Data-Driven Adaptive Control Method for Vibration of Elastomeric Aircraft

Abstract

The present application relates to a data-driven vibration adaptive control method for an elastomeric aircraft. The method includes: extracting spatial vibration features from vibration data by using the principal component analysis method, and obtaining spatial basis functions by determining the optimal dimension of the spatial vibration features through a threshold; based on the spatial basis functions, establishing corresponding fuzzy rules, and reconstructing the nonlinear time dynamics of the system based on the fuzzy rules to establish a nonlinear model, obtaining a low-dimensional nonlinear spatio-temporal model of the elastic vibration of the aircraft, and establishing a vibration state equation of the elastomeric aircraft; improving the vibration state equation, establishing a derivable control law according to the improved vibration state equation, constructing a T-S fuzzy model to approximate the uncertainty in the derivable control law, and designing an adaptive control law to actively suppress the elastic vibration of the aircraft. By using this method, the vibration of the elastomeric aircraft can be actively suppressed.

Description

Technical Field

[0001] This application relates to the technical field of aircraft control, and particularly to a data-driven vibration adaptive control method for an elastomeric aircraft. Background Art

[0002] With the continuous improvement of requirements for flight speed, maneuverability, and range, the shape of aircraft represented by missiles has become increasingly slender. When the length-diameter ratio of the aircraft is greater than 10, the stiffness of the airframe will decrease significantly, and the elastic characteristics are obvious. During both the launch phase and the flight process, obvious lateral bending vibrations are likely to occur, which has a great impact on the normal operation of equipment on the aircraft. However, the vibration system is a highly nonlinear and strongly coupled flexible system, and problems such as parameter perturbation, interference, and uncertainty need to be solved. These factors pose great challenges to vibration suppression strategies and controller design.

[0003] The elastic vibration of an elastomeric aircraft is a highly nonlinear dynamic process with strong space-time coupling. The modeling methods for space-time coupling dynamic systems mainly include two categories: 1) traditional separation variable methods represented by the finite element method, approximate inertial manifold method, Galerkin method, and spectral method; 2) data modeling methods represented by statistical models and space-time separation models. These methods are less applied in elastic body vibration. Currently, the modal superposition method is mostly used, and the elastic vibration is expressed as the sum of different vibration modes. Then, according to the orthogonality of the vibration modes, the generalized coordinate equations of each order of vibration modes are obtained by the separation variable method. In this process, the establishment of each order of vibration mode functions is mainly obtained through experimental methods or empirical methods. The whole process is relatively complex, and more effective methods need to be adopted to improve the extraction efficiency of vibration mode characteristics and the solution efficiency of vibration equations.

[0004] In addition, regarding the vibration problem of elastomeric aircraft, many scholars have conducted research from different perspectives. However, due to the complex characteristics of vibration, when dealing with vibration, such conventional robust control methods can only passively adapt to the changing characteristics of vibration and cannot effectively suppress vibration from an active level. Existing research mainly considers how to ensure the stability of the system, regarding the elastic mode as interference, and does not guarantee good dynamic performance while meeting the steady-state performance of the system. Summary of the Invention

[0005] Based on this, in view of the above technical problems, it is necessary to provide a data-driven vibration adaptive control method for an elastomeric aircraft that can actively suppress the vibration of the elastomeric aircraft.

[0006] A data-driven vibration adaptive control method for an elastomeric aircraft, the method includes:

[0007] Distribute multiple sensors on the surface of the elastomeric aircraft to collect vibration data, extract spatial vibration features from the vibration data using the principal component analysis method, and obtain spatial basis functions by determining the optimal dimension of the spatial vibration features through thresholds;

[0008] Map the system input and output data in a high-dimensional space based on the spatial basis functions to obtain a non-linear time series, establish corresponding fuzzy rules according to the characteristics of the non-linear time series, and establish a non-linear model based on the fuzzy rules to reconstruct the non-linear time dynamics of the system;

[0009] Obtain a low-dimensional non-linear spatio-temporal model of the elastic vibration of the aircraft according to the spatial basis functions and the non-linear model, and establish a vibration state equation of the elastomeric aircraft based on the non-linear model and the low-dimensional non-linear spatio-temporal model; Improve the vibration state equation to obtain an improved vibration state equation;

[0010] Establish a derivable control law according to the improved vibration state equation, approximate the uncertainties in the derivable control law by constructing a T-S fuzzy model, and design an adaptive control law to actively suppress the elastic vibration of the aircraft.

