Accurate regulation and control method for unsteady aerodynamic force of continuous rapid deformation wing

Abstract

The invention relates to the technical field of aerodynamics, in particular to a precise regulation and control method for unsteady aerodynamic force of a continuously and rapidly deformed wing, and the method comprises the following steps: simulating the wing under various working conditions by using CFD software, and collecting simulation results to construct a working condition data set; performing double-model cooperative training on the ARX model and the PI hysteresis model based on the working condition data set; inputting the target lift coefficient into the trained PI inverse model to obtain a corrected deflection angle; and correcting the corrected deflection angle through an ARX model to obtain a final corrected deflection angle.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of aerodynamics, in particular to a precise regulation method for unsteady aerodynamics of a continuously and rapidly deformed wing. BACKGROUND

[0002] A variable camber wing can quickly respond to flight control instructions to complete dynamic deformation in actual flight, such as emergency maneuvering and attitude adjustment.

[0003] Current research on deformed aircraft is mostly based on steady aerodynamic scenarios. The continuously deformed aircraft includes variable camber wings, variable sweep wings, variable span wings, and upper folding wings. The research focuses on wing structure optimization and maximum steady aerodynamic force, and mainly analyzes the influence of static changes in wing geometric camber on aerodynamic characteristics.

[0004] Although steady aerodynamic analysis can provide a basis for wing deformation capability evaluation, aerodynamic improvement capability analysis and quasi-static behavior prediction, it cannot predict the unsteady aerodynamic behavior of the wing in the case of rapid deformation, such as flow field structure hysteresis and additional motion effects. Therefore, there is a lack of effective flight control methods to compensate for the lift lag caused by the deformation of the variable camber wing during flight.

[0005] The existing control method for variable camber wings cannot effectively solve the problem of lift lag, which will cause delay in the adjustment of the attitude of the aircraft, and the over-regulation of resistance will increase the additional energy consumption and flight resistance. The over-regulation of lift at large attack angle / deflection may cause attitude oscillation of the aircraft, affecting the accuracy of wing aerodynamic control and flight stability.

[0006] In order to solve the problems of lift lag, resistance over-regulation and large attack angle / deflection lift over-regulation of the variable camber wing, a deformed trajectory feedforward compensation control method for precise regulation of unsteady aerodynamics of a deformed aircraft is urgently needed. The application provides a precise regulation method for unsteady aerodynamics of a continuously and rapidly deformed wing. SUMMARY

[0007] In order to overcome the problems in the related art, the application provides a precise regulation method for unsteady aerodynamics of a continuously and rapidly deformed wing, comprising: Simulate the wing under multiple working conditions by using CFD software, collect simulation results and construct a working condition data set; Based on the working condition data set, the ARX model and the PI hysteresis model are trained in cooperation; Input the target lift coefficient into the trained PI inverse model to obtain the corrected deflection angle; Correct the corrected deflection angle by using the ARX model to obtain the final corrected deflection angle.

[0008] In an embodiment, after inputting the target lift coefficient into the trained PI inverse model to obtain the corrected deflection angle, it further includes: Based on the quasi-static deformation condition of the wing, the proportion between the deflection angle and the lift coefficient is determined, and the corrected deflection angle is determined according to the correction formula and the corrected deflection angle, and the correction formula is:

[0009] Wherein, The quasi-static trajectory converted by the target lift coefficient, The terminal time of the deformation trajectory.

[0010] In an embodiment, the corrected deflection angle is corrected by an ARX model to obtain a final corrected deflection angle, specifically including: The predicted lift coefficient is calculated by inputting the corrected deflection angle into the ARX model to obtain the predicted lift coefficient, and the prediction error between the predicted lift coefficient and the target lift coefficient is calculated. The simulation lift coefficient is obtained by simulating the wing under the corrected deflection angle condition, and the simulation error between the simulation lift coefficient and the target lift coefficient is calculated. The time difference between the predicted lift coefficient reaching the expected stable value and the specified terminal time is calculated. If the prediction error is less than the first accuracy threshold, the simulation error is less than the second accuracy threshold, and the time difference is less than the time difference threshold, the corrected deflection angle is used as the wing control parameter; if not, the ARX model parameters and / or PI hysteresis model parameters are fine-tuned.

