Compensation method for rate-dependent hysteresis characteristics of precision mirrors

Abstract

This invention relates to a method for compensating for the rate-dependent hysteresis characteristics of a precision aiming mirror, solving the problem of missed scans in precision tracking systems and belonging to the field of piezoelectric ceramic hysteresis characteristic compensation. The invention includes: applying a sinusoidal signal with a full amplitude and a frequency below 1 Hz to the precision aiming mirror to identify the inverse hysteresis rising curve g(y); applying a sweeping signal with a full amplitude and a frequency above 1 Hz to the precision aiming mirror to identify the inverse hysteresis change effect curve h(v) caused by the increase in frequency or rate; the rate-dependent inverse hysteresis rising curve f(y,v) = g(y) + h(v) of the precision aiming mirror, where the previous inflection point A of the desired output angle y at the current moment is... c Let x be the left turning point, then x = x c -f(y-y) c ,v); If the previous inflection point A of the desired output angle y at the current moment is... c Let x be the right inflection point, and x = x c +f(y c -y,v); The compensated input voltage x is input to the precision sight, and the precision sight outputs an angle to complete the rate-related hysteresis compensation of the precision sight.

Description

Technical Field

[0001] This invention relates to a method for compensating for the rate-related hysteresis characteristics of a precision aiming scope, belonging to the field of piezoelectric ceramic hysteresis characteristic compensation. Background Technology

[0002] Currently, due to the urgent need for inter-satellite networking, laser communication terminals are developing towards low power consumption and miniaturization. Therefore, beacon-less light acquisition technology is one of the current research hotspots. Beacon-less light acquisition technology involves the laser communication transmitting terminal aiming only through signal light and using a corresponding scanning method to scan an uncertain area (the area where the receiving terminal might appear) until the receiving terminal is detected. One effective way to achieve beacon-less light acquisition technology is to choose a suitable scanning method. Compared to traditional coarse tracking system scanning, it is more suitable for composite scanning, i.e., coarse tracking and fine tracking systems scanning simultaneously. Generally, in practical engineering applications, the actuator of the fine tracking system is a fine aiming mirror or a voice coil motor. Due to the severe radiation effect between satellites, a piezoelectric ceramic-driven fine aiming mirror is a relatively suitable choice, such as... Figure 1 As shown.

[0003] Piezoelectric ceramics operate based on the inverse piezoelectric effect; when a voltage is applied across their ends, the ceramic stretches a corresponding distance. However, the inherent hysteresis of piezoelectric ceramics causes a hysteresis effect in the X and Y axes of a precision sight. This means the relationship between the input voltage signal and the deflection angle is not a simple linear one, but rather exhibits a hysteresis loop. Furthermore, the shape of this loop is related to the frequency or rate of the input signal, such as... Figure 2 As shown in the figure, when the frequency of the input sinusoidal signal is less than 1 Hz, the shape of the hysteresis loop remains basically unchanged; when the frequency of the input sinusoidal signal is greater than 1 Hz, and with the increase of frequency, the shape of the hysteresis loop becomes wider and wider. This characteristic is called rate-dependent hysteresis. In the precision aiming scope scanning stage, the rate-dependent hysteresis characteristic makes the actual spiral scanning curve ( Figure 3 The spiral line deviating from the standard before compensation Figure 3 The target trajectory is not cleared, which causes errors in the scanning trajectory, resulting in missed scans by the laser communication terminal and ultimately leading to capture failure.

[0004] Currently, there are two main strategies for addressing the hysteresis characteristics related to the accuracy of precision sights: closed-loop control and feedforward compensation. Closed-loop control of the precision sight increases the cost and size of the equipment and reduces its scanning bandwidth, making it less than optimal. Conversely, feedforward compensation control requires only a single compensation algorithm, eliminates the need for sensors, and does not reduce scanning bandwidth. However, the control accuracy of the feedforward compensation method depends on the accuracy of the hysteresis characteristic modeling; a simple and accurate modeling method is crucial for achieving feedforward compensation. Existing methods, such as the improved PI model, the Bouc-Wen model, the improved Preisach model, and AI-based neural network models, can all model the hysteresis characteristics related to the accuracy of precision sights with high precision, but their structures are relatively complex and require the identification of many parameters. Summary of the Invention

[0005] To address the issue of missed scans in precision tracking systems, this invention provides a method for compensating for the rate-related hysteresis characteristics of precision aiming scopes.

