A method and system for dynamic identification of small thrust

Abstract

The present invention relates to the technical field of micro-thrust measurement of aerospace micro-thrusters, and discloses a micro-thrust dynamic identification method and system. The identification method comprises: constructing a dynamic equation of a thrust measurement system, rewriting it into a state space form and integrating it to obtain a theoretical system response model at any time; rewriting the theoretical system response model into a numerical model in a step-by-step integral recursive format; constructing an actual system response sequence and combining it with the dynamic equation of the thrust measurement system to construct an empirical model, and rewriting the empirical model; configuring a micro-thrust increment expression, applying the expression to rewrite the numerical model and the empirical model, and further rewriting them into an augmented form; predicting the predicted output at future moments in the time domain; constructing and solving a cost function to minimize the sum of squares of the error 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, so that the predicted micro-thrust corresponding to the predicted output is equal to the 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 in particular to a micro-thrust dynamic identification method and system. Background Art

[0002] Modern space missions such as deep space exploration, gravitational wave detection, and micro-nano satellite networking place extremely high demands on spacecraft orbital control accuracy and attitude stability, requiring thrusters to have dynamic thrust adjustment capabilities at the micronewton level or even sub-micronewton level. Although electric propulsion systems have higher specific impulse than chemical thrusters, which can significantly reduce fuel consumption and increase payload ratio, their thrust is relatively low and the thrust rise time is relatively short, making it extremely difficult to capture their dynamic response characteristics (such as the rising edge of the thrust pulse). Therefore, existing traditional static calibration methods focus on measuring steady-state thrust, average thrust, and single-pulse impulse. However, in actual missions, thrusters need to be frequently started and stopped, and thrust adjusted (such as in pulse mode or continuously variable thrust). Traditional static calibration methods cannot meet the testing requirements of dynamic response characteristics. By acquiring data such as thruster frequency response and transient characteristics through dynamic measurement and correcting multi-physics coupling models (such as the interaction between fluid mechanics and electromagnetic fields), design reliability can be improved. Dynamic thrust signal analysis (such as ripple characteristics) can reveal thruster performance defects (such as hysteresis, drift, and response delay) in advance, avoiding satellite attitude loss or orbit deviation due to thrust errors and extending the thruster's on-orbit life. Accurate dynamic thrust measurement can optimize propellant usage strategies and reduce the fuel budget for deep space exploration missions. Ground-based dynamic micro-thrust measurement is the core link between thruster design and on-orbit application. Its research is not only related to the success or failure of space missions, but also a key driving force for advanced propulsion technology, precision measurement science, and interdisciplinary engineering innovation.

[0003] Currently, commonly used methods for dynamic thrust measurement of microthrusters can be roughly divided into open-loop dynamic measurement and closed-loop dynamic measurement. Open-loop dynamic measurement is primarily based on the theory of inverse dynamics, obtaining dynamic thrust by comprehensively utilizing the system response of the thrust test bench and inverting its system parameters. Examples include a least-squares-based microthrust dynamic measurement method disclosed in patent CN107562691B and a digital filter-based method for measuring thrust response time of satellite-borne microthrusters disclosed in patent CN114218750B. Closed-loop dynamic measurement, on the other hand, is based on the concept of closed-loop control. A known standard force is used to form a two-force balance with the force to be measured, maintaining the thrust test bench at zero position. This allows the applied standard force to reflect the force to be measured in real time. Examples include a closed-loop control-based micro-Newton-level microthrust dynamic test bench and test method disclosed in patent CN110413015B, and a fast-response closed-loop microthrust measurement method and equipment based on dynamic thrust inversion disclosed in patent CN119312534A. Summary of the Invention

[0004] The present invention aims to provide a method and system for dynamic identification of micro-thrust forces. By comprehensively utilizing system response information over a period of time in the future, this method imposes tight constraints on the calculation of external forces at a specific moment, effectively reducing the impact of ill-posed inverse problems. Furthermore, the method establishes an optimal cost function and a method for adaptively determining key parameters to achieve online identification of dynamic micro-thrust forces. The present invention is highly versatile and applicable to any thrust test bench that can be approximated as a second-order "mass-spring-damper" vibration system. Without adding additional equipment, it provides an effective approach for determining the micro-dynamic thrust of a micro-thruster.