[0011] In an embodiment, the ARX model and the PI hysteresis model are trained cooperatively based on the working condition data set, specifically including: The working condition data set is input into the ARX model, and the predicted lift coefficient is output. The parameters of the ARX model are adjusted by calculating the error between the predicted lift coefficient and the simulated lift coefficient.

[0012] In an embodiment, the ARX model and the PI hysteresis model are trained cooperatively based on the working condition data set, specifically including: The PI hysteresis model is constructed by superimposing the hysteresis operator and the creep operator, the hysteresis operator is constructed by linearly weighting and superimposing the Play operator, and the creep operator is constructed by weighting and superimposing the logarithmic creep operator. The PI hysteresis model is trained through the working condition data set.

[0013] In an embodiment, the wing under multiple working conditions is simulated by using CFD software, and the working condition data set is constructed by collecting simulation results, specifically including: Design a multi-dimensional flight condition parameter matrix; The CFD software is used to carry out aerodynamic simulation on a multi-dimensional flight condition parameter matrix, to obtain a corresponding relationship time sequence between the deflection angle and the lift coefficient by calculating the lift response curve of the wing during the deformation process; The processed corresponding relationship time sequence between the deflection angle and the lift coefficient is taken as a working condition data set.

[0014] In an implementation, before the processed corresponding relationship time sequence between the deflection angle and the lift coefficient is taken as a working condition data set, the method further comprises: The corresponding relationship time sequence between the deflection angle and the lift coefficient is subjected to data cleaning and denoising processing.

[0015] In an implementation, the data cleaning specifically comprises: An abnormal value is identified according to a criterion, and a mean value and a standard deviation of the lift coefficient time sequence are calculated. When the lift value at a certain moment satisfies , the value is determined as an abnormal value. The abnormal value is corrected by using a linear interpolation method.

[0016] In an implementation, the denoising processing specifically comprises: A moving average filter is used to eliminate high-frequency noise of the lift coefficient time sequence.

[0017] The technical scheme provided in the application can have the following beneficial effects: 1) The ARX model is used to simulate the lift response of the deflection angle output by the PI inverse model in advance, to identify potential deviations, to provide a quantitative basis for subsequent trajectory correction, and to solve the problem of insufficient accuracy of the trajectory obtained by directly using the PI model.

[0018] 2) The correction mechanism based on the quasi-static linear relationship designed by the method can directly adjust the deflection angle accurately, and significantly improve the terminal lift control accuracy; the fusion framework designed by the method directly realizes inverse compensation of the unsteady aerodynamic lag effect through the collaborative work of the ARX model and the PI lag model; 3) The data layer is compatible with CFD, wind tunnel and flight test data, the model layer supports alternative solutions such as neural network extension, meets the adaptability requirements of different application scenarios, and has good engineering practicability.

[0019] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the application. BRIEF DESCRIPTION OF DRAWINGS

[0020] ​The above and other objects, features and advantages of the present application will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which like reference characters refer to like parts throughout the figures, and in which:

[0021] Figure 1 Flow chart of the precise control method shown in the embodiments of the present application; Figure 2 Closed-loop control diagram of the precise control method shown in the embodiments of the present application; Figure 3 Flow chart of the ARX model training process shown in the embodiments of the present application; Figure 4 Flow chart of the PI hysteresis model training process shown in the embodiments of the present application; Figure 5 Schematic diagram of the relationship between the lag time and the lift coefficient; Figure 6 Structural schematic diagram of the variable camber wing shown in the embodiments of the present application; Figure 7 Sweeping frequency trajectory signal diagram shown in the embodiments of the present application; Figure 8A and Figure 8B Lift response training signal diagram shown in the embodiments of the present application; Figure 9A and Figure 9B Response result signal diagram of the PI hysteresis model predicting aerodynamic force; Figure 10 Deformation trajectory diagram before PI compensation in the embodiments of the present application; Figure 11 Deformation trajectory diagram after PI compensation in the embodiments of the present application. Figure 12 Verification effect schematic diagram of the ARX model in the embodiments of the present application. DETAILED DESCRIPTION

[0022] The preferred embodiments of the present application will be described in detail below with reference to the accompanying drawings. Although the preferred embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to make the present application more thorough and complete, and to fully convey the scope of the present application to those skilled in the art.

[0023] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0024] It should be understood that although the terms "first," "second," "third," etc., may be used in this application to describe various information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0025] like Figure 1 As shown, this application provides a method for precise control of unsteady aerodynamic forces of a continuously rapidly deformable wing, including steps 101 to 104.