[0006] The method for compensating for the rate-related hysteresis characteristics of the precision aiming scope of the present invention includes:

[0007] S1. Identify the rate-related inverse hysteresis rise curve of the precision sight:

[0008] When a sinusoidal signal with a full amplitude and a frequency below 1 Hz is applied to the precision aiming scope, the inverse hysteresis rising curve g(y) is identified. When a sweeping signal with a full amplitude and a frequency above 1 Hz is applied to the precision aiming scope, the inverse hysteresis change effect curve h(v) caused by the increase of frequency or speed is identified.

[0009] The rate-dependent inverse hysteresis rising curve of the precision aiming scope is f(y,v)=g(y)+h(v), where y is the desired output angle of the precision aiming scope, f(y,v) represents the precision aiming scope input voltage corresponding to y on the rate-dependent hysteresis rising curve, and v is the rate of the desired output angle.

[0010] S2. Determine the compensated input voltage x based on the desired output angle y at the current moment:

[0011] When the expected output angle y is at the previous inflection point A c Let x be the left turning point, then x = x c -f(yy c ,v), x c and y c Indicates inflection point A c The corresponding input voltage and desired output angle;

[0012] When the expected output angle y is at the previous inflection point A c Let x be the right inflection point, and x = x c +f(y c -y,v);

[0013] S3. Input the compensated input voltage x into the precision aiming mirror, and the precision aiming mirror outputs the angle to complete the rate-related hysteresis compensation of the precision aiming mirror.

[0014] As a preferred embodiment, in S1, the inverse hysteresis rising curve g(y) is:

[0015] g(y) = a5·y 5 +a4·y 4 +a3·y 3 +a2·y 2 +a1·y

[0016] a5, a4, a3, a2, a1 are the parameters of g(y).

[0017] As a preferred method, the method for identifying the inverse hysteresis rising curve g(y) is as follows:

[0018] The input voltage and output angle are obtained by applying a full-amplitude sinusoidal signal with a frequency below 1Hz to the precision sight, and the output angle during the rising phase is found. and input voltage The least squares method is used to identify g(y), and the parameters of g(y) are obtained as [a5, a4, a3, a2, a1]. T =(Λ) T ·Λ) -1 ·Λ T ·Ω;

[0019] (1)…(l) represents the corresponding data from time 1 to time l.

[0020] As a preferred embodiment, the curve h(v) representing the inverse hysteresis effect caused by an increase in frequency or rate is:

[0021] h(v) = b·v + c

[0022] b and c are parameters of h(v).

[0023] As a preferred method, the method for identifying the inverse hysteresis effect curve h(v) caused by the increase in frequency or rate is as follows:

[0024] The input voltage and output angle are obtained by applying a full-amplitude sweep signal with a frequency higher than 1Hz to the precision sight, and the input voltage X = [x(1), x(2), ..., x(l)] during the rising phase is found. T Output angle Y = [y(1), y(2), ..., y(l)] T The rate of output angle V = [v(1), v(2), ..., v(l)] T ;

[0025] Let Y = [y(1), y(2), ..., y(l)]T The input is fed into the identified inverse hysteresis rising curve g(y) to obtain the intrinsic inverse hysteresis effect vector G = [g(1), g(2), ..., g(l)]. T ;

[0026] Construct the rate data matrix of the output angle and inverse hysteresis output data matrix that is only related to frequency or rate Obtain the parameters of h(v) using the least squares method.

[0027] Preferably, S2 includes:

[0028] S21. Define stack X L Stack Y L Stack X R Stack Y R and variable y pre_1 =0, variable y pre_2 =0, variable x pre_1 =0, variable Flag;

[0029] S22. Input the desired output angle y(k) at the current time k, and use the forward difference of y(k) to calculate the rate v(k) of the input signal;

[0030] S23, If (y(k)-y pre_1 )(y pre_1 -y pre_2 If y < 0, then y pre_1 If it's an inflection point, execute S24; otherwise, y pre_1 This is not an inflection point; proceed with S26.

