and Under these conditions, the moving parts are positioned at zero (i.e., the distance between the standard target surface and the sensor probe is at the nominal zero point), and the sensor's output voltage is collected and recorded. and Zero-point temperature drift is used to describe the change in the zero point caused by temperature. The zero-point temperature drift coefficient is calculated using the following formula. :

[0069] ;in, The unit is millivolts per degree Celsius. This coefficient is then compared with a reference temperature. Zero-point voltage at (e.g., 20°C) This temperature is included as a temperature compensation parameter and written into the sensor signal processing unit. During actual sensor operation, it can be combined with real-time temperature... Dynamically correct zero-point offset:

[0070] ;

[0071] This method effectively suppresses zero-point drift caused by changes in ambient temperature. Zero-point drift is used to describe the slow shift over time or with changes in the environment, thus improving the measurement stability and long-term consistency of the sensor under variable temperature conditions.

[0072] In a preferred embodiment, when dividing the compensation interval, the second difference of the measurement deviation sequence is first calculated to characterize the curvature characteristics of the deviation change; a preset rate of change threshold is set; when the absolute value of the second difference exceeds the threshold, it is determined to be a nonlinear significant region, and the density of the compensation interval is increased in this region; when it does not exceed the threshold, it is divided in an equal-interval manner to achieve non-uniform adaptive partitioning.

[0073] To allocate calibration resources more rationally when dividing compensation intervals and avoid over-division in regions with gradual error changes and under-compensation in regions with drastic changes, this method employs an adaptive non-uniform partitioning strategy. First, the changing trend of the measurement deviation sequence is analyzed. The "curvature" of the deviation change, i.e., its curvature characteristic, is identified by calculating its second-order difference, which reflects the nonlinearity of the error as a function of displacement. When the deviation change is drastic in a certain segment, such as at the beginning or end of the measurement range where the error rises rapidly due to magnetic circuit saturation, the absolute value of its second-order difference will increase significantly. If this exceeds a preset rate of change threshold, the system determines that the region is a region of significant nonlinearity and automatically increases the density of the compensation interval division, increasing the number of compensation points in that segment to achieve more refined error correction. In the intermediate region where the deviation change is gradual and the linearity is good, the second-order difference is small and does not exceed the threshold. Therefore, it is divided using an equal-interval method to reduce unnecessary computation and storage overhead. This method of dynamically adjusting the partition density based on the error variation characteristics achieves intelligent partitioning that is dense when necessary and sparse when necessary. It not only improves the compensation accuracy of nonlinear regions but also takes into account overall efficiency, making error modeling more scientific, efficient, and practical.

[0074] In a preferred embodiment, when constructing the local error compensation function, displacement is used as the input variable and measurement deviation is used as the output variable in each compensation interval. The least squares method is used to perform quadratic or cubic polynomial fitting, and the obtained fitting coefficients are used as the parameters of the local error compensation function in that interval for real-time interpolation correction of the sensor output.

[0075] Within each compensation interval, using displacement as input and measured deviation as output, a mathematical model that accurately reflects the error change trend within that interval is constructed by performing quadratic or cubic polynomial fitting on the data points using the least squares method. For example, within the interval [1.0 mm, 2.0 mm], by collecting deviation data from multiple displacement points, a model of the form […] is fitted using the least squares method. The quadratic curve is obtained to make the curve as close as possible to the actual error distribution. This process can effectively suppress the influence of measurement noise and improve the stability and fitting accuracy of the model.

[0076] After fitting, the obtained polynomial coefficients (such as...) This parameter, representing the local error compensation function within that range, is incorporated into the sensor's compensation system or model. During actual sensor operation, the corresponding error estimate can be calculated in real time based on the current displacement value, and dynamic corrections can be made. This piecewise local modeling method ensures compensation accuracy in the nonlinear region while improving the continuity and flexibility of the correction, thereby enhancing the sensor's measurement accuracy and stability throughout its entire range.

