Micro thrust dynamic identification method and system

Abstract

The invention relates to the technical field of micro thrust measurement of spaceflight micro thrusters, and discloses a micro thrust dynamic identification method and system. The recognition method comprises the following steps: constructing a kinetic equation of a thrust measurement system, rewriting the kinetic equation into a state space form, and carrying out integration to obtain a theoretical system response model at any moment; rewriting the theoretical system response model into a numerical model in a step-by-step integral recursion format; constructing an actual system response sequence and constructing an empirical model in combination with the kinetic equation of the thrust measurement system, and rewriting the empirical model; configuring a micro-thrust increment expression, rewriting a numerical model and an empirical model by applying the expression, and further rewriting the numerical model and the empirical model into an augmented form; predicting the prediction output of the future # imgabs0 # moments in the time domain; and a cost function is constructed and solved, so that the sum of squares of errors of predicted output and expected output in an actual system response sequence is minimum, the smoothness of micro-thrust input is considered, and at the moment, predicted micro-thrust corresponding to the predicted output is equal to actually measured micro-thrust corresponding to the expected output.

Description

Technical Field

[0001] The present invention relates to the technical field of micro-thrust measurement of aerospace micro-thrusters, and particularly to a method and system for dynamically identifying micro-thrusts. Background Art

[0002] Modern space missions such as deep space exploration, gravitational wave detection, and micro-nano satellite networking have extremely high requirements for the orbital control accuracy and attitude stability of spacecraft, and require thrusters to have a dynamic thrust adjustment ability of the order of micronewtons or even sub-micronewtons. Although the electric propulsion system has a higher specific impulse compared to chemical thrusters, which can significantly reduce fuel consumption and increase the payload ratio, its thrust is small and the thrust rise time is short, making it extremely difficult to capture its dynamic response characteristics (such as the thrust pulse rising edge). Therefore, existing traditional static calibration methods mainly focus on the measurement of steady-state thrust, average thrust, and single-pulse impulse. However, in actual missions, the thruster needs to be frequently started and stopped and the thrust adjusted (such as in pulse mode or continuous variable thrust), and the traditional static calibration method cannot meet the test requirements of dynamic response characteristics. By dynamically measuring data such as the frequency response and transient characteristics of the thruster and correcting the multi-physical field coupling model (such as the interaction between fluid mechanics and electromagnetic fields), the design reliability can be improved; based on the analysis of dynamic thrust signals (such as ripple characteristics), the performance defects of the thruster (such as hysteresis, drift, response delay) can be exposed in advance, avoiding satellite attitude loss of control or orbit deviation caused by thrust errors and extending the on-orbit life of the thruster; accurate dynamic thrust measurement can optimize the propellant usage strategy and reduce the fuel budget for deep space exploration missions. Ground dynamic micro-thrust measurement is the core link connecting thruster design and on-orbit application, and its research not only concerns the success or failure of space missions, but is also the key driving force for promoting advanced propulsion technologies, precision measurement science, and interdisciplinary engineering innovation.

[0003] Currently, the methods commonly used for dynamic thrust measurement of micro-thrusters can be roughly divided into two types: open-loop dynamic measurement and closed-loop dynamic measurement. Open-loop dynamic measurement is mainly based on the theory of inverse dynamics problems, and the dynamic thrust is obtained by comprehensively using the system response of the thrust bench and its system parameters. For example, a method for dynamically testing micro-thrust based on the least squares method disclosed in patent CN107562691B, and a method for measuring the thrust response time of on-board micro-thrusters based on a digital filter disclosed in patent CN114218750B. Closed-loop dynamic measurement is based on the concept of closed-loop control, using a known standard force and the force to be measured to form a two-force balance, so that the thrust bench is maintained at the zero position, and thus the applied standard force reflects the force to be measured in real time. For example, a micro-newton level micro-thrust dynamic test bench and test method based on closed-loop control disclosed in patent CN110413015B, and a fast-response closed-loop micro-thrust measurement method and device based on dynamic thrust inversion disclosed in patent CN119312534A. Summary of the Invention

[0004] The object of the present invention is to provide a method and system for dynamically identifying a micro-thrust. By comprehensively utilizing the system response information in a future period of time, it has a compact constraint effect on the calculation of the external force at a certain moment, effectively weakens the influence of the ill-posedness of the inverse problem, and establishes an optimal cost function and a method for adaptively determining key parameters to realize the online identification of the dynamic micro-thrust. The present invention has strong versatility and is applicable to the thrust platforms that can be approximated as a "mass-spring-damper" second-order vibration system. Without adding additional equipment, it provides an effective way to solve the measurement of the micro-dynamic thrust of micro-thrusters.