[0031] S24, If (y(k)-y pre_1 )>0, y pre_1 If the left turn point is reached, execute S25_a; otherwise, execute y. pre_1 For the right turn point, execute S25_b;

[0032] S25_a, Turn the left turning point y pre_1 Stored in stack Y L The corresponding inflection point value x pre_1 Stored in stack X L And set Flag=0;

[0033] S25_b, turn the right turn point y pre_1 Stored in stack Y R The corresponding inflection point value x pre_1 Stored in stack X R And set Flag=1;

[0034] S26. Check if Flag = 0. If true, execute S27_a; otherwise, execute S27_b.

[0035] S27_a, Using binary search on stack Y R Define the position of y(k) in the code, delete all inflection points with values ​​less than y(k), and start from X. L and Y L Read the inflection point A respectively c x c and y c Output x(k) = x c +f(y c -y(k),v(k));

[0036] S27_b, using binary search on stack Y L Define the position of y(k) in X, delete all inflection points with values ​​greater than y(k), and start from X. R and Y R Read the inflection point A respectively c x c and y c Output x(k) = x c -f(y(k)-y c ,v(k));

[0037] S28. When y(k)≠y pre_1 At that time, let y pre_1 =y(k), y pre_2 =y pre_1 x pre_1 =x(k), k = k + 1, jump

[0038] Switch to S22.

[0039] The beneficial effects of this invention are as follows: Addressing the problem in existing technologies where the rate-related hysteresis characteristics of precision aiming scopes are complex to model due to numerous parameters and excessive computation, making real-time applications difficult, this invention proposes a method for modeling and compensating for rate-related hysteresis of precision aiming scopes. This method solves the rate-related dynamic hysteresis effect of precision aiming scopes below 200Hz, ensuring that the actual spiral scanning trajectory of the precision aiming scope almost coincides with the ideal spiral scanning trajectory. This reduces missed scans, improves the acquisition probability, and further lays a solid foundation for the research of beacon-less light acquisition technology. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the precision aiming scope structure;

[0041] Figure 2 The hysteresis characteristic related to the accuracy of the precision sight;

[0042] Figure 3For tracking the spiral scanning trajectory of the precision sight;

[0043] Figure 4 The modeling effect of the precision aiming scope rate-related hysteresis characteristics at different frequencies using the method of the present invention;

[0044] Figure 5 This invention demonstrates the compensation effect of the precision aiming scope rate-related hysteresis characteristics at different frequencies using the method of the present invention.

[0045] Figure 6 This describes the structural composition of the method of the present invention;

[0046] Figure 7 This is a feedforward compensation strategy for precision sights. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0049] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0050] This implementation proposes a corresponding inverse hysteresis modeling method for the rate-dependent hysteresis characteristics of precision aiming scopes, the framework of which is as follows: Figure 4 The diagram shows: The first part is the computer-executable inflection point erasure mechanism algorithm. The second part is a description of the hysteresis curve of the precision aiming scope. This implementation applies the separation concept to the rate-dependent hysteresis characteristic, that is, it considers the rate-dependent hysteresis characteristic of the precision aiming scope to be its inherent inverse hysteresis and the overall hysteresis effect related to the frequency or rate of the input signal. Here, f(y,v) is used to describe the rate-dependent inverse hysteresis curve of the precision aiming scope, that is, to describe the overall inverse hysteresis effect curve, which includes two parts:

[0051] 1. In actual phenomena, it is observed that when the input full-amplitude sine signal is below 1Hz, the shape of its hysteresis loop remains basically unchanged. This phenomenon is the inherent inverse hysteresis characteristic, and g(y) is used to describe the inverse hysteresis rising curve.

[0052] 2. When the input full-amplitude sinusoidal signal is greater than 1Hz, the width of the hysteresis loop increases with the increase of the frequency or speed of the input signal. Here, h(v) is used to describe the effect of the inverse hysteresis change caused by the increase of frequency or speed.

[0053] That is, f(y,v)=g(y)+h(v), where y is the desired output angle of the precision sight and v is the rate of the desired output angle.

