Fast-response closed-loop micro-thrust measurement method and equipment based on dynamic thrust inversion

Abstract

This invention relates to a fast-response closed-loop micro-thrust measurement method and device based on dynamic thrust inversion. The method includes the following steps: obtaining the dynamic equation parameters of the measurement system; calculating a control quantity in each control cycle, using this control quantity as the standard force; calculating the resultant force of the previous control cycle based on the displacement data obtained by the measurement system and the dynamic equation parameters in the current control cycle using a dynamic inversion algorithm; calculating the thrust to be measured in the previous control cycle based on the difference between the standard force and the resultant force in the previous control cycle; and performing low-pass filtering on the thrust to be measured to obtain the final result. Compared with the prior art, this invention can improve the measurement response speed without increasing the noise level.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano satellite technology and relates to a micro-thrust measurement method, particularly a fast-response closed-loop micro-thrust measurement method and device based on dynamic thrust inversion. Background Technology

[0002] Microsatellites and nanosatellites have become a key focus of research in space science and commercial aerospace in recent years. Compared to traditional large satellites, microsatellites and nanosatellites offer advantages such as lighter weight, smaller size, higher flexibility, and shorter development cycles. Furthermore, they can be deployed in formations to accomplish space missions of similar complexity at a lower cost than a single large satellite. Due to their inherent weight and size limitations, microsatellites and nanosatellites require propulsion systems with high specific impulse and high stability. Micro-thrusters, capable of generating micro-Newtons to millinewtons of thrust, are the core components of these propulsion systems. Ground-based testing of these micro-thrusters to measure and evaluate their performance is an indispensable step before their formal application.

[0003] Specific impulse and response time are crucial parameters affecting the dynamic performance of micro-thrusters. A thorough understanding and evaluation of these dynamic parameters is essential for designing and developing high-performance micro-thrusters. Many micro-thrusters have response times ranging from tens of milliseconds to even a few milliseconds. Therefore, to accurately measure the specific impulse, response time, and other dynamic parameters of micro-thrusters, the measurement methods employed must also possess a fast response speed.

[0004] Torsional pendulums, with their advantages of high precision and high resolution, are widely used micro-thrust measurement systems. Currently, there are two main methods for measuring the dynamic performance of micro-thrusters using torsional pendulums: open-loop dynamic measurement and closed-loop measurement. Open-loop dynamic measurement solves for the measured force as it changes over time by using the rotation angle of the torsional pendulum and the dynamic equations. Closed-loop measurement, on the other hand, uses closed-loop control to achieve torque balance between a known standard force and the measured force, keeping the torsional pendulum at zero position. This allows the magnitude of the measured force to be reflected by the magnitude of the standard force, as illustrated by patent application CN110413015A, which discloses a micro-Newton-level micro-thrust dynamic test bench and testing method based on closed-loop control.

[0005] The open-loop dynamic measurement principle of the torsion pendulum is simple and has a fast response speed. However, the measurement range is usually small due to the limitation of the torsion pendulum's rotation range, and when the torsion pendulum rotates at a large angle, the nonlinear error will increase due to the influence of factors such as the cables and air pipes carried by the thruster.

[0006] In closed-loop measurement, the torsion bar is controlled at zero, allowing for a larger measurement range by increasing the standard force range. Furthermore, nonlinear errors caused by factors such as cables and tubing during measurement are reduced. Therefore, closed-loop measurement is a better choice for scenarios requiring high precision. However, traditional closed-loop measurement has the following drawbacks:

[0007] 1. Traditional closed-loop measurements have poor performance in measuring dynamic parameters such as response time. This is because to measure response times on the order of tens of milliseconds, both the control frequency and response time of the closed-loop measurement must be relatively high. In this case, the closed-loop circuit will significantly amplify the impact of high-frequency measurement noise on the standard force, greatly increasing its noise level. Furthermore, due to the limitations of closed-loop system stability, low-pass filtering cannot effectively solve the problem of high-frequency noise. Therefore, when the noise level is the same, the response speed of closed-loop measurements is often slower than that of open-loop measurements.

[0008] 2. Traditional closed-loop measurement typically requires cumbersome controller design and adjustment. Because its measurement performance is significantly affected by the controller, the dynamic parameters of the measurement system will change each time the thrust under test is replaced. To obtain ideal response speed and noise levels, the controller should also be adjusted accordingly. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a fast-response closed-loop micro-thrust measurement method and device based on dynamic thrust inversion that can improve the measurement response speed without increasing the noise level.