[0005] In a first aspect, the present invention provides a method for dynamically identifying a micro-thrust. The identification method includes the following steps: Construct the dynamic equation of the thrust measurement system, configure a state vector capable of characterizing the displacement response and velocity response of the thrust measurement system, and rewrite the dynamic equation using the state vector to obtain the state-space form of the dynamic equation; Initialize the state vector at the initial moment, and integrate the state-space form of the dynamic equation to obtain the theoretical system response model at any moment; Use a preset time step to discretize the time domain into multiple equally spaced moments, and assume that the thrust received by the thrust measurement system is constant within any integration step. Then, the theoretical system response model is rewritten as a numerical model in a step-by-step integration recurrence format; Based on the mapping pointers of the displacement, velocity, and acceleration responses of the measured system and the displacement, velocity, and acceleration obtained by the system response sensor, construct the actual system response sequence; Combine the dynamic equation of the thrust measurement system and the actual system response sequence to construct an empirical model; Rewrite the empirical model into a discrete recurrence format; Configure the micro-thrust increment expression. After applying the micro-thrust increment expression to rewrite the numerical model and the empirical model in the discrete recurrence format, further rewrite them into an augmented form; Based on the thrust measurement system response at the current moment and the micro-thrust increments at future moments within the future control time domain, and combine the augmented-form numerical model and the empirical model in the discrete recurrence format to obtain the predicted outputs at future

[0006] As a possible implementation manner, constructing the cost function specifically includes the following sub-steps: From the initial moment to Within one integration step, sum the product of the transpose of the difference between the predicted output and the desired output vector, the weight matrix, and the difference between the predicted output and the desired output vector to obtain the state cost sum function; wherein, the weight matrix is a 2×2 diagonal matrix, and the elements on the main diagonal respectively correspond to the weight components of the desired output and the micro-thrust increment, and the weight component of the desired output is much greater than the weight component of the micro-thrust increment; From the initial moment to Within the number of integration steps, sum the product of the square of the micro-thrust increment and the penalty parameter to obtain the micro-thrust increment cost sum function; Sum the state cost sum function and the micro-thrust increment cost sum function to obtain the cost function.

[0007] As a possible implementation, after constructing the cost function and before solving the cost function, it further includes simplifying the cost function, specifically including the following steps: Decompose the weight matrix into the product of two sub-matrices and rewrite the cost function using the two sub-matrices; When the state parameter obtained by the system response sensor is displacement or velocity, the mapping pointer of the acceleration response in the actual system response sequence is zero, that is, the vector related to acceleration in the predicted output is a zero vector. Based on this, simplify the predicted output into matrix form, and at the same time simplify the rewritten cost function into matrix form.

[0008] As a possible implementation, transform the solution of the cost function into solving a quadratic programming problem under unconstrained conditions, that is, solve the extreme point of the cost function in matrix form to obtain the optimal micro-thrust increment sequence, extract the first item from the optimal micro-thrust increment sequence to obtain the micro-thrust increment at the current moment, and substitute the micro-thrust increment at the current moment into the micro-thrust increment expression to obtain the predicted micro-thrust at the next moment.

[0009] As a possible implementation, substitute the micro-thrust increment at the current moment into the augmented numerical model to obtain the system state response corresponding to the predicted output at the next moment; Combine the predicted output simplified into matrix form and the actually measured system state response to obtain the desired output vector required at the next moment.

[0010] As a possible implementation, determine within the prediction time domain based on the effectiveness of energy propagation, and maximize within the control time domain, that is = .

[0011] As a possible implementation, determine within the prediction time domain through the following method: Apply a unit excitation to the measurement system at the initial moment. At this time, the response of the measurement system is the unit displacement response or the unit velocity response. After a period of time, the measurement system returns to the initial static state. The prediction time domain can be determined according to the time taken for the measurement system to return to the initial static state. The period of time taken for the measurement system to return to the initial static state is , where

[0012] As a possible implementation, obtain the penalty parameter by applying any one of the Morozov deviation principle, Engl criterion, quasi-optimal criterion, generalized cross-validation criterion, or L-curve criterion.

