Error compensation method and system for inductive encoder based on six-dimensional force sensing and vibration decoupling

Abstract

The invention provides an inductance type encoder error compensation method and system based on six-dimensional force sensing and vibration decoupling. The device is characterized by comprising an inductance type encoder (1), a six-dimensional force sensor (2), a synchronous data acquisition unit (3), a real-time signal processor (4) and a decoding and angle resolving unit (5). The method can be applied to motion control systems such as high-precision servo motors, robot joints and precision rotary tables, and can be widely applied to the high-precision requirement fields such as numerical control machine tools, aerospace and semiconductor equipment.

Description

(I) Technical Field

[0001] This invention relates to an error compensation method and system for an inductive encoder based on six-dimensional force sensing and vibration decoupling, belonging to the fields of precision motion control and electromagnetic sensing technology, and particularly to a real-time compensation method and system for measurement errors caused by changes in the air gap between the stator and rotor in a mechanical vibration environment. (II) Background Technology

[0002] Inductive encoders, such as rotary transformers, are widely used in harsh environments such as industrial servo systems and aerospace due to their high reliability and strong anti-interference capabilities. Their working principle is based on the electromagnetic coupling between the stator and rotor, and the amplitude and phase of the output signal have a definite functional relationship with the mechanical angle.

[0003] However, in actual operation, the mechanical vibration of the motor or load is transmitted to the encoder, causing axial movement and relative tilting between the stator and rotor. This micron-level air gap change and micro-radian-level tilt angle directly alter the mutual inductance coefficient and electromagnetic field distribution symmetry between the two, introducing significant fundamental amplitude / phase modulation errors and higher harmonic distortion. In severe cases, this can lead to decoding errors, limiting its application in high-end precision applications.

[0004] In October 2024, Xu Qiwei et al. from Chongqing University disclosed a design method for a high-precision segmented multi-coil inductive displacement sensor (patent number: CN202410990272.4). Based on the truncated region characteristic function expansion method, a coil output voltage model under time-harmonic field is established to obtain the optimal region for linearity of each coil segment, including the optimal coil length, number of turns of the excitation coil, coil turns ratio, and excitation frequency parameters, to optimize the coil installation settings. However, no real-time compensation correction method is involved. In August 2025, Li Yongsheng et al. from Shandong Tianrui Heavy Industry Co., Ltd. provided a design method for an inductive displacement sensor and an inductive displacement sensor (patent number: CN202511020798.0). This method constructs a parameter model of the target design parameters of the inductive displacement sensor and optimizes the target design parameter values ​​based on the model. Similarly, no compensation algorithm is involved.

[0005] As can be seen from the current research status, existing traditional solutions mostly focus on mechanical structures, such as improving machining and assembly precision to enhance rigidity, but these are costly and have limited effectiveness in suppressing high-frequency vibrations. At the signal processing level, filtering algorithms are often used to suppress harmonics, but they cannot compensate for the deterministic amplitude and phase errors of the fundamental signal. Methods that indirectly estimate vibration displacement using accelerometers struggle to directly and accurately decouple the microscopic motions that cause changes in the air gap.

[0006] This invention is the first to propose using a six-dimensional force sensor to directly measure the interface force / torque that causes changes in the air gap. By establishing a physical model of "six-dimensional force → air gap vibration state → electromagnetic signal error", it realizes integrated, feedforward real-time compensation for the fundamental and harmonic errors of the inductive encoder, fundamentally improving the accuracy and robustness of the encoder in vibration environments. (III) Summary of the Invention

[0007] The purpose of this invention is to provide an error compensation method and system for inductive encoders based on six-dimensional force sensing and vibration decoupling: overcoming the shortcomings of existing technologies, this method can sense the mechanical excitation source that causes encoder performance degradation in real time, and perform online compensation through an accurate model, significantly reducing measurement errors caused by vibration.

[0008] The objective of this invention is achieved as follows:

[0009] The inductive encoder error compensation system based on six-dimensional force sensing and vibration decoupling consists of an inductive encoder (1), a six-dimensional force sensor (2), a synchronous data acquisition unit (3), a real-time signal processor (4), and a decoding and angle calculation unit (5). In this system, the six-dimensional force sensor (2) is installed close to the encoder and is used to directly capture the six-dimensional force / torque on the motor stator housing or support structure. The synchronous data acquisition unit (3) ensures the time synchronization between the force signal and the encoder electrical signal. The real-time signal processor (4) is the core calculation unit, which embeds a pre-calibrated transfer matrix, a mathematical model describing the relationship between air gap changes and electromagnetic errors, and a harmonic mapping database. The decoding and angle calculation unit (5) receives the compensated clean signal and outputs a high-precision angle.