[0077] Within each compensation interval, to more accurately describe the variation of sensor error with displacement, the system uses displacement as input and the measured deviation as output, employing the least squares method for curve fitting to construct a local error compensation function. This method can find a smooth curve that best represents the overall trend from multiple sets of measurement data, ensuring the stability of the overall fitting result even with minor fluctuations at individual data points. Depending on the complexity of the error variation, quadratic or cubic polynomials are selected for fitting, which effectively expresses nonlinear characteristics without increasing computational burden due to overly complex models. After fitting, the polynomial coefficients are used as the parameters of the local error compensation function for that interval and are embedded in the compensation model. When the sensor is actually operating, the system calculates the corresponding error estimate in real time based on the current displacement value and interpolates the output from the compensation function of the corresponding interval, thereby dynamically correcting the original voltage signal. This piecewise local fitting method balances accuracy and efficiency, making error compensation closer to real-world characteristics and significantly improving the sensor's output accuracy and stability across the entire measurement range.

[0078] In a preferred embodiment, the calibration parameters include zero-point correction parameters, gain adjustment parameters, and linearity compensation parameters, wherein the zero-point correction parameters are used to eliminate static bias, the gain adjustment parameters are used to correct sensitivity deviation, and the linearity compensation parameters are based on a piecewise polynomial function to achieve dynamic correction of nonlinear errors.

[0079] An inductive sensor has a nominal sensitivity of 8.0 mV / μm and a range of 0-1.0 mm. Testing revealed the following: when the displacement is 0, the output voltage is 16 mV (corresponding to a spurious reading of +2 μm), indicating a zero-point bias; at 0.5 mm, the ideal output should be 8.0 mV / μm × 500 μm = 4.0 V, but the measured value is only 3.92 V, resulting in a calculated actual sensitivity of 7.84 mV / μm, indicating a gain deviation; at 0.1 mm and 0.9 mm, the measured values ​​are 0.18 μm smaller and 0.22 μm larger than the theoretical values, respectively, and the error variation is uneven, indicating significant nonlinear errors. To address these issues, the system generates three types of calibration parameters: a zero-point correction parameter of -2 μm to compensate for static bias; and a gain adjustment parameter set to 1.0204 (i.e., 8.0 / 7.84) to proportionally correct the displacement calculation results, making the overall response more accurate.

[0080] Building upon this, a linearity compensation parameter is further introduced, and a piecewise polynomial function is used to finely correct the nonlinearity error. For example, a local error compensation function is established within the [0-0.2mm] interval:

[0081] ;in, displacement (Unit: mm) corresponds to the voltage deviation (unit: mV). This represents the corrected standard displacement. The fitting coefficients of this function are written as compensation parameters into the sensor signal processing unit for dynamically correcting nonlinear errors. During sensor operation, the original signal undergoes zero-point correction, gain correction, and nonlinear compensation sequentially: first, a -2μm offset is subtracted, then the slope is adjusted by multiplying by 1.0204, and finally, a polynomial function for the corresponding interval is called based on the current displacement for dynamic interpolation correction, improving measurement accuracy and stability across the entire range and meeting the application requirements of submicron-level precision detection.

[0082] Calibration parameters are crucial for improving the accuracy of inductive sensors. They primarily fall into three categories: zero-point correction parameters, gain adjustment parameters, and linearity compensation parameters, corresponding to the three most common types of system errors in sensors. Zero-point correction parameters eliminate the problem of non-zero output at zero position, i.e., static bias, ensuring accurate zeroing of the output when there is no displacement input. Gain adjustment parameters correct the deviation between the sensor's actual sensitivity and its nominal value, resolving the issue of inaccurate voltage output per unit displacement, ensuring the overall response slope matches the ideal value. Linearity compensation parameters address the nonlinear error caused by uneven response across the entire measurement range. This type of error is particularly pronounced at the extremes and cannot be resolved by simple zero-point or gain adjustments. Therefore, linearity compensation parameters are constructed based on piecewise polynomial functions, independently modeling the error characteristics of different displacement regions. During sensor operation, the compensation value for the corresponding interval is dynamically called based on the current displacement, achieving refined and adaptive correction of nonlinear errors. These three types of parameters work synergistically, optimizing the sensor output layer by layer from the overall system to the local level, significantly improving its measurement accuracy, consistency, and long-term stability, enabling the calibrated sensor to meet the stringent requirements of high-precision applications.