[0013] As a possible implementation, obtain the penalty parameter through the following steps: Generate a series of penalty parameters uniformly on a logarithmic scale, and calculate the residual norm and solution norm for each penalty parameter; In a double-logarithmic coordinate system, plot a curve with the residual norm as the horizontal axis and the solution norm as the vertical axis; Take the penalty parameter corresponding to the inflection point with the maximum curvature of the curve as the optimal penalty parameter value.

[0014] In a second aspect, the present invention provides a micro-thrust dynamic identification system, including: A dynamic equation determination unit in state-space form, configured to construct the dynamic equation of the thrust measurement system, configure a state vector capable of characterizing the displacement response and velocity response of the thrust measurement system, and rewrite the dynamic equation using the state vector to obtain the state-space form of the dynamic equation; An integration unit, which initializes the state vector at the initial moment and integrates the state-space form of the dynamic equation to obtain the theoretical system response model at any moment; A rewriting unit, which discretizes the time domain into multiple equally spaced moments using a preset time step, and assumes that the thrust received by the thrust measurement system is constant within any integration step, then the theoretical system response model is rewritten into a numerical model in a step-by-step integration recurrence format; An actual system response sequence construction unit, which constructs an actual system response sequence based on the mapping pointers of the displacement, velocity, and acceleration responses of the measured system and the displacement, velocity, and acceleration obtained by the system response sensor; An empirical model construction unit, configured to jointly construct an empirical model based on the dynamic equation of the thrust measurement system and the actual system response sequence, and rewrite the empirical model into a discrete recurrence format; An augmented rewriting unit, which configures a micro-thrust increment expression, and after applying the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recurrence format, further rewrite them into an augmented form; Prediction output unit, based on the thrust measurement system response at the current moment, future control time domain The micro-thrust increments at multiple moments in the prediction time domain are obtained by combining the numerical model in augmented form and the empirical model in discrete recursive format. Prediction output for multiple moments in the future; The cost function solving unit constructs and solves the cost function to minimize the sum of square errors between the predicted output and the expected output in the actual system response sequence, while taking into account the smoothness of the micro-thrust input. At this time, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the expected output.

[0015] Compared with the prior art, the present invention has the following effects: 1. The micro-thrust dynamic identification method provided by the present invention is to achieve a compacting effect on the external force obtained at a certain moment by comprehensively utilizing the measured system response information for a period of time in the future, effectively weaken the influence of the ill-posedness in the inverse problem, and effectively improve the calculation accuracy and the robustness of the algorithm.

[0016] 2. The micro-thrust dynamic identification method provided by the present invention can automatically determine appropriate parameters according to different external force forms, system response measurement noise levels and thrust test bench dynamic characteristics, realizes adaptive determination of all parameters, can smoothly reconstruct results, effectively suppress high-frequency noise interference, while retaining the mutation characteristics of dynamic thrust signals, and avoids the workload and blindness brought about by human experience attempts, which is helpful to realize online real-time dynamic thrust evaluation of micro-thrusters.

[0017] 3. The micro-thrust dynamic identification method provided by the present invention contains a rolling optimization strategy, which can effectively reduce the loss of measurement accuracy caused by model uncertainty and measurement noise, and avoid the performance degradation of traditional methods due to parameter estimation errors or model mismatch.

[0018] 4. The micro-thrust dynamic identification method provided by the present invention is not only applicable to the case where the measured system response is displacement, but also to the case where the measured system response is velocity. Since the vibration velocity of the system more essentially describes the motion process of the system, using it as a reference state quantity has more performance advantages than using displacement or acceleration as a reference state quantity.

[0019] 5. The micro-thrust dynamic identification method provided by the present invention can be applied to working conditions with low sampling frequency and is suitable for scenarios with limited measurement resources.

[0020] 6. The small-thrust dynamic identification method provided by the present invention improves the real-time performance by optimizing matrix decomposition and solving large linear equations, and further balances the smoothness and dynamic tracking accuracy by combining regularization techniques such as the Morozov deviation principle, Engl criterion, quasi-optimal criterion, generalized cross-validation criterion, or L-curve criterion. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The drawings described herein are used to provide a further understanding of the present invention, and constitute a part of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention, and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a diagram of the small-thrust dynamic identification system; Figure 2 is a flowchart of the small-thrust dynamic identification method provided by an embodiment of the present invention; Figure 3 is a detailed process diagram of the small-thrust dynamic identification method provided by an embodiment of the present invention; Figure 4 is a comparison diagram of the identification results of three external force waveforms and the system response using the displacement response as a reference; Figure 5 is a comparison diagram of the identification results of three external force waveforms and the system response using the velocity response as a reference. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] In order to make the technical problems, technical solutions, and beneficial effects to be solved by the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0023] It should be noted that when an element is referred to as being "fixedly disposed on" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element.