[0010] The objective of this invention can be achieved through the following technical solutions:

[0011] A fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion includes the following steps:

[0012] Obtain the dynamic equation parameters of the measurement system;

[0013] In each control cycle, a control quantity is calculated and used as the standard force.

[0014] In the current control cycle, based on the displacement data obtained by the measurement system and the parameters of the dynamic equation, the resultant force of the previous control cycle is calculated using a dynamic inversion algorithm;

[0015] Based on the difference between the standard force and the resultant force of the previous control cycle, the thrust to be measured in the previous control cycle is calculated.

[0016] The thrust to be measured is subjected to low-pass filtering to obtain the final result.

[0017] Furthermore, the parameters of the dynamic equations of the measurement system are obtained through measurement or calibration.

[0018] Furthermore, the expression for the dynamic equation of the measurement system is as follows:

[0019]

[0020] Where T is the thrust to be measured, and θ is the angular displacement output by the measurement system. and These are the corresponding second and first derivatives, respectively, where J is the system's moment of inertia, c is the system's damping coefficient, k is the system's stiffness coefficient, and L... T The length of the lever arm for the thrust;

[0021] The dynamic equations then include the system's moment of inertia J, the system's damping coefficient c, the system's stiffness coefficient k, and the lever arm length L of the thrust. T .

[0022] Furthermore, the control algorithm for calculating the control quantity includes the PID algorithm.

[0023] Furthermore, the formula for calculating the resultant force of the previous control cycle is:

[0024]

[0025] in, For the resultant force of the (k-1)th period, and It is the second and first derivatives of the angular displacement with respect to time in the kth period.

[0026] Furthermore, the second-order and first-order differentials are obtained by using backward difference approximation differential solution.

[0027] Furthermore, based on the measurement instructions, the thrust to be measured is calculated cyclically for each control cycle until the measurement ends.

[0028] The present invention also provides a fast-response closed-loop micro-thrust measurement device based on dynamic thrust inversion, comprising:

[0029] The parameter acquisition module is used to obtain the dynamic equation parameters of the measurement system;

[0030] The control quantity calculation module is used to calculate a control quantity in each control cycle, and use this control quantity as the standard force.

[0031] The dynamic inversion module is used to calculate the resultant force of the previous control cycle in the current control cycle based on the displacement data obtained by the measurement system and the parameters of the dynamic equation, using a dynamic inversion algorithm.

[0032] The preliminary calculation module for the thrust to be measured is used to calculate the thrust to be measured in the previous control cycle based on the difference between the standard force and the resultant force in the previous control cycle.

[0033] The low-pass filter module is used to perform low-pass filtering on the thrust to be measured to obtain the final result.

[0034] The present invention also provides a computer-readable storage medium including one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for performing the fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion as described above.

[0035] The present invention also provides an electronic device including one or more processors, a memory, and one or more programs stored in the memory, said one or more programs including instructions for executing the fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion as described above.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] Compared to traditional closed-loop measurements, this invention compensates for the tracking error and noise effects included in the standard force. The measurement response speed and noise level are independent of the standard force and, under stable system conditions, are no longer affected by the controller, but are only related to the cutoff frequency of the low-pass filter during dynamic thrust inversion. Experimental verification shows that this method can achieve a higher response speed while maintaining a lower noise level. Furthermore, as long as system stability is ensured, the measurement results of this invention are independent of the controller parameters, thus simplifying the design of the closed-loop controller.

[0038] Compared to traditional open-loop dynamic thrust inversion, this method retains the advantages of traditional closed-loop measurement, such as large range and low nonlinearity, while also being insensitive to distortion of dynamic parameters. This is because the measurement results of this invention consist of two parts—the standard force and the dynamic inversion result, with the dynamic inversion result only accounting for a portion of the measurement results. Therefore, when the dynamic parameters deviate from their true values, the final measurement error caused by this method will be less than the error caused by open-loop dynamic measurement. This means that when the dynamic parameters are not accurately calibrated due to noise interference or other reasons, using this method can achieve higher measurement accuracy.

[0039] In summary, compared with the prior art, the technical solution of the present invention has the following advantages:

[0040] First, compared with traditional closed-loop measurement, this invention eliminates the tracking error of the standard force to be measured force and the measurement noise amplified by the control loop in the traditional closed-loop measurement results, thereby improving the response speed of closed-loop measurement without increasing the noise level.