[0005] In a first aspect, the present invention provides a method for dynamically identifying a small thrust, the method comprising the following steps:

[0006] Construct the dynamic equations of the thrust measurement system and configure state vectors that can characterize the displacement response and velocity response of the thrust measurement system. Use the state vectors to rewrite the dynamic equations to obtain the state space form of the dynamic equations.

[0007] 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;

[0008] The time domain is discretized into multiple equally spaced moments using a preset time step, and assuming that the thrust applied to the thrust measurement system is constant within any integration step, the theoretical system response model is rewritten as a numerical model in a step-by-step integration recursive format.

[0009] 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;

[0010] An empirical model is constructed by combining the dynamic equations of the thrust measurement system and the actual system response sequence;

[0011] Rewrite the empirical model into a discrete recursive format;

[0012] Configure the micro-thrust increment expression, apply it to rewrite the numerical model and the empirical model in discrete recursive format, and then further rewrite it into an augmented form;

[0013] Based on the thrust measurement system response at the current moment and the future control time domain The micro-thrust increment at each moment is obtained by combining the numerical model in augmented form and the empirical model in discrete recursive format to obtain the future The predicted output at each moment;

[0014] A cost function is constructed and solved to minimize the sum of squared 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 point, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the expected output.

[0015] As a possible implementation method, constructing the cost function specifically includes the following sub-steps:

[0016] At the initial moment to In the integration step, the transpose of the vector difference between the predicted output and the expected output, the weight matrix, and the product of the vector difference between the predicted output and the expected output are summed to obtain the state cost and function; among them, the weight matrix is ​​a 2×2 diagonal matrix, and the elements on the main diagonal 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;

[0017] At the initial moment to In the integration steps, the product of the square of the micro-thrust increment and the penalty parameter is summed to obtain the micro-thrust increment cost and function;

[0018] The cost function is obtained by summing the state cost sum function and the microthrust increment cost sum function.

[0019] As a possible implementation method, after constructing the cost function and before solving the cost function, the cost function is simplified, which specifically includes the following steps:

[0020] Decompose the weight matrix into the product of two sub-matrices and rewrite the cost function using the two sub-matrices;

[0021] 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 acceleration-related vector in the predicted output is a zero vector. Based on this, the predicted output is simplified into a matrix form, and the rewritten cost function is also simplified into a matrix form.

[0022] As a possible implementation method, the cost function is transformed into a quadratic programming problem under unconstrained conditions, that is, the extreme points of the cost function in matrix form are solved to obtain the optimal micro-thrust increment sequence. The first item in the optimal micro-thrust increment sequence is extracted to obtain the micro-thrust increment at the current moment. The micro-thrust increment at the current moment is substituted into the micro-thrust increment expression to obtain the predicted micro-thrust at the next moment.

[0023] As a possible implementation method, the micro-thrust increment at the current moment is substituted into the augmented form numerical model to obtain the system state response corresponding to the predicted output at the next moment;

[0024] The predicted output simplified into matrix form and the actual measured system state response are combined to obtain the expected output vector required at the next moment.

[0025] As a possible implementation method, the effectiveness of energy propagation is used to determine the prediction time domain. , which will control the time domain Maximize, that is = .

[0026] As a possible implementation method, the following method is used to determine the prediction time domain :At the initial moment, a unit excitation is applied to the measurement system. At this time, the response of the measurement system is a unit displacement response or a unit velocity response. After a period of time, the measurement system returns to the initial static state. The prediction time domain can be determined based on the time taken for the measurement system to return to the initial static state. The size of the measurement system to return to the initial static state is , is the preset time step.