[0010] Based on the above system, the present invention further provides an error compensation method, comprising the following steps: S1: synchronously acquiring the encoder's original signal U raw (t) and the six-dimensional force signal [F] x ,F y ,F z M x M y M z ] T ; S2: Using the transfer matrix H gap The vibration state vector characterizing the air gap change is decoupled from the six-dimensional force signal. G(t) = [Δz(t), θ x (t),θ y (t)] T Where Δz(t) is the axial air gap change, θ x (t), θ y (t) represents the relative tilt angles about the X and Y axes; S3: Based on the electromagnetic coupling model, the compensation amount is calculated in real time according to G(t), including the amplitude compensation coefficient α(t) and the phase compensation amount. and the compensation signal U used to cancel out distortion harmonics harm (t); S4: Apply compensation amount to U raw (t) performs real-time dynamic correction and generates U corr (t)=α(t)*[U raw (t)-U harm (t)]; S5: For U corr (t) is decoded to obtain the final high-precision angle θ. corr (t);

[0011] The transfer matrix was obtained through a static calibration experiment of the system, ensuring the accuracy of the mapping relationship from "force" to "air gap change".

[0012] The harmonic compensation signal originates from a preset harmonic distortion mapping model. This model, through numerous offline experiments, has established a database of correspondences between different air gap states and the amplitude and phase of each harmonic in the output signal, thereby achieving targeted suppression of harmonic distortion. (iv) Description of the attached drawings

[0013] Figure 1 This is a schematic diagram of the overall structure and connection relationship of the inductive encoder error compensation method and system based on six-dimensional force sensing and vibration decoupling. It consists of an inductive encoder (1), a six-dimensional force sensor (2), a synchronous data acquisition unit (3), a real-time signal processor (4), and a decoding and angle calculation unit (5).

[0014] Figure 2 This is a schematic diagram of the changes in the air gap between the stator and rotor (axial movement and tilting around the shaft).

[0015] Figure 3 It is a flowchart of the entire process of "force-air gap-signal error" compensation.

[0016] Figure 4 This is a comparison diagram of the output signal spectrum of the rotary transformer before and after compensation in the embodiment. (V) Detailed Implementation

[0017] The present invention will be further illustrated below with reference to specific embodiments.

[0018] In this embodiment, a multi-pole rotary transformer is used as an inductive encoder (1) and applied to a high-performance servo motor. The six-dimensional force sensor (2) is a compact strain gauge sensor, which is installed near the non-drive end bearing seat of the motor stator housing via a flange to optimally sense the interfacial force that causes changes in the encoder air gap.

[0019] System calibration: Before implementing compensation, system calibration is required to obtain key model parameters. 1. Transfer matrix H gap Calibration: Fix the motor-encoder system onto a six-dimensional force calibration platform. Under static conditions, apply a series of known uniaxial forces / torques (e.g., F) covering the operating range through the calibration platform. z M x M y Simultaneously, a high-precision capacitive displacement sensor (resolution better than 0.1 μm) and a laser goniometer (resolution better than 1 μrad) are used to directly measure the axial displacement ΔZ and tilt angle θ between the stator and rotor. x θ y After collecting multiple sets of data, a multiple linear regression algorithm was used to identify the 3×6 transfer matrix H. gap For example, H is obtained through calibration. gap Typical partial element values ​​are: H gap (1,3) = 0.05 μm / N, representing an axial force F of 1 N. z This will cause an axial air gap change of 0.05 μm; H gap (3,5) = 0.2 μrad / (N·m), representing the torque M about the Y-axis of 1 N·m. y This will cause a tilt θ about the X-axis of 0.2 μrad. x ; 2. Establishment of Electromagnetic Error Model and Harmonic Mapping Database: The rotary transformer is driven on a controllable vibration table, and axial and radial vibrations of different frequencies and amplitudes are applied through an exciter to simulate ΔZ and θ. x θ y Changes. Simultaneous recording of six-dimensional force sensor signals (via H... gap The solution is G(t) and the encoder's original output signal U. raw The complete spectrum of G(t) was established through offline analysis, relating G(t) to the fundamental amplitude error ΔA / A0 and the phase error. And a mapping table between the amplitudes of the 3rd, 5th, and other major harmonics, or fitted empirical formula coefficients (such as β as described in the background art). i γ i These parameters and the mapping table are stored in the memory of the real-time signal processor (4).