[0026] Step 101: Use CFD software to simulate the wing under various operating conditions, collect simulation results and construct an operating condition dataset.

[0027] In this embodiment of the application, step 101 specifically includes: 301. Design a multi-dimensional flight condition parameter matrix; 302. Using CFD software, aerodynamic simulation was carried out on the multi-dimensional flight condition parameter matrix to calculate the lift response curve of the wing during the deformation process and obtain the time series of the corresponding relationship between the deflection angle and the lift coefficient. 303. The time series of the correspondence between the processed deflection angle and the lift coefficient is used as the working condition dataset.

[0028] like Figure 6 As shown, the aerodynamic characteristics of the variable-camber wing are significantly affected by changes in parameters such as angle of attack, flight speed, and Reynolds number during actual flight. For example, an increased angle of attack may lead to more pronounced lift nonlinearity, while a high Reynolds number flow field will exacerbate unsteady effects. If the model is trained based solely on data from a single flight condition, the compensation method will struggle to adapt to complex flight scenarios, resulting in decreased lift control accuracy. Therefore, a standardized dataset covering multiple flight conditions is first constructed to provide comprehensive and high-quality data samples for subsequent model training.

[0029] The specific processes of steps 301 to 303 are as follows: First, a multi-dimensional flight condition parameter matrix is ​​designed, covering angle of attack, flight speed, and Reynolds number to ensure coverage of typical flight states such as cruise and maneuvering. For each flight condition, two types of deformation trajectories are generated: one is a periodic trajectory (such as sine waves and frequency sweeps) to capture the high-frequency dynamic response of the wing; the other is a non-periodic trajectory (such as constant velocity on a ramp, parabolic curves, and cubic polynomials) to simulate the wing camber adjustment in actual flight. By combining the three-dimensional flight conditions of "angle of attack, speed, and Reynolds number" with the two-dimensional deformation trajectories of "periodic / non-periodic" trajectories, the multi-condition matrix constructed in this invention can cover typical working scenarios of continuously variable camber wings in the subsonic domain, from cruise to maneuvering, from low altitude to high altitude, and from periodic deformation to terminal deformation, providing comprehensive "deformation-aerodynamic response" samples for subsequent aerodynamic simulation and model training.

[0030] Subsequently, using CFD software (such as COMSOL and Fluent), aerodynamic simulations were conducted one by one for the aforementioned multi-condition combinations (covering angles of attack of 0° / 5° / 10° / 15°, flight speeds of 0.1Ma / 0.5Ma / 0.8Ma, Reynolds numbers of 3e6 / 5e6, and cross-combinations of periodic / non-periodic trajectories). The lift response curves of the wing during deformation were calculated, and the deflection angle was obtained. With lift coefficient The corresponding time series.

[0031] In one implementation, before constructing the dataset in step 303, the method further includes: performing data cleaning and noise reduction on the time series of the correspondence between the deflection angle and the lift coefficient.

[0032] Specifically, data cleaning includes: employing The criteria identify outliers and calculate the mean of the lift coefficient time series. with standard deviation When the lift value at a certain moment satisfies If the value is too high, it is considered an outlier. Linear interpolation is used to correct outliers.

[0033] Outliers are corrected using linear interpolation, with the following formula:

[0034] in, This is the corrected lift value. , These represent the normal lift values ​​before and after the anomaly point.

[0035] Specifically, the noise reduction process includes using a moving average filter to eliminate high-frequency noise in the lift coefficient time series.

[0036] For time series The filtered value is:

[0037] Where N is the window size, which preserves the characteristics of unsteady aerodynamic effects by smoothing local fluctuations.

[0038] In step 303, the work condition dataset is divided into a training set and a test set in a 7:3 ratio. Stratified sampling is used to ensure that the work condition distribution of the two sets of data is consistent, that is, the proportion of each work condition sample in the training set and the test set is the same. The core reason for this ratio design is that: the 70% proportion of the training set provides a sufficient sample size to ensure that the ARX and PI models can fully learn the "deformation-lift" coupling law under multiple work conditions (especially the nonlinear characteristics of unsteady effects), avoiding underfitting of the model; the 30% proportion of the test set can effectively verify the model's generalization ability - it includes work condition details that were not involved in the training (such as the combination of specific angle of attack and velocity), and can pass the statistical significance test (when the sample size meets 30%, the error distribution is closer to the real population), ensuring the reliability of the model in unknown scenarios.