[0083] In a preferred embodiment, during the verification measurement process, the calibrated inductor sensor is moved along the same trajectory again, and the standard displacement is synchronously acquired using a dual-frequency laser interferometer. The sensor output is processed by a compensation model to obtain the compensated displacement, and the absolute error sequence between it and the standard displacement is calculated. The maximum value is taken as the maximum residual error. If the maximum residual error is less than a preset accuracy threshold (e.g., 0.5 μm), the calibration is considered successful.

[0084] The calibration parameters include zero-point correction parameters, gain adjustment parameters, and linearity compensation parameters. Zero-point correction parameters eliminate the sensor's static bias at zero, while gain adjustment parameters correct the deviation between the actual sensitivity and the nominal value. Together, they achieve preliminary correction of the sensor's overall output characteristics. Linearity compensation parameters correct local errors caused by factors such as magnetic circuit nonlinearity throughout the measurement range. These parameters consist of a compensation value lookup table and a piecewise constructed local error compensation function, providing refined error correction capabilities across different displacement ranges. These three types of parameters are integrated to form a complete error compensation model, which is then written into the sensor's signal processing unit. During normal sensor operation, this model is invoked in real-time to dynamically compensate the original output, thereby significantly improving its measurement accuracy and consistency.

[0085] Verification measurement is the final step in the calibration process, used to verify whether the compensation effect truly achieves the expected accuracy. After the calibration parameters are written to the sensor, the system drives the macro-micro composite platform to move the sensor along the same trajectory again, ensuring that the test conditions are consistent with the calibration process. During this process, the dual-frequency laser interferometer synchronously records the precise displacement of the moving parts as a standard value, and simultaneously acquires the sensor's output signal after correction by the compensation model, converting it into the corresponding compensation displacement. The compensation displacement is compared point by point with the standard displacement measured by the laser, the absolute error at each moment is calculated, forming an error sequence, and the maximum value is extracted as the maximum residual error. This value reflects the most severe deviation that the sensor still has throughout the entire range after calibration, and is a key indicator for measuring the success or failure of calibration. If the maximum residual error does not exceed the preset accuracy threshold (e.g., 0.5 μm), it indicates that the sensor's zero-point, gain, and nonlinear errors have been effectively suppressed, meeting the requirements of high-precision applications, and the calibration is considered successful; otherwise, recalibration is required. This verification mechanism forms a closed-loop control, ensuring the repeatability and reliability of the calibration results, truly realizing an assessable and traceable high-reliability calibration process.

[0086] In a preferred embodiment, the macro-micro composite drive platform adopts a master-slave collaborative control strategy: the macro-motion module performs coarse positioning according to the preset motion trajectory, and the micro-motion module receives the real-time feedback signal from the dual-frequency laser interferometer, forming a closed-loop control system that dynamically compensates for the motion fluctuations, vibrations, and positioning lag of the macro-motion module, ensuring high stability and high repeatability of the motion of the moving parts.

[0087] The macro-micro composite drive platform employs a master-slave collaborative control strategy to balance the demands of large-stroke motion and high motion accuracy. The macro module is responsible for rapid, wide-range movement, performing coarse positioning according to a preset trajectory to ensure sensor accessibility throughout the entire measurement range. However, due to mechanical transmission backlash, guide rail errors, or external disturbances, the macro module inevitably experiences minor fluctuations, vibrations, or response lags during motion, affecting the smoothness and repeatability of the movement. To address this, a micro module is introduced as a precision adjustment unit, receiving real-time displacement feedback signals from a dual-frequency laser interferometer to form a high-response closed-loop control system. When a deviation from the ideal trajectory is detected, the micro module can quickly perform reverse fine-tuning, offsetting the motion error introduced by the macro module in real time, much like finely finishing rough machining marks. This collaborative mechanism of macro coarse adjustment and micro fine compensation effectively suppresses vibration and positioning deviations, ensuring that moving parts maintain high stability and repeatability during continuous displacement. This provides a stable and reliable motion foundation for subsequent high-precision data acquisition and error modeling, and is a key guarantee for achieving high-precision calibration.

[0088] In a preferred embodiment, during the data synchronization acquisition process, a hardware triggering mechanism is used to ensure strict synchronization of the signal acquisition time between the dual-frequency laser interferometer and the inductive sensor, thereby avoiding displacement-voltage misalignment caused by sampling timing deviation and ensuring the accuracy of measurement deviation calculation.