[0054] The compensation method for the precision aiming scope rate-related hysteresis characteristics in this embodiment includes:

[0055] Step 1: Identify the rate-dependent inverse hysteresis rise curve of the precision sight:

[0056] When a sinusoidal signal with a full amplitude and a frequency below 1 Hz is applied to the precision aiming scope, the inverse hysteresis rising curve g(y) is identified. When a sweeping signal with a full amplitude and a frequency above 1 Hz is applied to the precision aiming scope, the inverse hysteresis change effect curve h(v) caused by the increase of frequency or speed is identified.

[0057] The rate-dependent inverse hysteresis rising curve of the precision aiming scope is f(y,v)=g(y)+h(v), where y is the desired output angle of the precision aiming scope, f(y,v) represents the precision aiming scope input voltage corresponding to y on the rate-dependent hysteresis rising curve, and v is the rate of the desired output angle.

[0058] Step 2: Based on the desired output angle y at the current moment, use the inflection point erasure mechanism algorithm to determine the previous inflection point A of the desired output angle y. c Then, further determine the compensated input voltage x:

[0059] When the expected output angle y is at the previous inflection point A c Let x be the left turning point, then x = x c -f(yy c ,v), x c and y c Indicates inflection point A c The corresponding input voltage and desired output angle;

[0060] When the expected output angle y is at the previous inflection point A c Let x be the right inflection point, and x = x c +f(y c -y,v);

[0061] Step 3: Input the compensated input voltage x into the precision aiming scope, and the precision aiming scope outputs an angle to complete the rate-related hysteresis compensation of the precision aiming scope.

[0062] This implementation proposes a method for modeling and compensating for rate-related hysteresis of a precision aiming scope. Through a feedforward compensation strategy, the input voltage signal of the precision aiming scope is made approximately linearly related to the deflection angle. That is, during the scanning phase of inter-satellite laser communication, the actual scanning trajectory ( Figure 3 After compensation, the target trajectory is accurately tracked. Figure 3The method can track the target trajectory, thus avoiding missed scans by the precision tracking system. Compared with other methods, the method proposed in this invention has fewer parameters, is easier to identify, has a simple model structure, requires less computational resources, and can be used in online real-time applications.

[0063] In step one of this implementation method, the inverse hysteresis rising curve g(y) is:

[0064] g(y) = a5·y 5 +a4·y 4 +a3·y 3 +a2·y 2 +a1·y

[0065] a5, a4, a3, a2, a1 are the parameters of g(y).

[0066] Methods for identifying the g(y) parameter include:

[0067] A sinusoidal signal with a frequency below 1Hz and full amplitude is applied to the precision sight, and its deflection angle signal is acquired. The above input and output signals are normalized to obtain the input voltage vector X = [x(1), x(2), ..., x(n)]. T And the output angle vector Y = [y(1), y(2), ..., y(n)] T Where x(1), x(2), ..., x(n) and y(1), y(2), ..., y(n) are the input voltage and output angle corresponding to sampling times 1, 2, ..., n, respectively. Based on the standard that y(k) - y(k-1) > 0, it is determined whether the data is in the rising phase, and the rising phase data of the input and output signals X = [x(1), x(2), ..., x(l)] are obtained. T And Y = [y(1), y(2), ..., y(l)] T Construct the output angle of the rising phase and input voltage The least squares method is used to identify g(y), and the parameters of g(y) are obtained as [a5, a4, a3, a2, a1]. T =(Λ) T ·Λ) -1 ·Λ T ·Ω, this part completes the description of the inherent inverse hysteresis characteristic.

[0068] In step one of this implementation method, the curve h(v) representing the inverse hysteresis effect caused by the increase in frequency or rate is as follows:

[0069] h(v) = b·v + c

[0070] b and c are parameters of h(v).

