Speed measurement method of optimized speed observer

By introducing a nonlinear function and dynamic weight allocation mechanism into the speed observer, combining a hybrid filtering algorithm and centrifugal compensation coefficient, the angle estimation process is optimized, and the misjudgment problem caused by the angle error spans the cycle is solved, and the speed measurement accuracy and stability are improved.

CN120369982APending Publication Date: 2025-07-25ZHENGZHOU JIACHEN ELECTRIC CO LTD

Patent Information

Application Number
CN202510237533.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-03
Publication Date
2025-07-25

AI Technical Summary

Technical Problem

In the calculation of angle errors of existing speed observers, because the deviation angle spans the cycle, it is easy to treat smaller negative values as large positive values or small positive values as large negative values, resulting in a decrease in speed measurement accuracy and stability.

Method used

Add a nonlinear function to the speed observer, and through a dynamic weight allocation mechanism and a hybrid filtering algorithm, combined with centrifugal compensation coefficient, the angle estimation process is optimized, the error error and error judgment caused by periodic jumps are reduced, and the response rate and accuracy are improved.

Benefits of technology

It effectively reduces the error error and error caused by periodic jumps, improves the response rate and accuracy of the speed observer, improves the angle estimation accuracy under high-speed operating conditions, and improves the stability of the system.

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Abstract

The invention discloses a speed measurement method of an optimized speed observer, relates to the technical field of vehicle power control, and solves the problem that a small negative value is easily taken as a large positive value or a small positive value is easily taken as a large negative value due to the fact that a deviation angle crosses a period in angle error calculation of an existing speed observer. The speed measurement method comprises the following steps: the acquisition and processing module acquires and processes a pulse signal of the encoder to obtain a feedback angle; an angle estimation value is calculated; taking the difference between the feedback angle and the angle estimation value as a deviation angle, and performing nonlinear compensation to obtain an angle deviation value; inputting a matrix operation framework of a speed observer, and outputting a linear acceleration estimated value; the pulse signal of the encoder is collected and processed again, a feedback angle is obtained, M-method operation and filtering processing are carried out on the feedback angle and the last feedback angle, and the feed-forward speed is obtained; and the speed observer performs weighted fusion operation on the linear acceleration estimated value, the angle deviation value and the feedback angle to obtain a final angular velocity estimated value, so that a final estimated angle is obtained, and velocity measurement is completed.
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Description

Technical Field

[0001] The present invention relates to the technical field of vehicle power control, and particularly to a speed measurement method for an optimized speed observer. Background Art

[0002] In the field of motor drive and motion control, accurate measurement of rotational speed is crucial to ensure the dynamic performance of the system. Traditional speed measurement methods rely on physical devices such as optical encoders and Hall sensors. Although they can directly obtain rotational speed signals, they have significant drawbacks: on the one hand, the hardware cost of sensors is high, and they are prone to damage under harsh working conditions such as high temperature, high humidity, and strong vibration, resulting in a decrease in system reliability; on the other hand, problems such as mechanical installation errors, signal transmission delays, and electromagnetic interference will introduce noise and affect the speed measurement accuracy. With the development of industrial automation towards high speed and high precision, especially in high-dynamic scenarios such as electric vehicles, numerical control machine tools, and robots, traditional methods are difficult to meet the multiple requirements of real-time performance, robustness, and cost control.

[0003] With the gradual rise of sensorless speed measurement technology, its core is to indirectly estimate the rotational speed by combining the motor mathematical model (such as back electromotive force equation, flux linkage speed observer) with electrical signals (current, voltage).

[0004] Patent No. CN202411493062.0 discloses a wheel speed meter failure analysis system based on speed observer technology, including an accelerometer for measuring the acceleration signal of an electric bicycle; a wheel speed meter for measuring the wheel speed signal of the electric bicycle; a global positioning system module for measuring the ground speed of the electric bicycle; and a speed observer module for fusing the acceleration signal, wheel speed signal, and ground speed signal to determine whether the wheel speed meter fails. The above invention designs a speed observer to fuse IMU, GPS, and wheel speed meter data to obtain a more accurate speed measurement, realize the speed observation of the ebike carrier, and perform the failure analysis of the wheel speed meter.