[0024] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more, unless otherwise specifically defined.

[0025] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "upper" and "lower" is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0026] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the term "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected, or indirectly connected through an intermediate medium, and can be the communication inside two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meaning of the above terms in the present invention can be understood according to specific circumstances.

[0027] The embodiments of the present invention aim to provide a method and system for dynamically identifying a micro-thrust. The final micro-thrust magnitude is determined through the increment of the thrust, and a dynamic state space equation with the thrust increment and the system response as the state vector is established. Different from the prior art that uses the displacement system response as the input quantity or known condition, the present application uses displacement or velocity as the input quantity of the system response. Since the state vector includes the displacement response and the velocity response, and the velocity response can better reflect the essence of vibration, using the velocity response as the input quantity has more performance advantages. The specific implementation is as follows: In a first aspect, the embodiments of the present invention provide a method for dynamically identifying a micro-thrust, see Figure 1 、 Figure 2 and Figure 3 , the identification method includes the following steps: Construct the dynamic equation of the thrust measurement system, and configure a state vector that can characterize the displacement response and velocity response of the thrust measurement system. Rewrite the dynamic equation using the state vector to obtain the state space form of the dynamic equation; Exemplarily, the dynamic equation of the thrust measurement system has the expression: Among them, are respectively the inertia coefficient, damping coefficient, and stiffness coefficient of the thrust bench; represents the thrust to be measured; represents the force arm; represents the measurement arm, represents the system displacement response obtained by the displacement sensor, is the velocity response of the thrust measurement system; is the acceleration response of the thrust measurement system.

[0028] Configure a state vector capable of characterizing the displacement response and velocity response of the thrust measurement system, and the expression is as follows: Use the state vector to rewrite the dynamic equation into the state-space form, and the expression is as follows: Wherein, .

[0029] Initialize the state vector at the initial moment, and integrate the state-space form of the dynamic equation to obtain the theoretical system response model at any moment; Exemplarily, initialize the state vector at the initial moment, and denote the initial moment as , and denote the initialized state vector as .

[0030] Integrate the state-space form of the dynamic equation, specifically perform the Duhamel integral on the state-space form of the dynamic equation.

[0031] Obtain the theoretical system response model at any moment, and the expression is as follows: Wherein, is the integration variable, represents the thrust to be measured within the integration interval .

[0032] Use the preset time step to discretize the time domain into multiple equally spaced moments, and assume that the thrust received by the thrust measurement system is constant within any integration step, then the theoretical system response model can be rewritten into a numerical model in the form of a step-by-step integration recurrence format; Exemplarily, denote the preset time step as ; discretize the time domain into multiple equally spaced moments, denoted as , ; assume that the thrust received by the thrust measurement system is constant within any integration step, that is , .

[0033] Rewrite the theoretical system response model into a numerical model in the form of a step-by-step integration recurrence format, and the expression is as follows: Wherein, , is the identity matrix 。

[0034] Construct the actual system response sequence based on the mapping pointers of the displacement, velocity, and acceleration responses of the measured system and the displacement, velocity, and acceleration obtained by the system response sensor; Exemplarily, the mapping pointers for the displacement, velocity, and acceleration responses of the system under test are denoted as ; If the actual measured system responses are the state parameter displacements, the mapping pointers are as follows: If the actual measured system responses are the state parameter velocities, the mapping pointers are as follows: Construct the actual system response sequence, denoted as , and the expression is: Construct an empirical model by combining the dynamic equation of the thrust measurement system and the actual system response sequence; Exemplarily, the empirical model, the expression is: Where, ; ; is the stiffness coefficient of the thrust bench; is the damping coefficient of the thrust bench.

[0035] Rewrite the empirical model into a discrete recurrence format; Exemplarily, the empirical model is rewritten into a discrete recurrence format, and the expression is: Configure the micro-thrust increment expression. After applying the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recurrence format, it is further rewritten into an augmented form; Exemplarily, the micro-thrust increment expression is: Apply the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recurrence format, and the expression is: It is further rewritten into an augmented form, and the expression is: Where, .

[0036] Based on the thrust measurement system response at the current moment, the micro-thrust increments at moments within the future control time domain, and combined with the numerical model in augmented form and the empirical model in discrete recurrence format, obtain the future The predicted output at a certain moment; Exemplarily, the predicted output is denoted as , and the expression is: where the current moment is , is the response of the thrust measurement system, is the micro-thrust increment, is the prediction time domain, is the control time domain, , within . .