[0089] During data acquisition, the dual-frequency laser interferometer and inductive sensor record the true displacement value and voltage output, respectively. These two sets of data must be precisely time-corresponding to ensure that each voltage value accurately corresponds to the actual displacement at the time of its occurrence. If software-timed or asynchronous acquisition is used, system clock asynchrony or communication delays can easily cause sampling timing misalignment, leading to incorrect displacement and voltage data pairing and consequently distorted calculations, affecting the overall calibration accuracy. To address this issue, this method employs a hardware triggering mechanism, simultaneously activating the dual-frequency laser interferometer and sensor data acquisition system via a unified hardware signal. This triggering method is unaffected by software delays or operating system response fluctuations, achieving microsecond-level or even higher precision time synchronization. This ensures that both devices begin sampling at exactly the same time and continue acquiring data at the same clock cycle. The resulting displacement and voltage sequences are strictly aligned on the time axis, corresponding one-to-one, fundamentally avoiding misalignment caused by timing deviations. This guarantees the authenticity and accuracy of measurement deviation calculations and provides a high-quality data foundation for establishing a reliable error compensation model.

[0090] An error-compensated inductive sensor calibration system, comprising:

[0091] A macro-micro composite drive platform is used to drive a moving part equipped with an inductor sensor to be calibrated to move relative to a fixed standard target surface.

[0092] A dual-frequency laser interferometer is used to provide high-precision standard displacement data by measuring the displacement of the moving part;

[0093] The data synchronization acquisition module is used to synchronously acquire standard displacement data and the output voltage signal of the inductance sensor;

[0094] The ideal output calculation module is used to calculate the ideal output voltage based on nominal sensitivity and standard displacement data.

[0095] The deviation calculation module is used to align and match the ideal output voltage with the actual output voltage to generate a measurement deviation sequence;

[0096] The compensation modeling module is used to divide the measurement deviation sequence into multiple compensation intervals according to displacement, establish a compensation value lookup table in each interval and fit a local error compensation function.

[0097] The calibration parameter generation module is used to generate calibration parameters according to the lookup table and compensation function, and write them into the sensor signal processing unit;

[0098] The verification module is used to perform post-calibration verification and determine whether the accuracy requirements are met.

[0099] The error-compensated inductive sensor calibration system of this invention consists of multiple modules working collaboratively to ensure the smooth execution of a high-precision calibration process. First, a macro-micro composite drive platform drives a moving component, on which the inductive sensor to be calibrated is mounted, to continuously displace relative to a fixed standard target surface, providing a stable displacement excitation source. Simultaneously, a dual-frequency laser interferometer measures the actual displacement of the moving component in real time, generating high-precision standard displacement data as an ideal benchmark for subsequent calculations. The data synchronization acquisition module is responsible for simultaneously acquiring two sets of key data: the standard displacement and the sensor output voltage signal, ensuring strict time alignment between the two and avoiding data misalignment caused by timing deviations.

[0100] Next, the ideal output calculation module calculates the ideal output voltage value at each displacement point based on the sensor's nominal sensitivity and standard displacement data, forming a theoretical benchmark. The deviation calculation module compares these ideal voltage values ​​with the actual measured sensor output voltage, generating a measurement deviation sequence through time alignment and displacement matching, revealing the sensor's error distribution throughout the entire measurement range. The compensation modeling module further processes this deviation data, dividing it into multiple compensation intervals according to the displacement range, establishing a compensation value lookup table within each interval, and employing a polynomial fitting method to construct a local error compensation function, achieving refined error correction.

[0101] Subsequently, the calibration parameter generation module generates specific calibration parameters based on the aforementioned compensation value lookup table and local error compensation function, and writes them into the sensor's signal processing unit to complete the internal error compensation settings of the sensor. Finally, the verification module performs post-calibration verification measurements, again using the macro-micro composite drive platform and dual-frequency laser interferometer to synchronously acquire standard displacement and sensor output voltage, calculate the maximum residual error, and determine whether it meets the preset accuracy requirements. If the maximum residual error is within the allowable range, the calibration is considered successful; otherwise, the calibration parameters need to be readjusted. Through close cooperation between the modules, the entire system achieves full automation from data acquisition and error analysis to compensation model construction and verification, ensuring the high accuracy and high reliability of the inductive sensor after calibration.