[0011] The above data-driven vibration adaptive control method for an elastomeric aircraft uses a feature extraction method to obtain the main features of the vibration, acquires the spatial basis functions representing the main order vibration mode, accurately extracts the key information reflecting the spatial characteristics of the elastomeric aircraft vibration, clarifies the main modes of the vibration in the spatial dimension, and lays a foundation for establishing a model that can accurately reflect the vibration characteristics. Then, the original vibration data is projected onto the basis function space to obtain the time coefficients of the system. Based on this, a fuzzy-based time coefficient model is established to reflect the nonlinear dynamic characteristics of the elastic vibration in time. In this way, the variation law of the vibration in the time dimension is completely characterized, taking into account the nonlinear characteristics of the vibration. The time characteristics are crucial for accurately describing the vibration process, and the fuzzy model can handle this nonlinearity and uncertainty well, enabling a more accurate grasp of the dynamic characteristics of the vibration in time, thus providing a reliable basis for active suppression. Finally, a low-dimensional nonlinear spatio-temporal model of the elastic vibration of the aircraft is obtained based on the spatial basis function and the nonlinear model, and the vibration state equation of the elastomeric aircraft is established according to the nonlinear model and the low-dimensional nonlinear spatio-temporal model, integrating the spatial and time characteristics to construct an equation that can comprehensively reflect the vibration characteristics of the elastomer in time and space, providing a reliable basis for subsequent control; the vibration state equation is improved to obtain the improved vibration state equation; a derivable control law is established according to the improved vibration state equation, and the uncertainty in the derivable control law is approximated by constructing a T-S fuzzy model and an adaptive control law is designed. The T-S fuzzy model can effectively approximate the system uncertainty and solve the robustness problems caused by the change of the aircraft's center of mass, parameter uncertainty, and external disturbances. The adaptive control law can actively adjust the control strategy according to the changes in the system state and uncertainty, thus realizing the active suppression of the elastic vibration of the aircraft, solving the robustness problems caused by the change of the aircraft's center of mass, parameter uncertainty, and external disturbances, and overcoming the deficiency that the conventional robust control method can only passively adapt to the vibration change characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 FIG. is a schematic flowchart of a data-driven vibration adaptive control method for an elastomeric aircraft in an embodiment;

[0013] Figure 2 FIG. is a schematic diagram of the overall framework of the vibration control method for an elastomeric aircraft in an embodiment;

[0014] Figure 3 FIG. is an internal structure diagram of a computer device in an embodiment. DETAILED IMPLEMENTATION MANNER

[0015] To make the objectives, technical solutions, and advantages of this application clearer, the following further details this application in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining this application and are not used to limit this application.

[0016] In one embodiment, as Figure 1 and Figure 2 shown, a data-driven vibration adaptive control method for an elastomeric aircraft is provided. First, the main vibration characteristics of the system are extracted using the principal component analysis method to obtain a function representing the main vibration modes of the elastomer in space, that is, the spatial basis function. Then, the original vibration equation is projected onto the basis function space, and using the orthogonality of the basis functions, a time coefficient model representing the dynamic characteristics of vibration over time can be obtained. Integrating the spatial basis function and the time coefficient can obtain a vibration model with an explicit state equation, reconstructing the vibration characteristics of the elastomer in time and space. It mainly includes the following steps:

[0017] Step 102: Distribute multiple sensors on the surface of the elastomeric aircraft to collect vibration data. Use the principal component analysis method to extract the spatial vibration characteristics from the vibration data, and obtain the spatial basis function by determining the optimal dimension of the spatial vibration characteristics through a threshold.