[0039] The resulting standardized dataset contains both the high-frequency characteristics of periodic deformations and the transient responses of non-periodic deformations. Furthermore, it has been preprocessed to eliminate noise and abnormal interference, providing a data foundation with both completeness and reliability for the subsequent "ARX prediction-PI compensation" collaborative mechanism.

[0040] Step 102: Perform dual-model co-training on the ARX model and the PI hysteresis model based on the working condition dataset.

[0041] Step 102 specifically includes: inputting the working condition dataset into the ARX model, outputting the predicted lift coefficient, and adjusting the parameters of the ARX model by calculating the error between the predicted lift coefficient and the collected simulation lift coefficient. The training process of the ARX model is as follows: First, the ARX model is trained based on the standardized training set built in the first step. This model uses the wing deformation trajectory... Using historical lift and yaw angle data as input, the system learns from the correlation between these data and outputs a predicted lift value. Its mathematical expression is:

[0042] in, and For the lag operator polynomial (n and m are the model order, determined through training and optimization), This is white noise perturbation. Expanding the mathematical expression, we get:

[0043] After training and optimization to select the most suitable n and m, the corresponding values ​​are obtained. and By obtaining the value of [value], the required ARX model can be obtained, and then the deformation trajectory vector can be input. Then the predicted output lift value can be obtained as follows:

[0044] During training, the error between the ARX model prediction and the CFD calculation results is minimized by adjusting the polynomial coefficients, ensuring that ARX can capture the lift response trend in advance and provide accurate deviation reference for subsequent compensation. Figure 3 A flowchart of ARX model identification is provided.

[0045] Step 102 specifically includes: constructing a PI hysteresis model using a superposition structure of hysteresis and creep operators, wherein the hysteresis operator is constructed by linear weighted superposition of Play operators, and the creep operator is constructed by weighted superposition of logarithmic creep operators; and training the PI hysteresis model using a working condition dataset.

[0046] The training process of the PI hysteresis model is as follows: To address the hysteresis-creep coupling characteristics of unsteady aerodynamic forces in continuously variable camber wings, a feedforward inverse compensation method based on a PI hysteresis model is proposed to generate deformation trajectories that enable precise aerodynamic control. The specific process is as follows: First, a PI hysteresis model is constructed to depict a phenomenological model of the coupling between hysteresis and creep. This model employs a structure of "superposition of hysteresis and creep operators," using mathematical operators to describe the nonlinear mapping relationship between the equivalent wing deflection angle and the lift coefficient.

[0047] In the above formula, It is a hysteresis operator. It is a creep operator.

[0048] Among them, the hysteresis characteristic is constructed by linearly weighted superposition of Play operations to create a hysteresis operator. A single Play operator satisfies the following recurrence relation:

[0049] here For input (i.e., the equivalent deflection angle of the wing) ), For output (hysteresis component). The hysteresis threshold, This is used for historical output to reflect the delayed memory property. The final delayed operator is... We obtain the following by weighting the Play operators:

[0050] In the formula, These are the weighting coefficients. This is the gain coefficient. This is the initial value.

[0051] Creep properties are then constructed by weighted superposition of logarithmic creep operators to form a creep operator. The basic creep operator satisfies the nonlinear differential equation:

[0052] in These are creep characteristic values ​​used to control the creep rate. This represents the creep threshold. The logarithmic creep operator can be applied to operations with different creep characteristic values. But threshold The same This is achieved by superimposing the basic creep operators in an unweighted manner, thus obtaining the so-called basic logarithm log(t) creep operator:

[0053] In the formula: The number of creep eigenvalues. The final PI-form creep operator is derived from... We obtain the following by weighting the log-creep operators:

[0054] In the formula: For weighting coefficients, This is the initial value.

[0055] Then, by combining the creep operator with the hysteresis operator, we can obtain the nonlinear hysteresis creep model shown in the equation:

[0056] Model parameters (including thresholds) creep characteristic value Weight Identification is performed using the least squares method, based on test data, to minimize the error between the model output and the true response.

[0057] Step 103: Input the target lift coefficient into the trained PI inverse model to obtain the corrected deflection angle.