[0027] As a possible implementation method, any one of the Morozov deviation principle, Engl criterion, quasi-optimal criterion, generalized cross validation criterion or L-curve criterion is applied to obtain the penalty parameter.

[0028] As a possible implementation method, the penalty parameter is obtained by the following steps:

[0029] Generate a series of penalty parameters uniformly on the logarithmic scale, and calculate the residual norm and solution norm for each penalty parameter;

[0030] In the double logarithmic coordinate system, the curve is drawn with the residual norm as the horizontal axis and the solution norm as the vertical axis;

[0031] The penalty parameter corresponding to the inflection point where the curvature of the curve is the largest is taken as the optimal penalty parameter value.

[0032] In a second aspect, the present invention provides a micro-thrust dynamic identification system, comprising:

[0033] A unit for determining a dynamic equation in a state-space form is used 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;

[0034] The integration unit 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 time;

[0035] Rewrite the unit, discretize the time domain into multiple equally spaced moments using a preset time step, and assume that the thrust applied to the thrust measurement system is constant within any integration step. Then, rewrite the theoretical system response model into a numerical model in a step-by-step integration recursive format;

[0036] An actual system response sequence construction unit, which constructs an actual system response sequence based on mapping pointers of displacement, velocity, and acceleration responses of the measured system and displacement, velocity, and acceleration obtained by the system response sensor;

[0037] An empirical model building unit is used to build an empirical model by combining the dynamic equations of the thrust measurement system and the actual system response sequence, and rewrite the empirical model into a discrete recursive format;

[0038] The augmented rewriting unit configures the micro-thrust increment expression, applies the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recursive format, and then further rewrites them into augmented form;

[0039] Prediction output unit, based on the thrust measurement system response at the current moment and the 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;

[0040] The cost function solving unit constructs and solves the cost function to minimize the sum of squared 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.

[0041] Compared with the prior art, the present invention has the following effects:

[0042] 1. The micro-thrust dynamic identification method provided by the present invention comprehensively utilizes the measured system response information over a period of time in the future, thereby achieving a compacting effect on the external force obtained at a certain moment, effectively weakening the influence of ill-posedness in the inverse problem, and effectively improving the calculation accuracy and robustness of the algorithm.

[0043] 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, realizing adaptive determination of all parameters, smoothly reconstructing results, effectively suppressing high-frequency noise interference, while retaining the mutation characteristics of dynamic thrust signals, and avoiding the workload and blindness brought about by human experience attempts, which is conducive to the realization of online real-time dynamic thrust evaluation of micro-thrusters.

[0044] 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 caused by parameter estimation errors or model mismatch.

[0045] 4. The micro-thrust dynamic identification method provided by the present invention is applicable not only to cases where the measured system response is displacement, but also to cases where the measured system response is velocity. Since the vibration velocity of the system more essentially describes the system motion process, using it as a reference state quantity has greater performance advantages than using displacement or acceleration as a reference state quantity.

[0046] 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.

[0047] 6. The micro-thrust dynamic identification method provided by the present invention improves real-time performance by optimizing matrix decomposition and solving large linear equations, and further balances smoothness and dynamic tracking accuracy by combining regularization techniques such as the Morozov deviation principle, the Engl criterion, the quasi-optimal criterion, the generalized cross-validation criterion, or the L-curve criterion. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary 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:

[0049] Figure 1 It is a diagram of the system for dynamic identification of small thrust;

[0050] Figure 2 A flow chart of a method for dynamic identification of small thrust provided by an embodiment of the present invention;

[0051] Figure 3 A detailed process diagram of a method for dynamic identification of small thrust provided by an embodiment of the present invention;

[0052] Figure 4 To use displacement response as a reference, a comparison chart of three external force waveform identification results and system responses is shown;

[0053] Figure 5 To use the velocity response as a reference, a comparison chart of the three external force waveform identification results and system responses is shown. DETAILED DESCRIPTION

[0054] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0055] It should be noted that when an element is referred to as being “fixed on” or “disposed on” another element, it may 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 may be directly connected to the other element or indirectly connected to the other element.