[0018] N sensors are evenly distributed on the surface of the elastomer to collect spatio-temporal data , where represents the external force applied to the elastomer. represents the output of the -th sensor at moment. According to the spatio-temporal separation idea, such a system with spatio-temporal coupling characteristics can be transformed into the following model represented by an infinite number of characteristic basis functions and time coefficients:

[0019] (1)

[0020] where represents the basis function of the i-th feature, is the time coefficient corresponding to the i-th feature. They are respectively used to characterize the spatial distribution dynamics and non-linear time dynamics of the system. As is well known, the elastic deformation of the aircraft at each moment is the result of the superposition of different vibrations. Therefore, the vibration information can be processed to extract its main vibration characteristics to approximately characterize its spatial distribution characteristics. Here, the principal component analysis method is used to extract the key characteristics of the vibration. Further considering the strong non-linear distribution characteristics of the vibration in space, a spatial mapping function is used to linearly map the non-linear sample data in the low-dimensional space to the high-dimensional space, so as to retain the spatial non-linear dynamics during the transformation process. For the sake of convenience of representation, the output at moment Simplified to . In this way, by introducing the Gaussian kernel radial basis function, the non-linear mapping relationship from low dimension to high dimension of elastic vibration can be expressed as follows:

[0021] (2)

[0022] Where, represents the width parameter of the Gaussian kernel function. Assuming that the mapping of the sample in the new coordinate system is , then the error before and after the projection of the original data is:

[0023] (3)

[0024] Where, represents a set of orthogonal bases in the new coordinate system after the projection transformation.

[0025] The core problem here is to find a set of basis functions that meet the conditions and satisfy . From the above process, the following quadratic optimization problem can be constructed:

[0026] (4)

[0027] (5)

[0028] Using the Lagrange multiplier method, the objective function can be transformed into:

[0029] (6)

[0030] Let , a set of basis functions that meet the conditions can be obtained:

[0031] (7)

[0032] Where, represents a set of orthogonal basis functions that satisfy in the high-dimensional space after mapping. The corresponding orthogonal basis functions for the first M smallest eigenvalues can be obtained by the following formula:

[0033] (8)

[0034] represents the dimensionality reduction threshold. Therefore, for the original sample , the th coordinate after projection is:

[0035] (9)

[0036] Where, ; Denote the column vectors of the spatial basis functions .

[0037] Through the non - linear mapping of spatio - temporal data and the dimensionality reduction of the high - dimensional feature space, the spatial basis functions can be obtained as follows:

[0038] (10)

[0039] Finally, the system output can be approximated as the following M - order model:

[0040] (11)

[0041] Based on the finite - dimensional spatial basis functions in Equation (9), by mapping the system input and output data in this high - dimensional space, the time coefficients characterizing the non - linear time series of the system can be obtained.

[0042] It can be known from the orthogonality of the spatial basis functions that:

[0043] (12)

[0044] Step 104: Based on the spatial basis functions, map the system input and output data in the high - dimensional space to obtain the non - linear time series. According to the characteristics of the non - linear time series, establish the corresponding fuzzy rules, and based on the fuzzy rules, establish a non - linear model to reconstruct the non - linear time dynamics of the system.

[0045] Based on the above - mentioned finite - dimensional spatial basis functions, by mapping the system input and output data in this high - dimensional space, the non - linear time series of the system is obtained. According to the characteristics of the time - series data, establish the corresponding fuzzy rules, and a non - linear model based on the fuzzy algorithm is proposed to reconstruct the non - linear time dynamics of the system.

[0046] According to the idea of spatio - temporal separation, by projecting the elastic vibration data onto the kernel function, the time coefficients characterizing the time dynamics of the system can be obtained:

[0047] (13)

[0048] For the convenience of modeling the time coefficients, let , and establish the time - series variables as follows:

[0049] (14)

[0050] where is used to characterize the time dynamics of the elastic body at the position. The above formula shows that the time dynamics of the elastic vibration is not only related to the time coefficients at the adjacent g time moments, but also affected by dThe input influence at each moment is in line with the actual situation. Assume that represents the fuzzy set of the prior rule variable. Let , and establish the following fuzzy rules:

[0051] Rule s: If is and is and … and is ;

[0052] Then ;

[0053] Among them, , represents the rule number; represents the non - linear time dynamics of the system at moment, that is, the non - linear time series; represents the input of the system at moment; and respectively represent the coefficients of the output at the previous moment and the input at this moment. Usually, the bias term , parameters and can be solved by the Least Square method (LS).