[0058] The generation of the inverse compensation trajectory realizes the conversion from desired lift to compensated deflection angle. This process is based on the inverse operator of the PI hysteresis model. The existence and uniqueness of this inverse operator have been proven in relevant literature. Based on the previously established time-discrete hysteresis creep PI operator, a discretized recursive explicit inverse compensation implementation can be obtained, expressed as:

[0059] For the variable camber wing model in this patent, the input is the equivalent deflection angle, and the output is the wing lift coefficient. That is, the formula above can be used to... , Replace with and Therefore, once the parameters of the hysteresis creep model are determined, the input after inverse compensation can be directly calculated using the formula based on an expected output. Figure 4 A flowchart of PI hysteresis model identification and inverse compensation design is presented.

[0060] Although the PI inverse model can generate a preliminary compensated trajectory, the complex characteristics of the unsteady flow field may still lead to slight deviations in terminal lift. Therefore, this invention employs a closed-loop process of "quasi-static correction + three-dimensional verification" to further improve trajectory accuracy and ensure effective terminal lift control.

[0061] Following step 103, the process further includes: based on the quasi-static deformation condition of the wing, the ratio between the deflection angle and the lift coefficient is determined. The corrected deflection angle is then determined according to the correction formula and the corrected deflection angle. The correction formula is as follows:

[0062] in, This is the quasi-static trajectory calculated using the target lift coefficient. The value represents the endpoint of the deformed trajectory. This correction formula adjusts the ratio of the initial deformed trajectory endpoint value to the quasi-static trajectory endpoint value, effectively eliminating the endpoint deviation of the compensation trajectory.

[0063] Step 104: Correct the deflection angle using the ARX model to obtain the final corrected deflection angle.

[0064] Furthermore, step 104 specifically includes: 201. Input the corrected deflection angle into the predicted lift coefficient obtained by the ARX model, and calculate the prediction error between the predicted lift coefficient and the target lift coefficient; ARX ​​Prediction Validation: The core is to verify the accuracy of the ARX model in predicting lift, defining the root mean square error (RMSE) between the ARX predicted lift and the target lift:

[0065] If this error value ( If a preset accuracy threshold is set (e.g., 0.01), it indicates that the ARX model can accurately predict changes in lift, providing a reliable basis for subsequent compensation.

[0066] 202. Simulate the wing under the corrected deflection angle condition to obtain the simulated lift coefficient, and calculate the simulation error between the simulated lift coefficient and the target lift coefficient. CFD simulation verification: Utilizing the high-precision simulation capability of CFD for actual flow fields, the matching degree between the lift response under the corrected trajectory and the target value is verified, and the root mean square error of the CFD-calculated lift and the target lift is defined.

[0067] Considering that CFD needs to reflect the details of the flow field, a more stringent threshold is set. (e.g., 0.001), if This indicates that the corrected trajectory can achieve accurate lift tracking in a real flow field.

[0068] 203. Calculate the time difference between the predicted lift coefficient reaching the expected stable value and the specified terminal time; Late compensation verification: based on lag time The compensation effect is quantified for the core indicator, which is represented by the lift reaching the expected stable value. With the specified terminal time The time difference between them, such as Figure 5 As shown. If the lag time is satisfied... If the time is 0.1s, it means that the trajectory can effectively counteract the lift lag phenomenon.

[0069] 204. Determine whether the prediction error is less than the first accuracy threshold, whether the simulation error is less than the second accuracy threshold, and whether the time difference is less than the time difference threshold. If yes, use the corrected deflection angle as the wing control parameter; if no, fine-tune the ARX model parameters and / or the PI hysteresis model parameters.

[0070] In practice, Inputting the ARX model yields the predicted lift. Simultaneously, the actual lift was calculated using CFD. With the target lift Perform a three-way comparison. If the accuracy requirements are met, This is the final compensation trajectory; otherwise, fine-tune the ARX model parameters (e.g., ...). , , ) or PI hysteresis model parameters (such as , , Repeat the correction and verification process until the error meets the standard.

[0071] like Figure 2 As shown, this closed-loop process can quickly correct system deviations using quasi-static relationships, and ensure compensation accuracy through dual verification of ARX prediction and CFD calculation, ultimately achieving precise matching of lift and deformation trajectory under unsteady flow fields.

[0072] The feasibility of the invention has been verified, including using the ARX model to model the aerodynamics of the deformation process of the variable camber wing and using the PI inverse model to compensate for the effect of lift hysteresis.