[0037] Construct and solve the cost function to minimize the sum of the squares of the errors between the predicted output and the expected output in the actual system response sequence, taking into account the smoothness of the micro-thrust input. At this time, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the expected output.

[0038] As a possible implementation, constructing the cost function specifically includes the following sub-steps: From the initial moment to integral steps, sum the product of the transpose of the difference vector between the predicted output and the expected output, the weight matrix, and the difference vector between the predicted output and the expected output to obtain the state cost sum function; Exemplarily, the state cost sum function is expressed as: where is the system expected output, the predicted output, is the weight matrix.

[0039] Among them, the weight matrix is a 2×2 diagonal matrix, and the elements on the main diagonal respectively correspond to the weight components of the expected output and the micro-thrust increment, and the weight component of the expected output is much larger than the weight component of the micro-thrust increment; Exemplarily, the weight matrix is , and the diagonal elements of the weight matrix and respectively correspond to the weight components of the system response and the micro-thrust increment in the augmented vector , is much larger than .

[0040] From the initial moment to integral steps, sum the product of the square of the micro-thrust increment and the penalty parameter to obtain the micro-thrust increment cost sum function; Exemplarily, the micro-thrust increment cost sum function is expressed as: Among them, the penalty parameter is the micro-thrust increment.

[0041] Sum the state cost and function and the micro-thrust increment cost and function to obtain the cost function.

[0042] Exemplarily, the cost function has the expression: As a possible implementation, after constructing the cost function and before solving the cost function, it further includes simplifying the cost function to facilitate programming and solving in computer language. Specifically, it includes the following steps: Decompose the weight matrix into the product of two sub-matrices and rewrite the cost function using the two sub-matrices; Exemplarily, , decompose the weight matrix into the product of two terms, and the expression is: Among them, .

[0043] Rewrite the cost function, and the expression is: Among them, .

[0044] When the state parameter obtained by the system response sensor is displacement or velocity, the mapping pointer of the acceleration response in the actual system response sequence is zero, that is, the vector related to acceleration in the predicted output is a zero vector. Based on this, simplify the predicted output to matrix form, and at the same time simplify the rewritten cost function to matrix form.

[0045] Exemplarily, the predicted output is simplified to matrix form, that is: The rewritten cost function is simplified to matrix form, that is: As a possible implementation, transform solving the cost function into solving a quadratic programming problem under unconstrained conditions, that is, solve the extreme point of the cost function in matrix form to obtain the optimal micro-thrust increment sequence, extract the first item from the optimal micro-thrust increment sequence to obtain the micro-thrust increment at the current moment, and substitute the micro-thrust increment at the current moment into the micro-thrust increment expression to obtain the predicted micro-thrust at the next moment.

[0046] Exemplarily, let , according to matrix derivation, we can get: Among them, ; is the point where J takes the extreme value; = ， is a positive definite matrix, so the extreme value is J the minimum value of.

[0047] As a possible implementation, the predicted output simplified to matrix form is combined with the actually measured system state response to obtain the desired output vector required for the next moment.

[0048] Exemplarily, according to the requirements of rolling optimization and comprehensively considering factors such as the uncertainty and measurement error of the micro-thrust measurement system, only the first item needs to be extracted after calculating the optimal micro-thrust sequence , and combined with the micro-thrust increment expression, the micro-thrust at the th moment can be obtained, that is, ; according to the augmented form of the micro-thrust increment, the system state response at the th moment can be obtained, and the expression is: Combining the predicted output simplified to matrix form and the actually measured system state response can obtain the desired output vector required for the next moment .

[0049] As a possible implementation, based on the effectiveness of energy propagation, within the prediction time domain is determined, and within the control time domain is maximized, that is = .

[0050] As a possible implementation, the within the prediction time domain is determined by the following method: Apply a unit excitation to the measurement system at the initial moment. At this time, the response of the measurement system is the unit displacement response or the unit velocity response. After a period of time, the measurement system returns to the initial static state. According to the time taken for the measurement system to return to the initial static state, the prediction time domain can be determined; the period of time for the measurement system to return to the initial static state is , is the preset time step.