[0054] Thus, the time - coefficient model of elastic vibration can be constructed as follows:

[0055] (15)

[0056] Among them, represents the membership degree of the s - th rule function; is the membership function;

[0057] ;

[0058] (16)

[0059] represents the width parameter of the

[0060] th fuzzy set.

[0061] Combining the spatial basis functions and the nonlinear model, a low-dimensional nonlinear spatio-temporal model can be obtained to characterize the elastic vibration of the aircraft in time and space:

[0062] (17)

[0063] From equations (15) and (17), the vibration state equation of the elastic aircraft can be established as follows:

[0064] (18)

[0065] It can be further transformed into:

[0066] (19)

[0067] Where, , ;

[0068] However, considering the influence of complex uncertain factors such as the change of the aircraft's center of mass, data noise, and external disturbances, there will be a certain degree of perturbation in the parameters of model (19). That is:

[0069] (20)

[0070] After arrangement, we get:

[0071] (21)

[0072] Where, represents the sum of the internal uncertainty of the system and external disturbances.

[0073] Step 108, establish a derivable control law according to the improved vibration state equation, approximate the uncertainty in the derivable control law by constructing a T-S fuzzy model, and design an adaptive control law to actively suppress the elastic vibration of the aircraft.

[0074] Define the sliding mode surface , then we have

[0075] (22)

[0076] Based on the constant velocity reaching law , where T represents the sampling interval. Then we have:

[0077] (23)

[0078] Here, The value of can be predicted by the linear extrapolation method, that is . Usually, for vibration suppression control, The value represents the desired elastic displacement, and its value should be 0. Therefore, a control law needs to be designed to make the elastic displacement of the system tend to 0. The control law can be derived as follows:

[0079] (24)

[0080] Here, since the upper bound of is unknown, combining the adaptive idea, an adaptive T-S fuzzy model of is established. Similarly, the T-S fuzzy model is modeled as follows:

[0081] (25)

[0082] Among them, is H the model estimated value of, represents the fuzzy variable and , and this variable can also be selected according to needs. R represents the number of rules, and there is ; represents the fuzzy posterior coefficient, which can usually be obtained by the least squares method. is the prior coefficient of the fuzzy model, representing the membership degree of the p th rule of. Specifically as follows:

[0083] (26)

[0084] Here, is the membership function. For the sake of convenient representation, the following variables are defined:

[0085] , ;

[0086] Among them, is the adaptive fuzzy coefficient; is the vector related to the fuzzy. M and N are r-dimensional diagonal matrices, satisfying , ;

[0087] Then, formula (25) is further transformed into:

[0088] (27)

[0089] For the above fuzzy model, taking the parameter as an example, its optimal value satisfies:

[0090] (28)

[0091] Among them, , is the approximation error and has . Let , there is:

[0092] (29)

[0093] Therefore, the control law can be further transformed into:

[0094] (30)

[0095] And design the adaptive control law as follows:

[0096] .

[0097] By constructing a T-S fuzzy model, the uncertainty in the derivable control law is approximated and an adaptive control law is designed. The T-S fuzzy model can effectively approximate the system uncertainty and solve the robustness problems caused by the change of the aircraft's center of mass, parameter uncertainty, external disturbance, etc. The adaptive control law can actively adjust the control strategy according to the changes of the system state and uncertainty, so as to achieve the active suppression of the elastic vibration of the aircraft, solve the robustness problems caused by the change of the aircraft's center of mass, parameter uncertainty, external disturbance, etc., and overcome the deficiency that the conventional robust control method can only passively adapt to the vibration change characteristics.