[0005] Patent No. CN202411306616.1 discloses a multi-frame optoelectronic platform outer loop speed feedback method. By adding a state speed observer to the outer loop, in the outer loop control loop, a Smith state speed observer is added. Through the calculation of the speed observer, the rate information of the outer loop frame can be observed, thus replacing the tachometer, reducing the system hardware complexity, and in terms of rate feedback, compared with the tachometer, the state observation method will reduce the phase lag of the feedback rate and improve the system stability.

[0006] Although the above patents can measure the vehicle speed using a speed observer, the motor parameters (such as resistance and inductance) drift with factors like temperature and aging, resulting in the mismatch of the speed observer; when there are sudden load changes or external disturbances, the dynamic response of traditional observation algorithms (such as the Luenberger speed observer) lags, and steady-state errors are likely to occur; high-frequency noise and harmonic interference will reduce the signal-to-noise ratio of the estimated signal. In addition, in the process of calculating the angle error of the existing speed observer, due to the deviation angle spanning a cycle, a small negative value is easily regarded as a large positive value or a very small positive value is regarded as a large negative value. Summary of the Invention

[0007] The object of the present invention is to provide a speed measurement method for an optimized speed observer, which can reduce the error misjudgment caused by cycle jumps by adding a non-linear function to the speed observer; improve the response rate and accuracy of the speed observer through a dynamic weight allocation mechanism; combine the phase characteristics of IIR filtering and the stability of FIR filtering through a hybrid filtering algorithm; improve the angle estimation accuracy under high-speed conditions through a centrifugal compensation coefficient to enhance the stability of the speed observer.

[0008] The present invention uses the following technical solutions: A speed measurement method for an optimized speed observer includes the following steps; S1: The acquisition and processing module acquires and processes the pulse signal of the encoder to obtain the feedback angle; at the same time, the angle estimation value is calculated based on the historical feedback angle; S2: The difference between the feedback angle and the angle estimation value is used as the deviation angle, and the deviation angle is non-linearly compensated to obtain the angle deviation value input to the speed observer; S3: The angle deviation value is input into the matrix operation architecture of the speed observer to output the linear acceleration estimation value; S4: The acquisition and processing module acquires and processes the pulse signal of the encoder again to obtain the feedback angle, and performs M-method operation and hybrid filtering processing with the previous feedback angle to obtain the feedforward speed; S5: The speed observer performs weighted fusion addition operation on the linear acceleration estimation value, the angle deviation value, and the feedback angle to obtain the final angular velocity estimation value; S6: The speed observer performs operations on the final angular velocity estimation value to obtain the final estimated angle, thereby completing the speed measurement.

[0009] Preferably, in step S1, the acquisition and processing module uses a high-precision timer to capture and convert the AB-phase pulse signal of the incremental encoder preset to N times frequency to obtain the feedback angle; at the same time, the acquisition and processing module performs smoothing processing on the historical feedback angle using a sliding window Kalman filtering algorithm to obtain smoothed angle data; then, the data fitting algorithm is used to perform fitting operation on the smoothed angle data to obtain the angle estimation value.

[0010] Preferably, in step S2, the difference between the feedback angle and the angle estimated value is calculated to obtain the deviation angle; and the sine function is used to perform a non-linear operation on the deviation angle to obtain the non-linear deviation; the absolute value of the deviation angle is judged: if the absolute value of the deviation angle is less than the preset deviation threshold, the deviation angle is the angle deviation value input to the speed observer; if the absolute value of the deviation angle is greater than or equal to the preset deviation threshold, the non-linear deviation is the angle deviation value input to the speed observer.

[0011] Preferably, in step S3, the matrix operation architecture includes an L2 proportional coefficient matrix and an L3 integral coefficient matrix; the speed observer uses the matrix operation architecture to perform operations on the angle deviation value according to the preset limit value to obtain an angle deviation matrix, and discretizes the angle deviation matrix according to the preset sampling period to obtain a linear acceleration estimation value.

[0012] Preferably, in step S4, the M method operation is a dual-timer architecture, the first timer is used to capture the AB-phase pulse signal of an incremental encoder preset to be N times the frequency, and the second timer is used as the time base; the acquisition and processing module uses the dual-timer architecture to capture and process the AB-phase pulse signal to obtain an initial linear velocity signal; and a hybrid filtering algorithm is used to filter the initial linear velocity signal to obtain the feedforward velocity.