[0041] Secondly, compared with traditional closed-loop measurement, under the premise of system stability, the measurement performance of the present invention is almost independent of the controller parameters. It can achieve near-optimal measurement performance under any control parameters that stabilize the system, thereby greatly simplifying the design of the controller.

[0042] Third, compared with traditional open-loop dynamic measurement, this invention not only retains the advantages of low nonlinearity and high accuracy of traditional closed-loop measurement, but also has the advantage of more accurate measurement results when dynamic parameters are distorted, and has stronger robustness. Attached Figure Description

[0043] Figure 1 This is a schematic diagram illustrating the principle of traditional closed-loop measurement.

[0044] Figure 2 This is a schematic diagram illustrating the principle of the present invention;

[0045] Figure 3 This is a flowchart of the algorithm of the present invention;

[0046] Figure 4 The present invention provides measurement results of a 20mN amplitude step thrust under different control parameters using the method of the present invention.

[0047] Figure 5 The results of traditional closed-loop measurement of 20mN amplitude step thrust under different control parameters;

[0048] Figure 6 This is the measurement result of the 2mN step thrust using the method of the present invention when the dynamic parameters are distorted;

[0049] Figure 7 This is the measurement result of a 2mN step thrust under the condition of distorted dynamic parameters in traditional open-loop dynamic measurement. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0051] Before introducing the technical solution of this invention, it is necessary to analyze the reasons for the poor dynamic measurement performance of traditional closed-loop systems.

[0052] For example Figure 1 In the closed-loop measurement system shown, C(s), G(s), and H(s) are the transfer functions of the controller (including the actuator), the torsion pendulum, and the displacement sensor, respectively, where H(s) is typically 1. x is the actual displacement of the torsion pendulum, which is measured by the sensor after being contaminated by measurement noise n. n This represents the measured displacement. r is the expected displacement, typically equal to 0, and e is the displacement between r and x. n The error between them. T and F represent the force to be measured and the standard force, respectively.

[0053] The goal of closed-loop control is to stabilize the displacement x at zero, with the standard force F equal to the force to be measured, T. Based on the transfer functions of each module in the system, the error between the force to be measured T and the standard force F can be expressed as follows:

[0054]

[0055] Among them, S TF =1 / (1+CG), S nF =C / (1+CG), respectively called F err The sensitivity function to the force T to be measured and to the measurement noise n. In equation (1), S TF • T is the inherent tracking error of F to T in closed-loop control, S nF ·n represents the error caused by measurement noise.

[0056] In traditional closed-loop measurement, to improve the response speed, the tracking error of F to T should be reduced, i.e., S TF If the value should be reduced, then the controller gain C should be increased. However, when C increases, on the one hand, as C increases, S... nF It will also increase and gradually tend towards G. -1 From the transfer function model of the torsional pendulum, we know that G -1 =(Js 2 +cs+k) / L T This model, consisting of a first-order and a second-order differentiator, significantly amplifies high-frequency measurement noise, thus increasing the error caused by this noise. Furthermore, the increased open-loop gain reduces the phase and gain margins, worsening the stability of the closed-loop system. This makes it difficult to add a low-pass filter to handle high-frequency noise in the closed-loop circuit, as the low-pass filter introduces additional phase delay, which, at its low cutoff frequency, can degrade controller performance and even cause system divergence.

[0057] Therefore, the higher the response speed of traditional closed-loop measurement, the worse the system stability and the greater the noise in the measurement results.

[0058] This invention innovatively proposes to eliminate the two errors in equation (1) to resolve the contradiction between closed-loop measurement response speed, system stability, and measurement result noise. In closed-loop measurement, the actual thrust acting on the torsional pendulum is the resultant force F_r of the standard force and the force to be measured, which is the negative of the error between the standard force and the force to be measured. The displacement of the torsional pendulum is caused by the resultant force. Therefore, by calculating the resultant force through displacement inversion of the torsional pendulum and then subtracting the resultant force from the standard force, the measurement result without the two errors in equation (1) can be obtained.