[0056] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature identified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0057] In the description of the present invention, it should be understood that the terms "upper" and "lower" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are 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 understood as a limitation on the present invention.

[0058] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the term "connection" should be understood in a broad sense. For example, it can mean a fixed connection, a detachable connection, or an integral connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean internal communication between two elements or an interaction between two elements. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0059] The embodiment of the present invention aims to provide a method and system for dynamic identification of micro-thrust, which determines the final micro-thrust size through the thrust increment and establishes a dynamic state space equation with the thrust increment and system response as the state vector. Unlike the prior art, which uses the displacement system response as the input or known condition, the present application uses displacement or velocity as the input of the system response. Because the state vector contains the displacement response and velocity response, the velocity response can better reflect the essence of vibration, so the velocity response has more performance advantages as the input. The specific implementation method is as follows:

[0060] In the first aspect, the embodiment of the present invention provides a method for dynamic identification of small thrust, see Figure 1 、 Figure 2 and Figure 3 , the identification method comprises the following steps:

[0061] Construct the dynamic equations of the thrust measurement system and configure state vectors that can characterize the displacement response and velocity response of the thrust measurement system. Use the state vectors to rewrite the dynamic equations to obtain the state space form of the dynamic equations.

[0062] For example, the dynamic equation of the thrust measurement system is expressed as:

[0063]

[0064] in, They are the inertia coefficient, damping coefficient and stiffness coefficient of the thrust bench; Indicates the thrust to be measured; Indicates the lever arm; Indicates the measuring arm, Indicates that the displacement sensor obtains the system displacement response, The system speed response for thrust measurement; The acceleration response of the thrust measurement system.

[0065] The state vector that can characterize the displacement response and velocity response of the thrust measurement system is configured. The expression is:

[0066]

[0067] The dynamic equation is rewritten into state space form using the state vector, and the expression is:

[0068]

[0069] in, .

[0070] 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;

[0071] For example, the state vector at the initial time is initialized, and the initial time is recorded as , the initialization state vector is recorded as .

[0072] The state-space form of the dynamic equation is integrated, specifically, the state-space form of the dynamic equation is integrated by Duhamel integration.

[0073] The theoretical system response model at any time is obtained, and the expression is:

[0074]

[0075] in, is the integration variable, Indicates the integral interval The thrust to be measured.

[0076] The time domain is discretized into multiple equally spaced moments using a preset time step, and assuming that the thrust applied to the thrust measurement system is constant within any integration step, the theoretical system response model can be rewritten as a numerical model in a step-by-step integration recursive format.

[0077] For example, the preset time step is recorded as ; Discretize the time domain into multiple equally spaced moments, recorded as , ; Assume that the thrust on the thrust measurement system is constant in any integration step, that is , .

[0078] The theoretical system response model is rewritten as a numerical model in a step-by-step integration recursive format, expressed as follows:

[0079]

[0080] in, , is the identity matrix 。

[0081] 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;

[0082] For example, the mapping pointers of the displacement, velocity, and acceleration responses of the measured system are respectively recorded as ;

[0083] If the actual measured system responses are state parameter displacements, the mapping pointers are as follows:

[0084]

[0085] If the actual measured system responses are state parameter velocities, the mapping pointers are as follows:

[0086]

[0087] Construct the actual system response sequence, denoted as , the expression is:

[0088]

[0089] An empirical model is constructed by combining the dynamic equations of the thrust measurement system and the actual system response sequence;

[0090] For example, the empirical model is expressed as:

[0091]

[0092] in, ; ; is the stiffness coefficient of the thrust bench; is the damping coefficient of the thrust bench.

[0093] Rewrite the empirical model into a discrete recursive format;

[0094] For example, the empirical model is rewritten in discrete recursive format as follows:

[0095]

[0096] Configure the micro-thrust increment expression, apply it to rewrite the numerical model and the empirical model in discrete recursive format, and then further rewrite it into an augmented form;

[0097] For example, the micro-thrust increment expression is:

[0098]

[0099] The numerical model and the empirical model in discrete recursive format are rewritten using the micro-thrust increment expression, and the expression is:

[0100]

[0101]

[0102] Further rewritten into augmented form, the expression is:

[0103]

[0104]

[0105] in, .