[0013] Preferably, the hybrid filtering algorithm includes a non-recursive filter and a recursive filter; the non-recursive filter uses an all-pass filter to perform non-linear phase compensation on the initial linear velocity signal according to the dynamic weight distribution mechanism to obtain an all-pass linear velocity signal; the recursive filter uses a gradient descent adaptive algorithm with a preset update step of N to perform operations on the all-pass linear velocity signal according to the dynamic weight distribution mechanism to obtain the feedforward velocity.

[0014] Preferably, the dynamic weight distribution mechanism performs smooth dual-mode switching using an exponential decay function according to the signal change rate: if the signal change rate is greater than or equal to the preset change threshold, the weight of the non-recursive filter is greater than the weight of the recursive filter; if the signal change rate is less than the preset change threshold, the weight of the non-recursive filter is less than the weight of the recursive filter; at the same time, the pole configuration of the non-recursive filter and the zero position of the recursive filter are jointly optimized according to the constraint conditions.

[0015] Preferably, in step S5, the speed observer uses the trapezoidal integration method to perform an integration operation on the linear acceleration estimated value to obtain a first angular velocity component, uses the L1 proportional compensation matrix to perform a proportional operation on the angle deviation value to obtain a second angular velocity component, and simultaneously uses a differential filtering function to perform a differential operation on the feedback angle to obtain a third angular velocity component; the speed observer uses a weighted fusion algorithm according to the dynamic weight adjustment rule to perform a fusion addition operation on the first angular velocity component, the second angular velocity component, and the third angular velocity component to obtain a final angular velocity estimated value.

[0016] Preferably, the speed observer uses a preset integrator according to a preset period correction mechanism, and combines the centrifugal compensation coefficient to perform a closed-loop integration operation on the final angular velocity estimated value to obtain a final estimated angle.

[0017] In the present invention, by adding a non-linear function in the speed observer, the error misjudgment caused by period jumps is reduced; through the dynamic weight distribution mechanism, the response rate and accuracy of the speed observer are improved; through the hybrid filtering algorithm, the phase characteristics of the IIR filter and the stability of the FIR filter are combined; through the centrifugal compensation coefficient, the angle estimation accuracy under high-speed conditions is improved, and the stability of the speed observer is enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or related technologies, the following will briefly introduce the drawings required for use in the description of the embodiments or related technologies. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0019] Figure 1 is the principle block diagram of the speed measurement method; Figure 2 is the principle block diagram of the speed observer. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] The following will describe the present invention in detail with reference to the drawings and embodiments: As Figure 1 - Figure 2 shown, the speed measurement method of the optimized speed observer described in the present invention includes the following steps: S1: The acquisition and processing module acquires and processes the pulse signal of the encoder to obtain a feedback angle; at the same time, the angle estimated value is calculated based on the historical feedback angle; S2: The difference between the feedback angle and the angle estimated value is used as the deviation angle, and the deviation angle is non-linearly compensated to obtain the angle deviation value input to the speed observer; S3: The angle deviation value is input into the matrix operation architecture of the speed observer to output the linear acceleration estimated value; S4: The acquisition and processing module acquires and processes the pulse signal of the encoder again, obtains the feedback angle, and performs M-method operation and hybrid filtering processing on the current feedback angle and the previous feedback angle to obtain the feedforward speed. S5: The speed observer performs a weighted fusion addition operation on the linear acceleration estimated value, the angle deviation value, and the feedback angle to obtain the final angular velocity estimated value. S6: The speed observer operates on the final angular velocity estimated value to obtain the final estimated angle, thereby completing the speed measurement.

[0021] In the present invention, in step S1, the acquisition and processing module uses a high-precision timer to capture and convert the AB-phase pulse signals of an incremental encoder preset with N times frequency multiplication to obtain the feedback angle; at the same time, the acquisition and processing module performs smoothing processing on the historical feedback angle by using a sliding window Kalman filtering algorithm to obtain smoothed angle data; and then performs fitting operation on the smoothed angle data by using a data fitting algorithm to further obtain the angle estimated value.