[0098] In the above data-driven elastic aircraft vibration adaptive control method, the present application uses a feature extraction method to obtain the main features of vibration, acquires the spatial basis functions representing the main order vibration mode modal, accurately extracts the key information reflecting the spatial characteristics of the elastic aircraft vibration, clarifies the main modes of vibration in the spatial dimension, and lays a foundation for establishing a model that can accurately reflect the vibration characteristics. Then, the original vibration data is projected onto the basis function space to obtain the time coefficients of the system. On this basis, a fuzzy-based time coefficient model is established to reflect the nonlinear dynamic characteristics of elastic vibration in time. In this way, the variation law of vibration in the time dimension is completely characterized, taking into account the nonlinear characteristics of vibration. The time characteristics are crucial for accurately describing the vibration process, and the fuzzy model can handle this nonlinearity and uncertainty well, enabling a more accurate grasp of the dynamic characteristics of vibration in time, thereby providing a reliable basis for realizing active suppression. Finally, a low-dimensional nonlinear spatio-temporal model of the aircraft elastic vibration is obtained according to the spatial basis functions and the nonlinear model, and the vibration state equation of the elastic aircraft is established according to the nonlinear model and the low-dimensional nonlinear spatio-temporal model, integrating the spatial and time characteristics, constructing an equation that can comprehensively reflect the vibration characteristics of the elastic body in time and space, and providing a reliable basis for subsequent control; the vibration state equation is improved to obtain the improved vibration state equation; a derivable control law is established according to the improved vibration state equation, and the uncertainty in the derivable control law is approximated by constructing a T-S fuzzy model and an adaptive control law is designed. The T-S fuzzy model can effectively approximate the system uncertainty and solve the robustness problems caused by factors such as the change of the aircraft's center of mass, parameter uncertainty, and external disturbances. The adaptive control law can actively adjust the control strategy according to the changes of the system state and uncertainty, thereby realizing the active suppression of the aircraft elastic vibration, solving the robustness problems caused by factors such as the change of the aircraft's center of mass, parameter uncertainty, and external disturbances, and overcoming the deficiency that the conventional robust control method can only passively adapt to the vibration change characteristics.

[0099] In one embodiment, the optimal dimension of the spatial vibration characteristics is determined by a threshold to obtain the spatial basis functions as follows:

[0100] ;

[0101] Wherein, represents the spatial basis function of the i th feature, represents the spatial basis function of the j th feature.

[0102] In one embodiment, based on the spatial basis functions, the system input and output data are mapped in a high-dimensional space to obtain a nonlinear time series, including:

[0103] Map the system input and output data in a high-dimensional space based on spatial basis functions to obtain the non-linear time series as follows:

[0104] ;

[0105] where, represents the output of the sensor at time, represents the i th spatial basis function of the feature.

[0106] In one embodiment, establish corresponding fuzzy rules according to the characteristics of the non-linear time series, and establish a non-linear model based on the fuzzy rules to reconstruct the non-linear time dynamics of the system, including:

[0107] To facilitate the modeling of time coefficients, let , and establish the time series variables as follows:

[0108] ;

[0109] where, is used to characterize the time dynamics of the elastomer at position, that is, the time coefficient;

[0110] Assume represents the fuzzy set of the prior rule variable, let , and establish the corresponding fuzzy rules according to the characteristics of the non-linear time series as: If belongs to the set , belongs to the set , ……, belongs to the set , then ; where, , represents the rule number; represents the non-linear time series of the system at time; represents the input of the system at time; and respectively represent the coefficients of the output at the previous time and the input at the current time;

[0111] Establish the non-linear model based on the fuzzy rules as:

[0112] ;

[0113] where, represents the membership degree of the sth rule function, represents the time coefficient.

[0114] In one embodiment, a low-dimensional non-linear spatio-temporal model of the elastic vibration of an aircraft is obtained based on spatial basis functions and a non-linear model, including:

[0115] The low-dimensional non-linear spatio-temporal model of the elastic vibration of the aircraft obtained based on the spatial basis functions and the non-linear model is:

[0116] ;

[0117] Wherein, represents the spatial basis function of the i th feature, M represents the number of features.