[0106] Based on the thrust measurement system response at the current moment and the future control time domain The micro-thrust increment at each moment is obtained by combining the numerical model in augmented form and the empirical model in discrete recursive format to obtain the future The predicted output at each moment;

[0107] For example, the predicted output is recorded as , the expression is:

[0108]

[0109] The current time is , is the thrust measurement system response, is a micro thrust increment, is the prediction time domain, is the control time domain, ,exist Inside, .

[0110] A cost function is constructed and solved to minimize the sum of squared 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 point, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the expected output.

[0111] As a possible implementation method, constructing the cost function specifically includes the following sub-steps:

[0112] At the initial moment to In the integration step, the transpose of the difference between the predicted output and the expected output vector, the weight matrix, and the product of the difference between the predicted output and the expected output vector are summed to obtain the state cost and function;

[0113] For example, the state cost and function are expressed as:

[0114] in, is the expected output of the system, Prediction output, is the weight matrix.

[0115] The weight matrix is ​​a 2×2 diagonal matrix. The elements on the main diagonal correspond to the weight components of the desired output and the micro-thrust increment, and the weight component of the desired output is much larger than the weight component of the micro-thrust increment.

[0116] For example, the weight matrix is , the weight matrix The diagonal elements of and Corresponding to the augmented vectors The weight components of the system response and micro-thrust increment, Much greater than .

[0117] At the initial moment to In the integration steps, the product of the square of the micro-thrust increment and the penalty parameter is summed to obtain the micro-thrust increment cost and function;

[0118] For example, the micro-thrust increment cost and function are expressed as:

[0119] in, Penalty parameter, For micro thrust increments.

[0120] The cost function is obtained by summing the state cost sum function and the microthrust increment cost sum function.

[0121] For example, the cost function is expressed as:

[0122]

[0123] As a possible implementation method, after constructing the cost function and before solving the cost function, it is also necessary to simplify the cost function to facilitate programming and solving it in a computer language. The specific steps include the following:

[0124] Decompose the weight matrix into the product of two sub-matrices and rewrite the cost function using the two sub-matrices;

[0125] For example, , decompose the weight matrix into the product of two terms, the expression is:

[0126]

[0127] in, .

[0128] Rewrite the cost function, the expression is:

[0129]

[0130] in, .

[0131] 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 acceleration-related vector in the predicted output is a zero vector. Based on this, the predicted output is simplified into a matrix form, and the rewritten cost function is also simplified into a matrix form.

[0132] For example, the prediction output is simplified into a matrix form, namely:

[0133]

[0134]

[0135] The rewritten cost function is simplified to matrix form, namely:

[0136]

[0137] As a possible implementation method, the cost function is transformed into a quadratic programming problem under unconstrained conditions, that is, the extreme points of the cost function in matrix form are solved to obtain the optimal micro-thrust increment sequence. The first item in the optimal micro-thrust increment sequence is extracted to obtain the micro-thrust increment at the current moment. The micro-thrust increment at the current moment is substituted into the micro-thrust increment expression to obtain the predicted micro-thrust at the next moment.

[0138] For example, let , according to the matrix derivation, we can get:

[0139]

[0140] in, ; This is the order J Take the extreme value point; = ， is a positive definite matrix, so the extreme value is J The minimum value of .

[0141] As a possible implementation method, the predicted output simplified into a matrix form and the actually measured system state response are combined to obtain the expected output vector required at the next moment.

[0142] For example, according to the requirements of rolling optimization and taking into account the uncertainty of the micro-thrust measurement system, measurement error and other factors, it is only necessary to calculate the optimal micro-thrust sequence Then extract its first item , and combined with the micro-thrust increment expression, we can get The tiny push of the moment, ; According to the augmented form of micro-thrust increment, we can obtain System status response at any moment , the expression is:

[0143]

[0144] Combining the predicted output simplified into matrix form and the actual measured system state response can obtain the expected output vector required at the next moment .