[0022] In the present invention, in step S2, the difference between the feedback angle and the angle estimated value is calculated to obtain the deviation angle; and a non-linear operation is performed on the deviation angle by using the sin function to obtain the non-linear deviation; the absolute value of the deviation angle is judged: if the absolute value of the deviation angle is less than the preset deviation threshold, the deviation angle is the angle deviation value input to the speed observer; if the absolute value of the deviation angle is greater than or equal to the preset deviation threshold, the non-linear deviation is the angle deviation value input to the speed observer.

[0023] In this embodiment, when the deviation angle may cross a period (such as near the boundary of 0° and 360°), a small negative value (such as -5°) may be mistakenly regarded as a large positive value (355°), or a small positive value (such as 355°) may be mistakenly regarded as a large negative value (-5°). Therefore, the sin function is used to process this deviation angle to reduce the error misjudgment caused by the period jump.

[0024] Specifically, by calculating the sine value of the deviation angle (such as using sin(θ / 2)), the angle difference can be mapped to the continuous interval of [-1, 1], avoiding the numerical mutation caused by the angle periodicity, so as to more accurately reflect the actual minimum angle difference.

[0025] During the speed calculation process, all rely on the observer for speed estimation, and it is necessary to increase the relevant parameters of L1, L2, and L3, which makes the estimated speed value fluctuate greatly.

[0026] In the present invention, in step S3, the matrix operation architecture includes an L2 proportional coefficient matrix and an L3 integral coefficient matrix; the speed observer uses the matrix operation architecture to operate on the angle deviation value according to a preset limit value to obtain an angle deviation matrix, and discretizes the angle deviation matrix according to a preset sampling period to obtain a linear acceleration estimation value.

[0027] In the present invention, in step S4, the M method operation is a dual-timer architecture. The first timer is used to capture the AB-phase pulse signals of an incremental encoder preset to N times the frequency, and the second timer serves as the time base; the acquisition and processing module uses the dual-timer architecture to capture and process the AB-phase pulse signals to obtain an initial linear speed signal; and uses a hybrid filtering algorithm to filter the initial linear speed signal to obtain a feedforward speed.

[0028] In the present invention, the hybrid filtering algorithm includes a non-recursive filter and a recursive filter; the non-recursive filter uses an all-pass filter to perform non-linear phase compensation on the initial linear speed signal according to a dynamic weight distribution mechanism to obtain an all-pass linear speed signal; the recursive filter uses a gradient descent adaptive algorithm with a preset update step of N to operate on the all-pass linear speed signal according to a dynamic weight distribution mechanism to obtain a feedforward speed.

[0029] In this embodiment, the non-recursive filter is an IIR feedforward channel function, and the recursive filter is an FIR feedback channel function; In the present invention, the dynamic weight distribution mechanism performs smooth dual-mode switching using an exponential decay function according to the signal change rate: if the signal change rate is greater than or equal to a preset change threshold, the weight of the non-recursive filter is greater than the weight of the recursive filter; if the signal change rate is less than the preset change threshold, the weight of the non-recursive filter is less than the weight of the recursive filter; at the same time, the pole configuration of the non-recursive filter and the zero position of the recursive filter are jointly optimized according to the constraint conditions; In this embodiment, the constraint condition is that the amplitude product of the IIR transfer function and the FIR transfer function is less than 1.05, and the phase angle difference is less than 5 degrees; In the present invention, in step S5, the speed observer uses the trapezoidal integration method to perform an integration operation on the linear acceleration estimation value to obtain a first angular velocity component, and uses an L1 proportional compensation matrix to perform a proportional operation on the angle deviation value to obtain a second angular velocity component. At the same time, a differential filtering function is used to perform a differential operation on the feedback angle to obtain a third angular velocity component; the speed observer uses a weighted fusion algorithm according to the dynamic weight adjustment rule to perform a fusion addition operation on the first angular velocity component, the second angular velocity component, and the third angular velocity component to obtain a final angular velocity estimation value.

[0030] In the present invention, in step S6, the speed observer uses a preset integrator according to a preset periodic correction mechanism, combines the centrifugal compensation coefficient, and performs a closed-loop integration operation on the final angular velocity estimated value to obtain the final estimated angle.