[0073] The following is a summary of the verification work already performed: ARX ​​aerodynamic modeling verification: This validation was conducted under operating conditions of 0° angle of attack, 0.1 Ma velocity, and Reynolds number 3e6, aiming to verify the predictive performance of the ARX model on the lift response of a continuously variable camber wing. A 0Hz-12Hz-0Hz sweep frequency trajectory signal, which fully covers the typical dynamic deformation frequencies of the wing and excites unsteady aerodynamic characteristics, was selected as the training input, such as... Figure 7 As shown.

[0074] After training the ARX model, the model achieved an overall fit of 99.99% to the estimated dataset, indicating that it can accurately capture the characteristics of the lift response. Meanwhile, the root mean square error (RMSE) was 5.756e-9 and the final prediction error (FPE) was 3.049e-9. Both error values ​​are very small, indicating that the model not only has low fitting error but also good generalization prediction ability.

[0075] After completing model training, three different trajectories (terminal deformation times of 0.2s, 0.3s, and 0.4s) were selected in the test set to test the ARX's predicted lift response performance. During this process, continuous adjustments were needed to select the optimal autocorrelation output order. and autocorrelation input order Finally, for the trajectory with a terminal deformation time of 0.2s, the selected... , The values ​​are 91 and 4 respectively; for the trajectory with a terminal deformation time of 0.3s, the selected... , The values ​​are 84 and 4 respectively; for the trajectory with a terminal deformation time of 0.4s, the selected... , The values ​​are 90 and 5 respectively; and the lag step number of all three is selected as 1, indicating that the output at each time t is determined by the input and output at time t-1 and before time t-1, which is consistent with the actual physical laws.

[0076] Selecting an appropriate autocorrelation output order and autocorrelation input order Subsequently, simulations were performed using the ARX model. It can be seen that the overall consistency of the three cases is good, the maximum error can be controlled within 2%, and the terminal lift value expected by ARX is well matched. Table 1 shows the verification effect of the ARX model.

[0078] Validation of aerodynamic compensation for PI hysteresis model: This verification was conducted under the conditions of flow velocity 0.1 Ma, angle of attack 0°, and flow field Reynolds number 3e6. The core objective was to examine the compensation effect of this trajectory on the unsteady aerodynamic effects of a continuously variable cambered wing, and to ensure that the lift response lag caused by unsteady aerodynamic effects can be effectively offset under this deformed trajectory, so as to achieve precise control of aerodynamic forces.

[0079] First, the excitation signal for the deflection angle is designed as a frequency sweep signal with an amplitude of 15°, where the frequency changes from 0Hz to -10Hz and then back to 0Hz. Its lift response can be calculated using CFD. The training signal is as follows: Figure 8A and Figure 8B As shown.

[0080] The parameters of the PI hysteresis model in the case are uniformly set as follows: , , Then, the ability of the PI hysteresis model to predict aerodynamic forces is verified, which can be done by the following: Figure 9A and Figure 9B The response results show that the model's predicted values ​​are in very good agreement with the actual values.

[0081] Firstly, for the periodic deformation case, a feedforward inverse compensation design for the deformation trajectory was implemented. The predefined dynamic lift response curve is a sine curve with an amplitude of 10 degrees and a frequency of 2 Hz. From the following... Figure 10 The results show that by using the deformation trajectory after PI compensation, the expected lift response can be effectively tracked.

[0082] Then, for the terminal deformation, a feedforward inverse compensation design for the deformation trajectory is also performed. The predefined dynamic lift response curve is a trajectory based on a fifth-order polynomial. The control requirement for this case is that the lift coefficient at the terminal moment... When the terminal lift value is reached From below Figure 11 The results show that the dynamic lift response of the deformed trajectory after PI compensation during passage matches the predefined curve well. From the perspective of aerodynamic control, the lift lag at the terminal moment has been eliminated.

[0083] The solution of this application has been described in detail above with reference to the accompanying drawings. In the above embodiments, the descriptions of each embodiment have different emphases; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. Those skilled in the art should also understand that the actions and modules involved in the specification are not necessarily essential to this application. Furthermore, it is understood that the steps in the method of this application embodiment can be adjusted, combined, and deleted according to actual needs, and the modules in the device of this application embodiment can be combined, divided, and deleted according to actual needs.

[0084] Furthermore, the method according to this application can also be implemented as a computer program or computer program product, which includes computer program code instructions for performing some or all of the steps in the method described above.