[0071] Methods for identifying the h(v) parameter include: applying a full-amplitude frequency to the precision sight in the range of 0Hz-200Hz. The frequency sweep signal is used to acquire its deflection angle signal. The above input and output signals are normalized to obtain the input voltage vector X = [x(1), x(2), ..., x(n)]. T And the output angle vector Y = [y(1), y(2), ..., y(n)] T , and for Y=[y(1),y(2),…,y(n)] T Perform forward subtraction to obtain the velocity vector V = [v(1), v(2), ..., v(n)] of the output angle. T Where x(1), x(2), ..., x(n), v(1), v(2), ..., v(n), y(1), y(2), ..., y(n) are the input voltage, the rate of output angle, and the output angle at sampling times 1, 2, ..., n, respectively. The data is used to identify h(v) = b·v + c. Based on the criterion that y(k) - y(k-1) > 0, it is determined whether the data is in the rising phase, and the rising phase data of the input and output signals X = [x(1), x(2), ..., x(l)] are obtained. T And Y = [y(1), y(2), ..., y(l)] T Obtain the input voltage X = [x(1), x(2), ..., x(l)] during the rising phase. T Output angle Y = [y(1), y(2), ..., y(l)] T The rate of output angle V = [v(1), v(2), ..., v(l)] T ;Put Y=[y(1),y(2),…,y(l)] T The input is fed into the identified inverse hysteresis rising curve g(y) to obtain the intrinsic inverse hysteresis effect vector G = [g(1), g(2), ..., g(l)]. T Construct the rate data matrix of the output angle. and inverse hysteresis output data matrix that is only related to frequency or rate Obtain the parameters of h(v) using the least squares method. This section completes the description of the inverse hysteresis effect caused solely by the frequency or rate of the input signal.

[0072] The above content completes the description of the inverse hysteresis rise curve related to the accuracy of precision aiming scopes:

[0073] f(y,v)=a5·y 5 +a4·y 4 +a3·y 3 +a2·y 2 +a1·y+b·v+c.

[0074] Based on the identified inverse hysteresis rise curve f(y,v) related to the precision aiming scope rate, step 2 of this embodiment includes:

[0075] Step 21, Define stack X L Stack Y L Stack X R Stack Y R and variable y pre_1 =0, variable y pre_2 =0, variable x pre_1 =0, variable Flag;

[0076] Step 22: Input the desired output angle y(k) at the current time k, and use the forward difference of y(k) to calculate the rate v(k) of the input signal;

[0077] Step 23, if (y(k)-y pre_1 )(y pre_1 -y pre_2 If y < 0, then y pre_1 If it is an inflection point, proceed to step 24; otherwise, y pre_1 This is not an inflection point; proceed to step 26.

[0078] Step 24, if (y(k)-y pre_1 )>0, y pre_1 If it is a left turn point, proceed to step 25_a; otherwise, y pre_1 For the right turn point, proceed to step 25_b;

[0079] Step 25_a, turn the left turning point y pre_1 Stored in stack Y L The corresponding inflection point value x pre_1 Stored in stack X L And set Flag=0;

[0080] Step 25_b: Turn the right turn point y pre_1 Stored in stack Y R The corresponding inflection point value x pre_1 Stored in stack X R And set Flag=1;

[0081] Step 26: Determine if Flag = 0. If true, proceed to step 27_a; otherwise, proceed to step 27_b.

[0082] Step 27_a: Use binary search on stack Y R Define the position of y(k) in the code, delete all inflection points with values ​​less than y(k), and start from X. L and Y L Read the inflection point A respectively c x c and yc Output x(k) = x c +f(y c -y(k),v(k));

[0083] Step 27_b: Use binary search on stack Y L Define the position of y(k) in X, delete all inflection points with values ​​greater than y(k), and start from X. R and Y R Read the inflection point A respectively c x c and y c Output x(k) = x c -f(y(k)-y c ,v(k));

[0084] Step 28, when y(k) ≠ y pre_1 At that time, let y pre_1 =y(k),y pre_2 =y pre_1 x pre_1 =x(k), k = k+1, jump to step 22.

[0085] use Figure 7 The feedforward compensation strategy shown completes rate-related hysteresis compensation for the precision sight.

[0086] This concludes the method of this embodiment. Its precision aiming scope-related hysteresis compensation effect is as follows: Figure 5 As shown.

[0087] First, the method of this embodiment achieves compensation below 200Hz with high accuracy. Second, the tracking effect of the method of this embodiment on the spiral scanning curve was tested experimentally, such as... Figure 3 As shown, compared to before compensation, the scan curve after compensation almost coincides with the target trajectory. The method of this invention requires fewer identification parameters, has a simple structure, and requires less computational resources. It can be programmed into a corresponding computer program for online real-time application during the spiral scanning stage of the precision aiming scope in a laser communication terminal, thereby enabling the actual spiral scanning curve to track the ideal spiral scanning curve with high precision.