[0031] Embodiment: The acquisition and processing module uses a high-precision timer to capture and convert the AB-phase pulse signals of an incremental encoder preset to N times frequency, and obtains the feedback angle; at the same time, the acquisition and processing module smooths the historical feedback angle using a sliding window Kalman filtering algorithm to obtain smoothed angle data; then uses a data fitting algorithm to perform a fitting operation on the smoothed angle data, and further obtains an angle estimated value; Calculate the difference between the feedback angle and the angle estimated value to obtain the deviation angle; and perform a non-linear operation on the deviation angle using the sin function to obtain the non-linear deviation; judge the absolute value of the deviation angle: if the absolute value of the deviation angle is less than the preset deviation threshold, then the deviation angle is the angle deviation value input to the speed observer; if the absolute value of the deviation angle is greater than or equal to the preset deviation threshold, then the non-linear deviation is the angle deviation value input to the speed observer; The speed observer uses a matrix operation architecture (L2 proportional coefficient matrix and L3 integral coefficient matrix) to operate on the angle deviation value according to the preset limit value, obtains an angle deviation matrix, and discretizes the angle deviation matrix according to the preset sampling period to obtain a linear acceleration estimated value; The acquisition and processing module acquires and processes the encoder pulse signals again to obtain the feedback angle, and performs an M method operation (dual-timer architecture, the first timer is used to capture the AB-phase pulse signals of an incremental encoder preset to N times frequency, and the second timer is used as the time base; the acquisition and processing module uses the dual-timer architecture to capture and process the AB-phase pulse signals to obtain the initial linear velocity signal) and hybrid filtering processing (non-recursive filter and recursive filter, the non-recursive filter uses an all-pass filter according to a dynamic weight distribution mechanism (according to the signal change rate, uses an exponential decay function for smooth dual-mode switching: if the signal change rate is greater than or equal to the preset change threshold, then the weight of the non-recursive filter is greater than the weight of the recursive filter; if the signal change rate is less than the preset change threshold, then the weight of the non-recursive filter is less than the weight of the recursive filter; at the same time, jointly optimize the pole configuration of the non-recursive filter and the zero position of the recursive filter according to the constraint conditions), performs non-linear phase compensation on the initial linear velocity signal to obtain an all-pass linear velocity signal; the recursive filter uses a gradient descent adaptive algorithm with a preset update step of N, and operates on the all-pass linear velocity signal according to the dynamic weight distribution mechanism) to obtain the feedforward velocity; The speed observer uses the trapezoidal integration method to integrate the estimated value of linear acceleration to obtain the first angular velocity component, uses the L1 proportional compensation matrix to perform proportional operation on the angle deviation value to obtain the second angular velocity component, and at the same time uses the differential filtering function to perform differential operation on the feedback angle to obtain the third angular velocity component; the speed observer uses the weighted fusion algorithm according to the dynamic weight adjustment rule to perform fusion addition operation on the first angular velocity component, the second angular velocity component and the third angular velocity component to obtain the final estimated angular velocity value; The speed observer uses a preset integrator according to the preset period correction mechanism to perform closed-loop integration operation on the final estimated angular velocity value in combination with the centrifugal compensation coefficient to obtain the final estimated angle.

Claims

1. A speed measurement method for an optimized speed observer, characterized in that: It includes the following steps: S1: The acquisition and processing module acquires and processes the pulse signal of the encoder to obtain the feedback angle; meanwhile, the angle estimation value is calculated based on the historical feedback angle; S2: The difference between the feedback angle and the angle estimation value is used as the deviation angle, and the deviation angle is non-linearly compensated to obtain the angle deviation value input to the velocity observer; S3: The angle deviation value is input into the matrix operation architecture of the velocity observer to output the estimated linear acceleration value; S4: The acquisition and processing module acquires and processes the pulse signal of the encoder again to obtain the feedback angle, and performs M-method operation and hybrid filtering on the current feedback angle and the previous feedback angle to obtain the feedforward velocity; S5: The velocity observer performs weighted fusion addition operation on the estimated linear acceleration value, the angle deviation value, and the feedback angle to obtain the final estimated angular velocity value; S6: The velocity observer operates on the final estimated angular velocity value to obtain the final estimated angle, thereby completing the speed measurement.