[0059] It is important to note that dynamic thrust inversion typically amplifies high-frequency noise in the measured displacement. Therefore, a low-pass filter needs to be added after the inversion to filter the results. When the cutoff frequency of the low-pass filter is chosen to be low, the suppression of high-frequency noise will be enhanced, but the response speed will decrease. Conversely, when the cutoff frequency is chosen to be high, the response speed will increase, but the suppression of high-frequency noise will decrease. Thus, due to the influence of measurement noise, there is still a certain contradiction between the response speed and noise level in this invention. However, this contradiction is inherent in almost all measurements affected by high-frequency noise interference, and its cause differs from that in traditional closed-loop measurements; its impact on measurement performance is also far less than the latter.

[0060] Based on the above innovative research results, this invention provides a fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion. The aim is to improve the response speed of closed-loop measurement without increasing noise levels, thereby making closed-loop measurement more suitable for measuring the dynamic parameters of micro-thrusters. The method includes the following steps:

[0061] Step 1: Obtain the parameters in the dynamic equation of the measurement system through measurement or calibration.

[0062] This method is applicable to dynamic equations where... Or a similar measurement system, where T is the thrust to be measured, θ is the angular displacement output by the measurement system, J is the system moment of inertia, c is the system damping coefficient, k is the system stiffness coefficient, and L... T This is the length of the lever arm for the thrust.

[0063] The kinetic equation parameters obtained in step 1 include J, c, k, and L. T .

[0064] Step 2: In the k-th control cycle, calculate a control quantity F(k) using any control algorithm (e.g., PID, proportional-integral-derivative control algorithm). This control quantity is the standard force.

[0065] Step 3: Calculate the resultant force of the standard force F(k-1) and the measured force T(k-1) in the (k-1)th period using the measured displacement data and the dynamic inversion algorithm.

[0066]

[0067] in and It represents the second and first derivatives of the angular displacement with respect to time in the k-th period. In specific embodiments, there are many ways to calculate the derivative of discrete data; the following is a method using backward difference approximation:

[0068]

[0069] Where T s The sampling period.

[0070] In addition to the discrete data differentiation methods mentioned above, other methods such as forward difference, central difference, and Savitzky-Golay differentiation can also be used for calculation.

[0071] Step 4: Subtract the calculated resultant force from the standard force F(k-1) of the (k-1)th period. Thus, the force to be measured in the (k-1)th period is obtained:

[0072]

[0073] Step 5, for Perform a low-pass filter to obtain the final result.

[0074] Repeat steps 2 through 5 above until the measurement is complete.

[0075] To verify the measurement advantages of the proposed method, a set of horizontal torsion pendulums was used, based on... Figure 2 The schematic diagram shown is Figure 3 The flowchart shown illustrates two sets of experiments using a PID control algorithm. In the first set of experiments, a step thrust of approximately 20 mN was measured using both the method of this invention and a traditional closed-loop measurement method, under three different control parameters. This verifies the improved response speed of the method of this invention compared to the traditional closed-loop method, and the advantage that the measurement performance is almost unaffected by controller parameters. In the second set of experiments, a step thrust of approximately 2 mN was measured using both the method of this invention and a traditional open-loop dynamic measurement method. During the measurement, the moment of inertia J and damping coefficient c in the dynamic parameters were deviated from the calibration results by 5%, 10%, and 15% respectively, to verify the strong robustness of the method of this invention to dynamic parameter distortion.

[0076] Figure 4 The measurement results of step thrust under different control parameters (including control parameter 1, control parameter 2 and control parameter 3) are shown. It can be seen that the measurement results under different control parameters are basically consistent. Taking the time required for the measured value to first reach the ±5% error band of 20mN as the measurement response time, the response time of the method of the present invention is about 325ms. Figure 5The results of traditional closed-loop measurement of step thrust under different control parameters show significant variations. Specifically, the results under control parameter 1 exhibit substantial overshoot and oscillation. This is because control parameter 1 results in a higher controller gain, leading to a larger open-loop gain, smaller gain margin and phase margin, and decreased system stability. Furthermore, the presence of a low-pass filter during measurement introduces additional phase delay, further reducing system stability and thus causing overshoot and oscillation. The shortest response time of traditional closed-loop measurement is approximately 990 ms, significantly slower than the method described in this invention.