[0102] In a preferred embodiment, the compensation modeling module is further configured to: dynamically adjust the division density of the compensation interval according to the second-order difference rate of change of the measurement deviation sequence, increase the number of intervals in regions of drastic nonlinear change, and decrease the number of intervals in regions of gradual change, thereby achieving adaptive partitioning modeling.

[0103] The compensation modeling module does not use a fixed, equal-interval method when dividing compensation intervals. Instead, it intelligently judges and dynamically adjusts based on the changing characteristics of the measurement deviation. The system first analyzes the changing trend of the deviation sequence, identifying the severity of error changes by calculating the "curvature" of the change. When the deviation change in a certain displacement region is relatively steep, such as at the beginning or end of the measurement range where the error rises rapidly due to magnetic circuit nonlinearity, the system determines this region as a significantly nonlinear region. In this case, it automatically densifies the division of compensation intervals, increasing the number of intervals in that segment to more precisely capture and correct local errors. In the intermediate region where the deviation change is relatively gentle and the linearity is good, the number of intervals is appropriately reduced, and a wider interval is used to avoid unnecessary resource waste. This strategy of adaptively adjusting the partition density based on error change characteristics achieves optimized modeling where finer details are needed and simpler details are needed. This improves the compensation accuracy in nonlinear regions while ensuring overall modeling efficiency, making the error compensation model more scientific, reasonable, and practical.

[0104] In a preferred embodiment, the calibration parameter generation module also integrates a polynomial coefficient extraction function, which encapsulates the quadratic or cubic fitting coefficients in each compensation interval into a local error compensation function parameter set, and together with the lookup table data, constitutes a complete error compensation model.

[0105] After completing error modeling, the calibration parameter generation module needs to convert the compensation information into a parameter form that the sensor can recognize and execute. This module not only generates a compensation value lookup table but also integrates a polynomial coefficient extraction function to handle the error variation patterns obtained through fitting within each compensation interval. For each interval, the system has used quadratic or cubic polynomials to curve-fit the measurement deviation to describe its local nonlinear characteristics. At this point, the module extracts and encapsulates the coefficients corresponding to these fitted curves—the key values ​​determining the curve shape—into a set of structured local error compensation function parameters. These parameters accurately reflect the trend of error variation with displacement within the interval, supporting dynamic interpolation calculations during real-time sensor operation and avoiding the accuracy loss caused by relying solely on discrete lookup tables. Finally, these local compensation function parameter sets and the compensation value lookup table are combined to form a complete error compensation model with both high accuracy and high responsiveness, ensuring that the sensor obtains accurate and continuous error correction at different displacement positions, thereby comprehensively improving its measurement performance.

[0106] In a preferred embodiment, the data synchronization acquisition module includes a high-precision time synchronization circuit, which realizes hardware-level synchronization between the dual-frequency laser interferometer and sensor data acquisition through an external trigger signal or PPS pulse, ensuring that displacement and voltage data are accurately aligned on the time axis.

[0107] The data synchronization acquisition module is a crucial component for ensuring calibration accuracy, its core function being to resolve the time alignment issue between displacement and voltage signals. This module incorporates a high-precision time synchronization circuit, independent of software clocks or system time. Instead, it simultaneously activates the data acquisition systems of the dual-frequency laser interferometer and the inductor sensor via an external unified trigger signal or standard PPS pulses (one pulse per second). This hardware-level synchronization method bypasses uncontrollable factors such as computer operating system response delays and network transmission jitter, ensuring that both devices begin sampling at exactly the same time and continuously record data at the same rate. Since the laser interferometer measures the actual displacement, while the sensor outputs the voltage signal at the corresponding moment, only when their times are strictly aligned can it be accurately determined whether a voltage value corresponds to the correct displacement value. Through this hardware triggering mechanism, the system achieves microsecond-level or even higher precision time synchronization, fundamentally avoiding error calculation distortion caused by sampling timing misalignment, ensuring the accuracy of subsequent deviation analysis and compensation modeling, and providing a reliable data foundation for the entire calibration process.