[0088] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for compensating for the rate-related hysteresis characteristics of a precision aiming scope, characterized in that, The method includes: S1. Identify the rate-related inverse hysteresis rise curve of the precision sight: By applying a sinusoidal signal with a frequency below 1Hz at full amplitude to the precision sight, the inverse hysteresis rising curve was identified. By applying a full-amplitude sweep signal with a frequency higher than 1 Hz to the precision sight, the inverse hysteresis effect curve caused by the increase in frequency or rate is identified. ; Rate-related inverse hysteresis rise curve of precision sight , This represents the desired output angle of the precision sight. This indicates that the related hysteresis rising curve is related to... The corresponding precision sight input voltage, The rate at which the desired output angle is reached; S2, Output angle based on the current moment Determine the compensated input voltage : When the desired output angle The previous inflection point The left turn point , and Indicating the inflection point The corresponding input voltage and desired output angle; When the desired output angle The previous inflection point The right turn point ; S2 includes: S21, Define the stack Stack Stack Stack and variables ,variable ,variable ,variable ; S22, Input current Expected output angle at any moment ,use Forward subtraction is used to calculate the rate of the input signal. ; S23, if ,but If it's an inflection point, execute S24; otherwise, This is not an inflection point; proceed with S26. S24, if , If it's a left turn point, execute S25_a; otherwise, For the right turn point, execute S25_b; S25_a, Turn left at the point Stored in the stack Corresponding inflection point value Stored in the stack and set ; S25_b, Turn right point Stored in the stack Corresponding inflection point value Stored in the stack and set ; S26, Judgment If true, execute S27_a; otherwise, execute S27_b. S27_a, Using binary search on the stack Definition in Chinese Position where the value is less than All inflection points were deleted, and from and Read the inflection points separately of and Output ; S27_b, Using binary search on the stack Definition in Chinese Position where the value is greater than All inflection points were deleted, and from and Read the inflection points separately of and Output ; S28, when season , , , Jump to S22; S3, adjust the compensated input voltage The input is fed into the precision sight, which outputs the angle, thus completing the rate-related hysteresis compensation for the precision sight.

2. The compensation method for the correlation hysteresis characteristic of the precision aiming scope according to claim 1, characterized in that, In S1, the inverse hysteresis rising curve for: ； for The parameters.

3. The compensation method for the correlation hysteresis characteristics of the precision aiming scope according to claim 2, characterized in that, Identify the inverse hysteresis rising curve The method is as follows: The input voltage and output angle are obtained by applying a full-amplitude sinusoidal signal with a frequency below 1Hz to the precision sight, and the output angle during the rising phase is found. and input voltage Using the least squares method To identify and obtain parameters ; Indicates time 1 to The corresponding data at any given time.

4. The compensation method for the correlation hysteresis characteristic of the precision aiming scope according to claim 1, characterized in that, Inverse hysteresis effect curve caused by increase in frequency or rate : ； , for The parameters.

5. The compensation method for the correlation hysteresis characteristic of the precision aiming scope according to claim 4, characterized in that, Identify the inverse hysteresis effect curve caused by the increase in frequency or rate. The method is as follows: The input voltage and output angle are obtained by applying a full-amplitude sweep signal with a frequency higher than 1Hz to the precision sight, and the input voltage during the rising phase is found. Output angle and the rate of output angle ; Bundle The inverse hysteresis rising curve obtained from the input and identification In this process, the inherent inverse hysteresis effect vector is obtained. ; Construct the rate data matrix of the output angle Hysteresis output data matrix that is only related to frequency or rate Obtain using the least squares method parameters .

6. A computer-readable storage device storing a computer program, characterized in that, When the computer program is executed, it implements the compensation method for the rate-related hysteresis characteristics of the precision sight as described in any one of claims 1 to 5.

7. A compensation device for the rate-related hysteresis characteristics of a precision sight, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to implement the compensation method for the rate-related hysteresis characteristics of the precision sight as described in any one of claims 1 to 5.

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