2. The speed measurement method of the optimized speed observer according to claim 1, characterized in that: In step S1, the acquisition and processing module uses a high-precision timer to capture and convert the AB-phase pulse signals of the incremental encoder preset with N times frequency to obtain the feedback angle; meanwhile, the acquisition and processing module smooths the historical feedback angle using the sliding window Kalman filtering algorithm to obtain the smoothed angle data; then, the data fitting algorithm is used to perform fitting operation on the smoothed angle data to obtain the angle estimation value.

3. The speed measurement method of the optimized speed observer according to claim 1, characterized in that: In step S2, the difference between the feedback angle and the angle estimation value is calculated to obtain the deviation angle; and the sin function is used to perform non-linear operation on the deviation angle to obtain the non-linear deviation; the absolute value of the deviation angle is judged: if the absolute value of the deviation angle is less than the preset deviation threshold, the deviation angle is the angle deviation value input to the velocity observer; if the absolute value of the deviation angle is greater than or equal to the preset deviation threshold, the non-linear deviation is the angle deviation value input to the velocity observer.

4. The speed measurement method of the optimized speed observer according to claim 1, characterized in that: In step S3, the matrix operation architecture includes an L2 proportional coefficient matrix and an L3 integral coefficient matrix; the velocity observer operates on the angle deviation value using the matrix operation architecture according to the preset limit value to obtain the angle deviation matrix, and discretizes the angle deviation matrix according to the preset sampling period to obtain the estimated linear acceleration value.

5. The speed measurement method of the optimized speed observer according to claim 1, characterized in that: In step S4, the M-method operation is a dual-timer architecture, where the first timer is used to capture the AB-phase pulse signals of the incremental encoder preset with N times frequency, and the second timer serves as the time base; the acquisition and processing module uses the dual-timer architecture to capture and process the AB-phase pulse signals to obtain the initial linear velocity signal; and the initial linear velocity signal is filtered using the hybrid filtering algorithm to obtain the feedforward velocity.

6. The speed measurement method of the optimized speed observer according to claim 5, characterized in that: The hybrid filtering algorithm includes a non-recursive filter and a recursive filter; the non-recursive filter uses an all-pass filter to perform non-linear phase compensation on the initial linear velocity signal according to the dynamic weight distribution mechanism to obtain the all-pass linear velocity signal; the recursive filter uses the gradient descent adaptive algorithm with a preset update step of N to operate on the all-pass linear velocity signal according to the dynamic weight distribution mechanism to obtain the feedforward velocity.

7. The speed measurement method of the optimized speed observer according to claim 6, characterized in that: The dynamic weight allocation mechanism performs smooth dual-mode switching using an exponential decay function based on the signal change rate: if the signal change rate is greater than or equal to a preset change threshold, the weight of the non-recursive filter is greater than that of the recursive filter; if the signal change rate is less than the preset change threshold, the weight of the non-recursive filter is less than that of the recursive filter; at the same time, the pole configuration of the non-recursive filter and the zero position of the recursive filter are jointly optimized according to the constraint conditions.

8. The speed measurement method of the optimized speed observer according to claim 1, characterized in that: In step S5, the velocity observer uses the trapezoidal integration method to integrate the linear acceleration estimated value to obtain the first angular velocity component, uses the L1 proportional compensation matrix to perform proportional operation on the angle deviation value to obtain the second angular velocity component, and at the same time uses the differential filtering function to perform differential operation on the feedback angle to obtain the third angular velocity component; the velocity observer uses the weighted fusion algorithm according to the dynamic weight adjustment rule to perform fusion addition operation on the first angular velocity component, the second angular velocity component and the third angular velocity component to obtain the final angular velocity estimated value.

9. The speed measurement method of the optimized speed observer according to claim 1, characterized in that: In step S6, the velocity observer uses a preset integrator according to the preset period correction mechanism, and combines the centrifugal compensation coefficient to perform closed-loop integration operation on the final angular velocity estimated value to obtain the final estimated angle.

Citation Information

Patent Citations

  • Wheel speed meter failure analysis system based on observer technology

    CN119310309A

  • Multi-frame photoelectric platform outer ring speed feedback method

    CN119311045A

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