[0077] Figure 6 This is the measurement result of step thrust using the method of this invention when the dynamic parameters are distorted. Figure 7 These are the measurement results of traditional open-loop dynamic measurement when the dynamic parameters are distorted. It can be observed that the method of this invention exhibits a much smaller change in measurement results when the dynamic parameters are distorted compared to traditional open-loop dynamic measurement. When J and c are greater than the calibration results by 15%, the maximum error between the open-loop dynamic measurement results and those with accurate dynamic parameters is 0.2976 mN, and the average error is 0.0453 mN. In contrast, the maximum error of the measurement results obtained by the method of this invention is 0.0860 mN, and the average error is 0.0149 mN. The error of the method of this invention when the dynamic parameters are distorted is significantly smaller than that of traditional open-loop dynamic measurement; therefore, the method of this invention has stronger robustness.

[0078] In other embodiments, a fast-response closed-loop micro-thrust measurement device based on dynamic thrust inversion is also provided, comprising:

[0079] The parameter acquisition module is used to obtain the dynamic equation parameters of the measurement system;

[0080] The control quantity calculation module is used to calculate a control quantity in each control cycle, and use this control quantity as the standard force.

[0081] The dynamic inversion module is used to calculate the resultant force of the previous control cycle in the current control cycle based on the displacement data obtained by the measurement system and the parameters of the dynamic equation, using a dynamic inversion algorithm.

[0082] The preliminary calculation module for the thrust to be measured is used to calculate the thrust to be measured in the previous control cycle based on the difference between the standard force and the resultant force in the previous control cycle.

[0083] The low-pass filter module is used to perform low-pass filtering on the thrust to be measured to obtain the final result.

[0084] If the above methods are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0085] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0086] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion, characterized in that, Includes the following steps: Obtain the dynamic equation parameters of the measurement system; In each control cycle, a control quantity is calculated and used as the standard force. In the current control cycle, based on the displacement data obtained by the measurement system and the parameters of the dynamic equation, the resultant force of the previous control cycle is calculated using a dynamic inversion algorithm; Based on the difference between the standard force and the resultant force of the previous control cycle, the thrust to be measured in the previous control cycle is calculated. The thrust to be measured is subjected to low-pass filtering to obtain the final result.

2. The fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion according to claim 1, characterized in that, The parameters of the dynamic equations of the measurement system are obtained through measurement or calibration.

3. The fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion according to claim 1 or 2, characterized in that, The expression for the dynamic equation of the measurement system is: Where T is the thrust to be measured, and θ is the angular displacement output by the measurement system. and These are the corresponding second and first derivatives, respectively, where J is the system's moment of inertia, c is the system's damping coefficient, k is the system's stiffness coefficient, and L... T The length of the lever arm for the thrust; The dynamic equations then include the system's moment of inertia j, the system's damping coefficient c, the system's stiffness coefficient k, and the lever arm length L of the thrust. T .

4. The fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion according to claim 1, characterized in that, The control algorithm for calculating the control quantity includes the PID algorithm.

5. The fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion according to claim 3, characterized in that, The formula for calculating the resultant force in the previous control cycle is: in, For the resultant force of the (k-1)th period, and It is the second and first derivatives of the angular displacement with respect to time in the kth period.

6. The fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion according to claim 5, characterized in that, The second-order and first-order differentials are obtained by using backward difference approximation differential solution.

7. The fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion according to claim 1, characterized in that, According to the measurement command, the thrust to be measured is calculated cyclically for each control cycle until the measurement ends.

8. A fast-response closed-loop micro-thrust measurement device based on dynamic thrust inversion, characterized in that, include: The parameter acquisition module is used to obtain the dynamic equation parameters of the measurement system; The control quantity calculation module is used to calculate a control quantity in each control cycle, and use this control quantity as the standard force. The dynamic inversion module is used to calculate the resultant force of the previous control cycle in the current control cycle based on the displacement data obtained by the measurement system and the parameters of the dynamic equation, using a dynamic inversion algorithm. The preliminary calculation module for the thrust to be measured is used to calculate the thrust to be measured in the previous control cycle based on the difference between the standard force and the resultant force in the previous control cycle. The low-pass filter module is used to perform low-pass filtering on the thrust to be measured to obtain the final result.

9. A computer-readable storage medium, characterized in that, It includes one or more programs that are executed by one or more processors of an electronic device, the one or more programs including instructions for executing the fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion as described in any one of claims 1-7.

10. An electronic device, characterized in that, It includes one or more processors, a memory, and one or more programs stored in the memory, said one or more programs including instructions for executing the fast-response closed-loop micro-thrust measurement method based on dynamic thrust inversion as described in any one of claims 1-7.

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