[0020] Real-time compensation process: During system operation, the synchronous acquisition unit (3) synchronously acquires the two sine / cosine outputs U of the rotary transformer at a sampling rate of 100kHz. raw_sin (t), U raw_cos (t) and the six channel signals of the six-dimensional force sensor (2); 1. In a real-time signal processor (4) (such as an FPGA), the current six-dimensional force vector is first multiplied by H. gap The matrix is ​​used to obtain real-time air gap state estimates, such as Δz. est = +1.8μm, θ x_est =0.08mrad, θ y_est =0.02mrad; 2. According to Δz est Through the model M(t) = M0 * (d0 / (d0 + Δz) est )) k Calculate the current change in mutual inductance coefficient ΔM(t) / M0. Combine this with θ. x_est t and θ y_est Substitute into the calibrated error model: ΔA(t) / A0=β1*(ΔM(t) / M0)+β2*θ x_est +β3*θ y_est The calculated amplitude compensation coefficient is: α(t)=1 / (1+ΔA(t) / A0)≈0.97 Calculated phase compensation amount 3. At the same time, with [ΔZ est ,θ x_est ,θ y_est Using [index], query the harmonic mapping database to obtain the amplitude A of the third harmonic compensation signal that should be injected in the current state. h3 With phase Synthetic U harm (t); 4. Perform comprehensive compensation on the original signal: U corr_sin (t)=α(t)*[U raw_sin (t)-U harm_sin (t)] And perform phase analysis on the compensated signal. Rotational correction; 5. The corrected two orthogonal signals U corr_sin (t) and U corr_cos(t) is fed into the decoding and angle calculation unit (5) (usually a dedicated decoding chip or processor software algorithm), and uses decoding methods such as arctangent to finally output a high-precision angle θ that is resistant to interference. corr (t).

Claims

1. A method and system for error compensation of an inductive encoder based on six-dimensional force sensing and vibration decoupling. Its features are: It consists of an inductive encoder (1), a six-dimensional force sensor (2), a synchronous data acquisition unit (3), a real-time signal processor (4), and a decoding and angle calculation unit (5). In the system, the inductive encoder (1) includes an excitation coil installed on the rotor and an array of induction coils installed on the stator. The six-dimensional force sensor (2) is installed on the motor stator housing or the encoder stator support structure and is used to measure the six-dimensional force / torque signal at the mechanical interface. The synchronous data acquisition unit (3) simultaneously acquires the original electrical signal of the inductive encoder (1) and the output signal of the six-dimensional force sensor (2). The real-time signal processor (4) is embedded with transfer matrix parameters, electromagnetic error model parameters, and harmonic mapping model, which are used to decouple the air gap vibration state according to the six-dimensional force signal and calculate the real-time compensation amount. The decoding and angle calculation unit (5) decodes the compensated signal and outputs high-precision angle information.

2. The system according to claim 1, characterized in that: System Compensation Includes the following steps: S1: Synchronous acquisition step: The original electrical signal output by the induction coil of the inductive encoder (1) and the six-dimensional force / torque signal output by the six-dimensional force sensor (2) are synchronously acquired by the synchronous data acquisition unit (3); S2: Air gap vibration state decoupling step: In the real-time signal processor (4), the six-dimensional force signal is processed by the preset transfer matrix, decoupled and extracted to extract the vibration state vector that directly causes the change of air gap between the encoder stator and rotor; S3: Electromagnetic error modeling and compensation calculation step: Based on the electromagnetic coupling model of the inductive encoder (1), a quantitative relationship model between the air gap vibration state vector and the encoder output signal error is established, and the amplitude compensation coefficient, phase compensation amount and harmonic compensation signal are calculated in real time; S4: Signal dynamic compensation and harmonic suppression step: The original signal is corrected by the compensation amount calculated in step S3, and the signal phase is offset compensation is applied; S5: High-precision calculation step: In the decoding and angle calculation unit (5), the compensated signal is decoded to obtain the high-precision angle of the motor shaft that is resistant to vibration interference.

3. The system according to claim 1, characterized in that: In step S2, the transfer matrix is ​​a 3×6 matrix, and its parameters are obtained through static calibration and multiple linear regression identification. Specifically, when the system is in a static state, a set of known six-dimensional static forces / torques are applied to the mechanical interface, and at the same time, a precision micrometer or capacitive sensor is used to directly measure the air gap change and tilt angle between the stator and rotor. The values ​​of each element in the transfer matrix are obtained by fitting multiple linear regression.

4. The system according to claim 1, characterized in that: In step S3, the generation of the harmonic compensation signal is obtained by inputting the air gap change and tilt angle into a pre-trained harmonic distortion mapping model. This mapping model is obtained by offline measurement of the harmonic components of the encoder output signal under different vibration states and establishing a database.

5. The system according to claim 1, characterized in that: The inductive encoder (1) is a rotary transformer or an inductive displacement sensor.

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