[0051] Exemplarily, when the micro-thrust , the numerical model of the step-by-step integration recurrence format can be simplified to , where the exponential matrix is the state transition matrix, The elements in j satisfy the following conditions. If the η -th state variable is given a unit value at the initial time, while the values of other state variables are 0, then after a time step i the value of the -th state variable is the element in the i -th row and j -th column of the matrix . Therefore, the element in the -th column of the exponential matrix j represents the response of all state variables after a time step j when only the η -th state variable is given a unit value at the initial time and the values of other state variables are 0.

[0052] Exemplarily, at the initial time, only a unit displacement response is applied to the thrust stand, i.e., , after a time step , the displacement response and velocity response of the thrust stand are and , respectively.

[0053] Exemplarily, at the initial time, only a unit velocity response is applied to the thrust stand, i.e., , after a time step , the displacement response and velocity response of the thrust stand are and , respectively.

[0054] The system response after a period of time is: When the measured reference quantity is the system displacement response, by determining the that makes hold as the prediction time domain size; when the measured reference quantity is the system velocity response, by determining the that makes hold as the prediction time domain size.

[0055] The specific implementation statement is as follows: where is the index of the non-zero elements in the obtained vector .

[0056] As a possible implementation, a penalty parameter is obtained by applying any one of the Morozov deviation principle, Engl criterion, quasi-optimal criterion, generalized cross-validation criterion, or L-curve criterion.

[0057] As a possible implementation, the penalty parameter is obtained through the following steps: Generate a series of penalty parameters uniformly on a logarithmic scale, and calculate the residual norm and solution norm for each penalty parameter; Exemplarily, each penalty parameter The residual norm is calculated as , and the solution norm is .

[0058] In a double-logarithmic coordinate system, plot a curve with the residual norm as the horizontal axis and the solution norm as the vertical axis; Exemplarily, logarithmic coordinates are applied to expand the difference and more significantly reflect the slope change, so as to ensure the high-precision determination of the maximum curvature at the inflection point. In the double-logarithmic coordinate system, with as the horizontal axis and as the vertical axis, plot a curve.

[0059] The penalty parameter corresponding to the inflection point with the maximum curvature of the curve is used as the optimal penalty parameter value.

[0060] To improve the calculation efficiency, the matrix decomposition can be preformed using the generalized singular value decomposition method (cgsvd) to avoid repeatedly solving large linear equations.

[0061] Next, a simulation is carried out through typical dynamic micro-thrust identification to evaluate the feasibility, effectiveness, and high precision of the identification method proposed in this embodiment.

[0062] The inertial parameters, stiffness coefficients, and damping coefficients of the micro-thrust measurement system are respectively set as , the measurement arm and the force arm are equal, both being . The displacement response and velocity response are respectively used as the measured reference quantities, the measurement noise is set as zero-mean Gaussian white noise with a variance of 0.005, the sampling frequency is set as 100 Hz, and the entire simulation duration is 25 s. The reference thrust (unit: μN) is respectively set as a sine wave, a triangular wave, and a trapezoidal wave, and their ideal waveforms are respectively represented by the following piecewise functions: The piecewise function of the sine wave is: The piecewise function of the triangular wave is: The piecewise function of the trapezoidal wave is: The root mean square error (RMSE) and correlation coefficient (CC) are used as metrics to quantitatively evaluate the recognition performance. Among them, is the number of sample points; is the recognition result; is the reference thrust; are respectively and the average values of.

[0063] The comparison results of the recognition performance of different waveform external forces using the above recognition method are shown in Table 1.

[0064] Table 1 Quantitative comparison table of the performance of the recognition method When the displacement response is used as the reference response, the system responses and recognition results corresponding to the three types of waveform external forces predicted by the above recognition method are as Figure 4 shown.

[0065] When the velocity response is used as the reference response, the system responses and recognition results corresponding to the three types of waveform external forces predicted by the above recognition method are as Figure 5 shown.

[0066] According to Table 1, Figure 4 and Figure 5 the results show that the recognition method of the present invention is feasible and effective, and has a high recognition accuracy. Especially when the velocity response is used as the reference input, the root mean square errors corresponding to the three recognized waveforms are all smaller than those when the displacement response is used as the reference input, and its correlation coefficient is closer to 1, that is, the recognition result has a higher consistency with the reference solution. Therefore, choosing the velocity response as the reference input has more advantages in recognition performance.