[0145] As a possible implementation method, the effectiveness of energy propagation is used to determine the prediction time domain. , which will control the time domain Maximize, that is = .

[0146] As a possible implementation method, the following method is used to determine the prediction time domain :At the initial moment, a unit excitation is applied to the measurement system. At this time, the response of the measurement system is a unit displacement response or a unit velocity response. After a period of time, the measurement system returns to the initial static state. The prediction time domain can be determined based on the time taken for the measurement system to return to the initial static state. The size of the measurement system to return to the initial static state is , is the preset time step.

[0147] For example, when the micro thrust When , the numerical model of the step-by-step integration recursive format can be simplified to , where the exponential matrix is the state transition matrix, The elements in the equation satisfy the following conditions: if the initial moment is given j state variable unit value, and the other state variables are 0, then after a time step η Afterwards, i The values ​​of the state variables are matrices Middle i Row, No. j Elements of a column Therefore, the exponential matrix Middle j The column elements indicate that the initial moment is only given to the j When the state variables have a unit value and the other state variables have a value of 0, after one time step η After that, all state variables are affected.

[0148] For example, at the initial moment, only a unit displacement response is applied to the thrust rig, i.e. , after a time step , the displacement response and velocity response of the thrust bench are and .

[0149] For example, at the initial moment, only a unit velocity response is applied to the thrust rig, i.e. , after a time step , the displacement response and velocity response of the thrust bench are and .

[0150] a period of time The system response after that is:

[0151]

[0152] When the measured reference quantity is the system displacement response, Established As the predicted time domain size; when the measured reference quantity is the system speed response, by determining Established As the predicted time domain size.

[0153] The specific implementation statements are as follows:

[0154]

[0155] in, Is to obtain the vector The indices of the nonzero elements in .

[0156] As a possible implementation method, any one of the Morozov deviation principle, Engl criterion, quasi-optimal criterion, generalized cross validation criterion or L-curve criterion is applied to obtain the penalty parameter.

[0157] As a possible implementation method, the penalty parameter is obtained by the following steps:

[0158] Generate a series of penalty parameters uniformly on the logarithmic scale, and calculate the residual norm and solution norm for each penalty parameter;

[0159] For example, each penalty parameter The residual norm is calculated as , the solution norm is .

[0160] In the double logarithmic coordinate system, the curve is drawn with the residual norm as the horizontal axis and the solution norm as the vertical axis;

[0161] For example, logarithmic coordinates are used to expand the differences and more significantly reflect the slope changes, so as to ensure high-precision determination of the maximum curvature at the inflection point. As the horizontal axis, Draw a curve for the vertical axis.

[0162] The penalty parameter corresponding to the inflection point where the curvature of the curve is the largest is taken as the optimal penalty parameter value.

[0163] In order to improve computational efficiency, the generalized singular value decomposition (CGSVD) method can be used to perform matrix decomposition in advance to avoid repeatedly solving large linear equations.

[0164] Next, a typical dynamic micro-thrust recognition simulation is performed to evaluate the feasibility, effectiveness, and high accuracy of the recognition method proposed in this embodiment.

[0165] The inertia parameters, stiffness coefficient and damping coefficient of the micro-thrust measurement system are set as , the measuring arm and the force arm are equal, both The displacement response and velocity response were used as measured reference quantities. The measurement noise was set to zero-mean Gaussian white noise with a variance of 0.005, the sampling frequency was set to 100 Hz, and the entire simulation duration was 25 seconds. The reference thrust (unit: μN) was set to a sine wave, a triangular wave, and a trapezoidal wave, respectively. Their ideal waveforms were represented by the following piecewise functions:

[0166] The sine wave piecewise function is:

[0167]

[0168] The triangle wave piecewise function is:

[0169]

[0170] The trapezoidal wave piecewise function is:

[0171]

[0172] The root mean square error (RMSE) and correlation coefficient (CC) are used as metrics to quantitatively evaluate the recognition performance.