[0118] In one embodiment, a vibration state equation of an elastic aircraft is established based on the non-linear model and the low-dimensional non-linear spatio-temporal model, including:

[0119] The vibration state equation of the elastic aircraft established based on the non-linear model and the low-dimensional non-linear spatio-temporal model is:

[0120] ;

[0121] Wherein, , , represents the time series variable, represents the membership degree of the and respectively represent the coefficients of the output at the previous moment and the input at the current moment, represents the time coefficient, represents the input of the system at the th moment, represents the spatial basis function of the i th feature, M represents the number of features, represents the output of the sensor at the th moment.

[0122] In one embodiment, the vibration state equation is improved to obtain an improved state equation, including:

[0123] The improved state equation obtained by improving the vibration state equation is:

[0124] ;

[0125] Wherein, represents the expected elastic displacement at the th moment, T represents the sampling interval, represents the sum of the internal uncertainty and external disturbance of the system, represents The sliding mode surface at a moment is a constant, representing the coefficient of the exponential reaching term.

[0126] In one embodiment, a derivable control law is established according to the improved vibration state equation, including:

[0127] The derivable control law established according to the vibration state equation is:

[0128] .

[0129] In one embodiment, the T-S fuzzy model is modeled as:

[0130] ;

[0131] where is the sum of the system internal uncertainty and external disturbance H the model estimated value of represents the fuzzy variable and , R represents the number of rules, and there is ; represents the fuzzy posterior coefficient, which can usually be obtained by the least square method, is the prior coefficient of the fuzzy model, representing the membership degree of the sum of the system internal uncertainty and external disturbance in the p th rule.

[0132] In one embodiment, the adaptive control law is designed as:

[0133] ;

[0134] where is the adaptive fuzzy coefficient, represents the spatial basis function of the i th feature, M represents the number of features, , is the prior coefficient of the fuzzy model, represents the fuzzy variable, represents the sliding mode surface at a moment, represents the gain coefficient for adjusting the adaptive control law.

[0135] In a specific embodiment, the stability of this application is proved:

[0136] Define the Lyapunov function as follows:

[0137] ;

[0138] Then there is:

[0139] ;

[0140] Among them, . Then the Lyapunov function difference equation satisfies:

[0141] ;

[0142] When the sampling period T is small enough, and the discrete sliding mode satisfies the existence and reaching conditions, that is:

[0143] .

[0144] This application utilizes the uniform convergence of T-S fuzzy and fully combines the advantages of sliding mode variable structure control in adaptive control, that is, it can quickly reach stability in each cycle, and finally realizes the effective suppression of elastic vibration under unknown terms and external disturbances in the controlled object.

[0145] It should be understood that although Figure 1 the steps in the flowchart of Figure 1 are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear indication in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover,

[0146] In one embodiment, a computer device is provided. The computer device can be a terminal, and its internal structure diagram can be as shown in Figure 3As shown in the figure. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes a data-driven vibration adaptive control method for an elastomer aircraft. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or a button, a trackball, or a touchpad provided on the housing of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0147] Those skilled in the art can understand that Figure 3 the structure shown in the figure is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0148] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0149] The above-described embodiments only represent several implementation manners of this application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of this application, several modifications and improvements can still be made, and these all belong to the protection scope of this application. Therefore, the protection scope of this application should be subject to the appended claims.

Claims

1. A data-driven vibration adaptive control method for an elastomer aircraft, characterized in that, The method includes: Distributing multiple sensors on the surface of the elastomeric aircraft to collect vibration data, extracting spatial vibration features from the vibration data by using the principal component analysis method, and obtaining spatial basis functions by determining the optimal dimension of the spatial vibration features through a threshold; Mapping the system input and output data in a high-dimensional space based on the spatial basis functions to obtain a non-linear time series, establishing corresponding fuzzy rules according to the characteristics of the non-linear time series, and establishing a non-linear model based on the fuzzy rules to reconstruct the non-linear time dynamics of the system; Obtaining a low-dimensional non-linear spatio-temporal model of the aircraft elastic vibration according to the spatial basis functions and the non-linear model, and establishing a vibration state equation of the elastomeric aircraft according to the non-linear model and the low-dimensional non-linear spatio-temporal model; improving the vibration state equation to obtain an improved vibration state equation; Establishing a derivable control law according to the improved vibration state equation, and approximating the uncertainty in the derivable control law by constructing a T-S fuzzy model and designing an adaptive control law to actively suppress the elastic vibration of the aircraft.