[0067] On the second aspect, the present invention provides a micro-thrust dynamic recognition system, which specifically includes: A dynamic equation determination unit in state space form, which is used to construct the dynamic equation of the thrust measurement system, configure a state vector that can characterize the displacement response and velocity response of the thrust measurement system, and rewrite the dynamic equation using the state vector to obtain the state space form of the dynamic equation; An integration unit, which initializes the state vector at the initial moment and integrates the state space form of the dynamic equation to obtain the theoretical system response model at any moment; The rewriting unit discretizes the time domain into multiple equally spaced moments using a preset time step, and assuming that the thrust received by the thrust measurement system is constant within any integration step, the theoretical system response model is rewritten into a numerical model in a step-by-step integration recurrence format; The actual system response sequence construction unit constructs an actual system response sequence based on the mapping pointers of the displacement, velocity, and acceleration responses of the system under test and the displacement, velocity, and acceleration obtained by the system response sensors; The empirical model construction unit is used to jointly construct an empirical model from the dynamic equation of the thrust measurement system and the actual system response sequence, and rewrite the empirical model into a discrete recurrence format; The augmented rewriting unit configures a micro-thrust increment expression, and after applying the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recurrence format, further rewrite them into an augmented form; The prediction output unit is based on the thrust measurement system response at the current moment, the micro-thrust increments at multiple moments within the future control time domain Combined with the numerical model in augmented form and the empirical model in discrete recurrence format, to obtain the predicted outputs at multiple future moments within the prediction time domain ; The cost function solving unit constructs and solves a cost function to minimize the sum of the squared errors between the predicted output and the desired output in the actual system response sequence, taking into account the smoothness of the micro-thrust input. At this time, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the desired output.

[0068] Although the present invention has been described in connection with various embodiments, however, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the drawings, the disclosure content, and the description of the drawings, etc. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude the case of multiple. A single processor or other unit can implement several functions listed in the specification. Certain measures are recited in mutually different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0069] Although the present invention has been described in combination with specific features and their embodiments, it is obvious that various modifications and combinations can be made without departing from the spirit and scope of the present invention. Accordingly, the present specification and the drawings are merely exemplary descriptions of the present invention, and are considered to have covered any and all modifications, variations, combinations, or equivalents within the scope of the present invention. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. A method for dynamically identifying a tiny thrust, characterized in that, It includes the following steps: Construct the dynamic equation of the thrust measurement system, configure a state vector that can characterize the displacement response and velocity response of the thrust measurement system, and rewrite the dynamic equation using the state vector to obtain the state-space form of the dynamic equation; Initialize the state vector at the initial moment, and integrate the state-space form of the dynamic equation to obtain the theoretical system response model at any moment; Discretize the time domain into multiple equally spaced moments using a preset time step, and assume that the thrust received by the thrust measurement system is constant within any integration step. Then, the theoretical system response model is rewritten as a numerical model in a step-by-step integration recurrence format; Construct an actual system response sequence based on the mapping pointers of the displacement, velocity, and acceleration responses of the measured system and the displacement, velocity, and acceleration obtained by the system response sensor; Construct an empirical model by combining the dynamic equation of the thrust measurement system and the actual system response sequence; Rewrite the empirical model into a discrete recurrence format; Configure a micro-thrust increment expression, and after applying the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recurrence format, further rewrite them into an augmented form; Based on the thrust measurement system response at the current moment and the micro-thrust increments at moments within the future control time domain, and combining the augmented numerical model and the empirical model in discrete recurrence form, the predicted outputs at future moments within the prediction time domain are obtained; Construct and solve a cost function to minimize the sum of the squared errors between the predicted output and the desired output in the actual system response sequence, taking into account the smoothness of the micro-thrust input. At this time, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the desired output.

2. The micro-thrust dynamic recognition method according to claim 1, characterized in that Constructing the cost function specifically includes the following sub-steps: From the initial moment to Within the first integration steps, sum the product of the transpose of the difference between the predicted output and the desired output vector, the weight matrix, and the difference between the predicted output and the desired output vector to obtain the state cost sum function; where the weight matrix is a 2×2 diagonal matrix, and the elements on the main diagonal correspond to the weight components of the desired output and the micro-thrust increment respectively, and the weight component of the desired output is much larger than the weight component of the micro-thrust increment; From the initial moment to within integration steps, sum the product of the square of the micro-thrust increment and the penalty parameter to obtain the micro-thrust increment cost sum function; Sum the state cost sum function and the micro-thrust increment cost sum function to obtain the cost function.