[0108] In a preferred embodiment, the verification module is configured to: drive the macro-micro composite drive platform to repeat the calibration trajectory motion once after calibration is completed, collect the compensated sensor output, calculate the maximum absolute error between it and the standard displacement, and output a calibration success signal when the error is less than 0.5μm.

[0109] The verification module verifies whether the calibration effect truly achieves the expected accuracy, ensuring the compensated sensor possesses reliable measurement performance. After the calibration parameters are written to the sensor, this module automatically drives the macro-micro composite drive platform to run again along the exact same trajectory as the calibration process, causing the sensor to experience the same displacement change. During this process, the dual-frequency laser interferometer synchronously records the high-precision standard displacement and simultaneously acquires the sensor output signal corrected by the compensation model, converting it into the corresponding displacement value. The system compares the compensated displacement with the standard displacement point by point, calculates the absolute error at each moment, and identifies the maximum value. If this maximum error does not exceed the preset accuracy threshold of 0.5μm, it indicates that the sensor error has been effectively controlled throughout the entire measurement range, meeting the requirements for high-precision applications. At this point, the verification module outputs a "calibration successful" signal, indicating that the calibration process is successfully completed. This process forms a closed-loop verification mechanism, not only avoiding the risk of "calibrating without verification" but also ensuring that every calibration result is quantifiable, traceable, and verifiable, significantly improving the reliability and practicality of the calibration system.

[0110] The above description is merely an exemplary embodiment of the present invention. Those skilled in the art, upon understanding the core ideas of the present invention, can make various modifications and adjustments. Therefore, the scope of protection of the present invention should be determined by the claims. Any equivalent substitutions, improvements, or derivative solutions made within the spirit and principles of the present invention should be considered as included within the scope of protection of the present invention.

Claims

1. A method of calibrating an inductance sensor for error compensation, characterized by, The method comprises the following steps: controlling a macro-micro compound driving platform to drive a moving part on which a to-be-calibrated inductance sensor is installed to perform continuous displacement motion relative to a fixed standard target surface, the macro-micro compound driving platform being used to realize large-stroke motion and having a positioning and motion error compensation function; measuring actual displacement of the moving part to obtain a standard displacement sequence; synchronously collecting actual output voltage of the to-be-calibrated inductance sensor during motion to form an actual measurement value sequence; based on nominal sensitivity of the sensor and the standard displacement sequence, calculating ideal output voltage of each corresponding displacement point, and performing time alignment and displacement matching with the actual output voltage to obtain measurement deviation, generating a measurement deviation sequence, and dividing the sequence into no less than three compensation intervals according to displacement range; establishing a compensation value lookup table in each compensation interval, and constructing a local error compensation function by using a polynomial fitting method; when the compensation value lookup table is established, for each compensation interval, repeatedly measuring at the same position point multiple times, calculating an arithmetic mean value of deviation between actual output voltage and ideal output voltage in the interval as an initial compensation value of the interval, and writing the initial compensation value into a corresponding entry of the lookup table to improve compensation stability; when the compensation intervals are divided, first, a second-order difference of the measurement deviation sequence is calculated to represent curvature characteristics of deviation change; a preset change rate threshold is set; when an absolute value of the second-order difference exceeds the threshold, it is determined that a nonlinear significant region exists, and the compensation interval division density is increased in the region; when the threshold is not exceeded, an equal-interval division is adopted to realize non-uniform adaptive partitioning; based on the compensation value lookup table and the local error compensation function, calibration parameters for correcting zero-point offset, gain drift and nonlinear characteristics are generated; the calibration parameters are written into a signal processing unit of the to-be-calibrated inductance sensor; verification measurement is performed, and if a maximum residual error is less than a preset precision threshold, it is determined that calibration is completed; before formally starting standard displacement measurement and data collection, the system first controls the macro-micro compound driving platform to drive the moving part to perform a low-speed pre-scanning motion covering a full range of the sensor; in this process, output voltage signals of the inductance sensor are synchronously collected, and actual response slopes between adjacent sampling points are calculated: ； wherein and are the output voltages of the first and points, and are the corresponding standard displacement values, is the actual sensitivity; this value is compared with the nominal sensitivity of the sensor to satisfy the following condition: ； wherein The maximum deviation between the actual sensitivity and the nominal sensitivity is allowed to be 0.5% of the nominal sensitivity. When the above condition is met and the inequality is satisfied for consecutive N sampling points, it is determined that the sensor has entered the working zone, where N is a preset minimum number of consecutive points; at this time, the corresponding displacement point is taken as the starting point of effective calibration ; Similarly, the termination point of the effective calibration is determined in the reverse scanning ; the subsequent standard displacement measurement, voltage acquisition and error modeling are all carried out in the interval , effectively avoiding the nonlinear interference caused by the incomplete coupling or saturation of the magnetic circuit. The above effective interval identification method excludes the unreliable edge region caused by mechanical limits or magnetic circuit saturation, improving the accuracy and stability of error modeling.