[0173]

[0174]

[0175] in, is the number of sample points; is the recognition result; is the reference thrust; They are and The average value of .

[0176] The comparison results of the recognition performance of different waveform external forces using the above recognition methods are shown in Table 1.

[0177] Table 1 Quantitative comparison of recognition method performance

[0178]

[0179] When the displacement response is used as the reference response, the system responses and identification results corresponding to the three types of waveform external forces predicted by the above identification method are as follows: Figure 4 shown.

[0180] When the velocity response is used as the reference response, the three types of waveform external forces predicted by the above identification method correspond to the system response and identification results, such as Figure 5 shown.

[0181] 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 high recognition accuracy. Especially when the speed response is used as the reference input, the root mean square errors corresponding to the three recognition waveforms are all smaller than the root mean square errors when the displacement response is used as the reference input, and their correlation coefficients are closer to 1, that is, the recognition results are more consistent with the reference solution. Therefore, the recognition performance of using the speed response as the reference input is more advantageous.

[0182] In a second aspect, the present invention provides a micro-thrust dynamic identification system, specifically comprising:

[0183] A unit for determining a dynamic equation in a state-space form is used 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;

[0184] The integration unit 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 time;

[0185] Rewrite the unit, discretize the time domain into multiple equally spaced moments using a preset time step, and assume that the thrust applied to the thrust measurement system is constant within any integration step. Then, rewrite the theoretical system response model into a numerical model in a step-by-step integration recursive format;

[0186] An actual system response sequence construction unit, which constructs an actual system response sequence based on mapping pointers of displacement, velocity, and acceleration responses of the measured system and displacement, velocity, and acceleration obtained by the system response sensor;

[0187] An empirical model building unit is used to build an empirical model by combining the dynamic equations of the thrust measurement system and the actual system response sequence, and rewrite the empirical model into a discrete recursive format;

[0188] The augmented rewriting unit configures the micro-thrust increment expression, applies the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recursive format, and then further rewrites them into augmented form;

[0189] Prediction output unit, based on the thrust measurement system response at the current moment and the 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;

[0190] The cost function solving unit constructs and solves the cost function to minimize the sum of squared 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.

[0191] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the accompanying drawings. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple situations. A single processor or other unit can implement several functions listed in the specification. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0192] Although the present invention has been described with reference to specific features and embodiments thereof, it will be apparent that various modifications and combinations thereof may be made without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the present invention and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the invention. It will be apparent that various modifications and variations of the present invention may be made by those skilled in the art without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such modifications and variations as fall within the scope of the invention and its equivalents.

Claims

1. A method for dynamic identification of small thrust, characterized in that: The steps include: Construct the dynamic equations of the thrust measurement system and configure state vectors that can characterize the displacement response and velocity response of the thrust measurement system. Use the state vectors to rewrite the dynamic equations to obtain the state space form of the dynamic equations. 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; The time domain is discretized into multiple equally spaced moments using a preset time step, and assuming that the thrust applied to the thrust measurement system is constant within any integration step, the theoretical system response model is rewritten as a numerical model in a step-by-step integration recursive format. 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; An empirical model is constructed by combining the dynamic equations of the thrust measurement system and the actual system response sequence; Rewrite the empirical model into a discrete recursive format; Configure the micro-thrust increment expression, apply it to rewrite the numerical model and the empirical model in discrete recursive format, and then further rewrite it into an augmented form; Based on the thrust measurement system response at the current moment and the future control time domain The micro-thrust increment at each moment is obtained by combining the numerical model in augmented form and the empirical model in discrete recursive format to obtain the future The predicted output at each moment; A cost function is constructed and solved to minimize the sum of squared 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 point, the predicted micro-thrust corresponding to the predicted output is equal to the measured micro-thrust corresponding to the expected output.