3. The dynamic recognition method for tiny thrust according to claim 2, characterized in that Before solving the cost function after constructing the cost function, it also includes simplifying the cost function, which specifically includes the following steps: Decompose the weight matrix into the product of two sub-matrices and rewrite the cost function using the two sub-matrices; When the state parameter obtained by the system response sensor is displacement or velocity, the mapping pointer of the acceleration response in the actual system response sequence is zero, that is, the vector related to acceleration in the predicted output is a zero vector. Based on this, simplify the predicted output into a matrix form, and at the same time simplify the rewritten cost function into a matrix form.

4. The dynamic identification method for tiny thrust according to claim 3, characterized in that Transform the solution of the cost function into solving a quadratic programming problem under unconstrained conditions, that is, solve the extreme point of the cost function in matrix form to obtain the optimal micro-thrust increment sequence. Extract the first term from the optimal micro-thrust increment sequence to obtain the micro-thrust increment at the current moment, and substitute the micro-thrust increment at the current moment into the micro-thrust increment expression to obtain the predicted micro-thrust at the next moment.

5. The dynamic recognition method for tiny thrust according to claim 4, characterized in that, Substitute the micro-thrust increment at the current moment into the augmented-form numerical model to obtain the system state response corresponding to the predicted output at the next moment; Combine the predicted output simplified into matrix form and the actually measured system state response to obtain the desired output vector required at the next moment.

6. The dynamic identification method for tiny thrust according to claim 2, wherein Determine the within the prediction time domain based on the effectiveness of energy propagation, and maximize the within the control time domain, that is, = .

7. The dynamic identification method for tiny thrust according to claim 6, characterized in that Determine within the prediction time domain by the following method : Apply a unit excitation to the measurement system at the initial moment. At this time, the response of the measurement system is the unit displacement response or the unit velocity response. After a period of time, the measurement system returns to the initial stationary state. The prediction time domain can be determined according to the time taken for the measurement system to return to the initial stationary state The period of time taken for the measurement system to return to the initial stationary state is , is the preset time step 8. The dynamic recognition method of tiny thrust according to claim 6, characterized in that Apply any one of the Morozov deviation principle, Engl criterion, quasi-optimal criterion, generalized cross-validation criterion, or L-curve criterion to obtain a penalty parameter.

9. The dynamic identification method for micro thrust according to claim 8, characterized in that, Obtain the penalty parameter through the following steps: Uniformly generate a series of penalty parameters on a logarithmic scale, and calculate the residual norm and solution norm for each penalty parameter; In a double-logarithmic coordinate system, plot a curve with the residual norm as the horizontal axis and the solution norm as the vertical axis; The penalty parameter corresponding to the inflection point with the maximum curvature of the curve is used as the optimal penalty parameter value.

10. A micro-thrust dynamic recognition system, characterized in that, It includes: A dynamic equation determination unit in state space form, which is used to construct the dynamic equation of the thrust measurement system, configure a state vector that can characterize the displacement response and velocity response of the thrust measurement system, and rewrite the dynamic equation using the state vector to obtain the state space form of the dynamic equation; An integration unit that initializes the state vector at the initial moment and integrates the state space form of the dynamic equation to obtain the theoretical system response model at any moment; A rewriting unit that discretizes the time domain into multiple equally spaced moments using a preset time step, and assuming that the thrust received by the thrust measurement system is constant within any integration step, the theoretical system response model is rewritten into a numerical model in a step-by-step integration recurrence format; An actual system response sequence construction unit that constructs an actual system response sequence based on the mapping pointers of the displacement, velocity, and acceleration responses of the measured system and the displacement, velocity, and acceleration obtained by the system response sensor; An empirical model construction unit that is used to jointly construct an empirical model based on the dynamic equation of the thrust measurement system and the actual system response sequence, and rewrite the empirical model into a discrete recurrence format; An augmented rewriting unit that configures a micro-thrust increment expression, and after applying the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recurrence format, further rewrite them into an augmented form; A prediction output unit, based on the response of the thrust measurement system at the current moment, the micro-thrust increments at multiple moments within the future control time domain, and combining the numerical model in augmented form and the empirical model in discrete recurrence format, obtains the prediction outputs at multiple future moments within the prediction time domain; Within the future control time domain, the micro-thrust increments at multiple moments, and combining the numerical model in augmented form and the empirical model in discrete recurrence format, obtain the prediction outputs at multiple future moments within the prediction time domain; Within the prediction time domain, the prediction outputs at multiple future moments; A cost function solving unit that constructs and solves a cost function to minimize the sum of the squared errors between the predicted output and the desired output in the actual system response sequence, taking into account the smoothness of the micro-thrust input. At this time, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the desired output.

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