2. The method of claim 1, wherein, raw displacement data are obtained by using a dual-frequency laser interferometer, and the method further comprises a step of correcting the raw displacement data in space projection: by detecting a pitch angle and a yaw angle of the moving part in real time, the raw displacement data measured by the laser interferometer are corrected by using a cosine function to eliminate projection errors caused by non-collinearity between a motion axis and a measurement axis, and corrected standard displacement is obtained as a subsequent calculation reference.

3. The method of claim 1, wherein, the ideal output voltage is obtained by multiplying nominal sensitivity of the sensor and measured standard displacement, and is used as a theoretical reference value for calculating measurement deviation, and is used to evaluate static response characteristics of the sensor.

4. The method of claim 1, wherein, when the local error compensation function is constructed, in each compensation interval, the standard displacement is used as an input variable, and the measurement deviation is used as an output variable, a least square method is used to perform quadratic or cubic polynomial fitting, fitting coefficients obtained are used as local error compensation function parameters of the interval, and are used for real-time interpolation correction of sensor output.

5. The method of claim 1, wherein, The calibration parameters include a zero correction parameter, a gain adjustment parameter and a linearity compensation parameter, wherein the zero correction parameter is used to eliminate static bias, the gain adjustment parameter is used to correct sensitivity deviation, and the linearity compensation parameter is used to realize dynamic correction of nonlinear error based on a segmented polynomial function.

6. The method of claim 1, wherein, In the verification measurement process, the calibrated inductive sensor is moved along the same trajectory again, the standard displacement is synchronously collected by using the dual-frequency laser interferometer, the sensor output is processed by a compensation model composed of a compensation value lookup table and a local error compensation function to obtain a compensated displacement, and the absolute error sequence between the compensated displacement and the standard displacement is calculated, and the maximum value is taken as the maximum residual error; if the maximum residual error is less than a preset precision threshold, it is determined that the calibration is successful.

7. The method of claim 1, wherein, The macro-micro composite driving platform adopts a master-slave collaborative control strategy: the macro module performs coarse positioning according to a preset motion trajectory, the micro module receives real-time feedback signals of the dual-frequency laser interferometer to form a closed-loop control system, dynamically compensates the motion fluctuation, vibration and positioning lag of the macro module, and ensures the high stability and high repeatability of the motion of the motion component.

8. An error-compensated inductance sensor calibration system implemented based on the error-compensated inductance sensor calibration method of any one of claims 1-7, characterized by, The method comprises the following steps: The macro-micro composite driving platform is used to drive the motion component on which the inductive sensor to be calibrated is installed to move relative to a fixed standard target surface. The dual-frequency laser interferometer is used to provide high-precision standard displacement data by measuring the displacement of the motion component. The data synchronous acquisition module is used to synchronously acquire the standard displacement data and the output voltage signal of the inductive sensor. The ideal output calculation module is used to calculate the ideal output voltage based on the nominal sensitivity and the standard displacement data. The deviation calculation module is used to align and match the ideal output voltage with the actual output voltage to generate a measurement deviation sequence. The compensation modeling module is used to divide the measurement deviation sequence into multiple compensation intervals according to displacement, establish a compensation value lookup table in each interval, and fit a local error compensation function. The calibration parameter generation module is used to generate calibration parameters according to the lookup table and the compensation function, and write the calibration parameters into the sensor signal processing unit. The verification module is used to perform verification after calibration and determine whether the accuracy requirement is met.

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