2. The method for dynamic identification of small thrust according to claim 1, characterized in that: Constructing the cost function specifically includes the following sub-steps: At the initial moment to In the integration step, the transpose of the vector difference between the predicted output and the expected output, the weight matrix, and the product of the vector difference between the predicted output and the expected output are summed to obtain the state cost and function; among them, the weight matrix is ​​a 2×2 diagonal matrix, and the elements on the main diagonal 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; At the initial moment to In the integration steps, the product of the square of the micro-thrust increment and the penalty parameter is summed to obtain the micro-thrust increment cost and function; The cost function is obtained by summing the state cost sum function and the microthrust increment cost sum function.

3. The method for dynamic identification of small thrust according to claim 2, characterized in that: After constructing the cost function and before solving the cost function, the cost function is simplified, which 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 acceleration-related vector in the predicted output is a zero vector. Based on this, the predicted output is simplified into a matrix form, and the rewritten cost function is also simplified into a matrix form.

4. The method for dynamic identification of small thrust according to claim 3, characterized in that: The cost function is transformed into a quadratic programming problem under unconstrained conditions, that is, solving the extreme points of the cost function in matrix form to obtain the optimal micro-thrust increment sequence. The first item in the optimal micro-thrust increment sequence is extracted to obtain the micro-thrust increment at the current moment. The micro-thrust increment at the current moment is substituted into the micro-thrust increment expression to obtain the predicted micro-thrust at the next moment.

5. The method for dynamic identification of small thrust according to claim 4, characterized in that: Substitute the current micro-thrust increment into the augmented form numerical model to obtain the system state response corresponding to the predicted output at the next moment; The predicted output simplified into matrix form and the actual measured system state response are combined to obtain the expected output vector required at the next moment.

6. The method for dynamic identification of small thrust according to claim 2, characterized in that: Determine the prediction time domain based on the effectiveness of energy propagation , which will control the time domain Maximize, that is = .

7. The method for dynamic identification of small thrust according to claim 6, characterized in that: The prediction time domain is determined by the following method :At the initial moment, a unit excitation is applied to the measurement system. At this time, the response of the measurement system is a unit displacement response or a unit velocity response. After a period of time, the measurement system returns to the initial static state. The prediction time domain can be determined based on the time taken for the measurement system to return to the initial static state. The size of the measurement system to return to the initial static state is , is the preset time step.

8. The method for dynamic identification of small thrust according to claim 6, characterized in that: The 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.

9. The method for dynamic identification of small thrust according to claim 8, characterized in that: The penalty parameters are obtained by the following steps: Generate a series of penalty parameters uniformly on the logarithmic scale, and calculate the residual norm and solution norm for each penalty parameter; In the double logarithmic coordinate system, the curve is drawn with the residual norm as the horizontal axis and the solution norm as the vertical axis; The penalty parameter corresponding to the inflection point where the curvature of the curve is the largest is taken as the optimal penalty parameter value.

10. A micro-thrust dynamic identification system, characterized in that: include: A unit for determining a dynamic equation in a state-space form is used 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; The integration unit 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 time; Rewrite the unit, discretize the time domain into multiple equally spaced moments using a preset time step, and assume that the thrust applied to the thrust measurement system is constant within any integration step. Then, rewrite the theoretical system response model into a numerical model in a step-by-step integration recursive format; An actual system response sequence construction unit, which constructs an actual system response sequence based on mapping pointers of displacement, velocity, and acceleration responses of the measured system and displacement, velocity, and acceleration obtained by the system response sensor; An empirical model building unit is used to build an empirical model by combining the dynamic equations of the thrust measurement system and the actual system response sequence, and rewrite the empirical model into a discrete recursive format; The augmented rewriting unit configures the micro-thrust increment expression, applies the micro-thrust increment expression to rewrite the numerical model and the empirical model in discrete recursive format, and then further rewrites them into augmented form; Prediction output unit, based on the thrust measurement system response at the current moment and the 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 squared 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.

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