[0085] Alternatively, this application may be implemented as a non-transitory machine-readable storage medium (or computer-readable storage medium, or machine-readable storage medium) storing executable code (or computer program, or computer instruction code) thereon, which, when executed by a processor of an electronic device (or electronic device, server, etc.), causes the processor to perform part or all of the steps of the methods described above according to this application.

[0086] Those skilled in the art will also understand that the various exemplary logic blocks, modules, circuits, and algorithm steps described in connection with the present application can be implemented as electronic hardware, computer software, or a combination of both.

[0087] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems and methods according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0088] The various embodiments of this application have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for precise control of unsteady aerodynamic forces in a continuously rapidly deformable wing, characterized in that, include: CFD software was used to simulate the airfoil under various working conditions, and the simulation results were collected to construct a working condition dataset. A dual-model collaborative training was performed on the ARX model and the PI hysteresis model based on the working condition dataset. Input the target lift coefficient into the trained PI inverse model to obtain the corrected deflection angle; The final corrected deflection angle is obtained by correcting the deflection angle using the ARX model.

2. The precise control method as described in claim 1, characterized in that, After inputting the target lift coefficient into the trained PI inverse model to obtain the corrected deflection angle, the process also includes: Based on the quasi-static deformation condition of the wing, the ratio between the deflection angle and the lift coefficient is fixed. The corrected deflection angle is determined according to the correction formula and the corrected deflection angle. The correction formula is as follows: in, This is the quasi-static trajectory calculated using the target lift coefficient. This represents the final moment of the deformation trajectory.

3. The precise control method as described in claim 2, characterized in that, The corrected deflection angle is obtained by correcting the deflection angle using the ARX model, specifically including: The corrected deflection angle is input into the predicted lift coefficient obtained from the ARX model, and the prediction error between the predicted lift coefficient and the target lift coefficient is calculated. The airfoil under the corrected deflection angle condition was simulated to obtain the simulated lift coefficient, and the simulation error between the simulated lift coefficient and the target lift coefficient was calculated. Calculate the time difference between the predicted lift coefficient reaching the expected stable value and the specified terminal time; Determine whether the prediction error is less than the first accuracy threshold, whether the simulation error is less than the second accuracy threshold, and whether the time difference is less than the time difference threshold. If so, use the corrected deflection angle as the wing control parameter; otherwise, fine-tune the ARX model parameters and / or the PI hysteresis model parameters.

4. The precise control method as described in claim 1, characterized in that, Based on the working condition dataset, a dual-model collaborative training of the ARX model and the PI hysteresis model is performed, specifically including: The working condition dataset is input into the ARX model, which outputs the predicted lift coefficient. The parameters of the ARX model are adjusted by calculating the error between the predicted lift coefficient and the collected simulation lift coefficient.

5. The precise control method as described in claim 4, characterized in that, Based on the working condition dataset, a dual-model collaborative training of the ARX model and the PI hysteresis model is performed, specifically including: A PI hysteresis model is constructed by superimposing hysteresis operators and creep operators. The hysteresis operators are constructed by linear weighted superposition of Play operators, and the creep operators are constructed by weighted superposition of logarithmic creep operators. The PI hysteresis model was trained using a working condition dataset.

6. The precise control method as described in claim 1, characterized in that, The airfoil under various operating conditions was simulated using CFD software, and the simulation results were collected to construct an operating condition dataset, which specifically includes: Design a multi-dimensional flight condition parameter matrix; Aerodynamic simulation was carried out on the multi-dimensional flight condition parameter matrix using CFD software. The lift response curve of the wing during the deformation process was calculated, and the time series of the relationship between the deflection angle and the lift coefficient was obtained. The time series of the correspondence between the processed deflection angle and the lift coefficient is used as the working condition dataset.

7. The precise control method as described in claim 1, characterized in that, Before using the time series of the correspondence between the processed deflection angle and the lift coefficient as the working condition dataset, the following is also included: Data cleaning and noise reduction were performed on the time series of the relationship between deflection angle and lift coefficient.

8. The precise control method as described in claim 7, wherein data cleaning specifically includes: use The criteria identify outliers and calculate the mean of the lift coefficient time series. with standard deviation When the lift value at a certain moment satisfies If the value is too high, it is considered an outlier. Linear interpolation is used to correct outliers.

9. The precise control method as described in claim 8, characterized in that, Noise reduction processing specifically includes: Moving average filtering is used to eliminate high-frequency noise in the lift coefficient time series.

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