2. The method according to claim 1, wherein Obtaining spatial basis functions by determining the optimal dimension of the spatial vibration features through a threshold, including: Obtaining spatial basis functions by determining the optimal dimension of the spatial vibration features through a threshold as: ； Among them, represents the spatial basis function of the i th feature, represents the spatial basis function of the j th feature.

3. The method according to claim 1, characterized in that Mapping the system input and output data in a high-dimensional space based on the spatial basis functions to obtain a non-linear time series, including: Mapping the system input and output data in a high-dimensional space based on the spatial basis functions to obtain a non-linear time series as: ； Among them, represents the output of the sensor at moment, represents the i spatial basis function of the 4. The method according to any one of claims 1 to 3, characterized in that Establishing corresponding fuzzy rules according to the characteristics of the non-linear time series, and establishing a non-linear model based on the fuzzy rules to reconstruct the non-linear time dynamics of the system, including: To facilitate the modeling of the time coefficient, let , and establish the time series variables as follows: ； Among them, used to characterize the time dynamics of the elastomer at the position, that is, the time coefficient; Hypothesis Denote the fuzzy set of the prior rule variable as, and let , and establish the corresponding fuzzy rule according to the characteristics of the non - linear time series as: If belongs to the set , belongs to the set , ……, belongs to the set , then ; where denotes the rule number; denotes the non - linear time series of the system at the moment; denotes the input of the system at the moment; and respectively denote the coefficients of the output at the previous moment and the input at the current moment; Establishing a non-linear model based on the fuzzy rules as: ； Among them, represents the membership degree of the s-th rule function, represents the time coefficient.

5. The method according to claim 4, wherein Obtaining a low-dimensional non-linear spatio-temporal model of the aircraft elastic vibration according to the spatial basis functions and the non-linear model, including: Obtaining a low-dimensional non-linear spatio-temporal model of the aircraft elastic vibration according to the spatial basis functions and the non-linear model as: ； Among them, represents the i spatial basis function of the M th feature, and M represents the number of features.

6. The method according to claim 1, characterized in that, Establishing a vibration state equation of the elastomeric aircraft according to the non-linear model and the low-dimensional non-linear spatio-temporal model, including: Establishing a vibration state equation of the elastomeric aircraft according to the non-linear model and the low-dimensional non-linear spatio-temporal model as: ； Among them, , , represents a timing variable, represents the membership degree of the s-th rule function, and respectively represent the coefficients of the output at the previous moment and the input at the current moment, represents a time coefficient, represents at the input of the system at the moment, represents the i th spatial basis function of the feature, M represents the number of features, represents the output of the sensor at the moment.

7. The method according to claim 6, wherein Improving the vibration state equation to obtain an improved state equation, including: Improving the vibration state equation to obtain an improved state equation as: ； Among them, represents the expected elastic displacement at the moment, T represents the sampling interval, represents the sum of the internal uncertainties and external disturbances of the system, represents the sliding mode surface at the moment, is a constant, representing the coefficient of the exponential reaching term.

8. The method according to claim 7, wherein Establishing a derivable control law according to the improved vibration state equation, including: Establishing a derivable control law according to the vibration state equation as: 。 9. The method according to claim 1, characterized in that, Modeling the T-S fuzzy model as: ； Among them, is the sum of the internal uncertainty of the system and external disturbances H is the model estimated value of represents a fuzzy variable and , R represents the number of rules, and there is ; represents the fuzzy posterior coefficient, obtained by the least squares method, is the prior coefficient of the fuzzy model, representing the membership degree of the p th rule of the sum of the internal uncertainty of the system and external disturbances.

10. The method according to claim 1, characterized in that, The designed adaptive control law is: ； Among them, is the adaptive fuzzy coefficient, represents the spatial basis function of the i th feature, M represents the number of features, , is the prior coefficient of the fuzzy model, represents the fuzzy variable, represents the sliding mode surface at time represents the gain coefficient for adjusting the adaptive control law.

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