Data-driven elastomer aircraft vibration adaptive control method

Abstract

The invention relates to a data-driven elastomer aircraft vibration adaptive control method. The method comprises the following steps: extracting spatial vibration characteristics from vibration data by using a principal component analysis method, and determining an optimal dimension of the spatial vibration characteristics through a threshold value to obtain a spatial basis function; establishing a corresponding fuzzy rule based on the space basis function, establishing a nonlinear model based on the fuzzy rule to reconstruct the nonlinear time dynamic state of the system, obtaining a low-dimensional nonlinear space-time model of the elastic vibration of the aircraft, and establishing a vibration state equation of the elastomer aircraft; a vibration state equation is improved, a derivable control law is established according to the improved vibration state equation, a T-S fuzzy model is constructed to approach uncertainty in the derivable control law, and an adaptive control law is designed to actively suppress elastic vibration of the aircraft. By adopting the method, the vibration of the elastomer aircraft can be actively inhibited.

Description

Technical Field

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

[0002] With the continuous improvement of the requirements for flight speed, maneuverability, and range, the shape of aircraft represented by missiles is becoming more and more 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. It is very easy to generate obvious lateral bending vibrations during both the launch stage and the flight process, which has a great impact on the normal operation of the 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 the vibration suppression strategy and controller design.

[0003] The elastic vibration of an elastomeric aircraft is a highly spatiotemporally coupled nonlinear dynamic process. The modeling methods for spatiotemporally coupled 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 spatiotemporal 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 through 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, these conventional robust control methods can only passively adapt to the changing characteristics of vibration and cannot effectively suppress vibration from an active level. The 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, 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 in view of the above technical problems.

[0006] A data-driven vibration adaptive control method for an elastomeric aircraft, the method includes: 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 a threshold; 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; Obtain a low-dimensional non-linear spatio-temporal model of the aircraft's elastic vibration based on the spatial basis functions and the non-linear model, and establish a vibration state equation for the elastomeric aircraft according to 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; 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.

[0007] The above-mentioned data-driven vibration adaptive control method for an elastomeric aircraft 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 elastomeric 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, thus providing a reliable basis for active suppression. Finally, a low-dimensional nonlinear spatio-temporal model of the aircraft elastic vibration is obtained based on the spatial basis functions 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 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 in 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 FIG. is a schematic flow chart of a data-driven vibration adaptive control method for an elastomeric aircraft in an embodiment; Figure 2 FIG. is a schematic overall framework diagram of a vibration control method for an elastomeric aircraft in an embodiment; Figure 3 FIG. is an internal structure diagram of a computer device in an embodiment. DETAILED IMPLEMENTATION MANNER

[0009] To make the objectives, technical solutions and advantages of this application more clear and understandable, 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 only used to explain this application and are not used to limit this application.

[0010] 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 principal component analysis method is used to extract the main vibration characteristics of the system, and a function representing the main vibration modes of the elastomer in space, that is, the spatial basis function, is obtained; then, the original vibration equation is projected onto the basis function space, and by 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: 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.

[0011] 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 time. 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: (1) 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, the spatial mapping function is used to linearly map the non-linear sample data in the low-dimensional space in 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 is 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: (2) Among them, represents the width parameter of the Gaussian kernel function. Assuming that the sample is mapped in the new coordinate system as , the error before and after the projection of the original data is: (3) Among them, represents a set of orthogonal bases in the new coordinate system after the projection transformation.

[0012] The core problem here is to find a set of basis functions that meet the conditions and satisfy . The following quadratic optimization problem can be constructed from the above process: (4) (5) Using the Lagrange multiplier method, the objective function can be transformed into: (6) Let , and a set of basis functions that meet the conditions can be obtained: (7) Among them, represents a set of orthogonal basis functions in the high-dimensional space after mapping that satisfy . The corresponding orthogonal basis functions for the first M minimum eigenvalues can be obtained by the following formula: (8) represents the dimensionality reduction threshold. Therefore, for the original sample , the th coordinate after projection is: (9) Among them, ; represents the column vector of the spatial basis function .

[0013] Through the non-linear mapping of spatio-temporal data and the dimensionality reduction of the high-dimensional feature space, the spatial basis function can be obtained as follows: (10) Finally, the system output can be approximated as the following M-order model: (11) Based on the basis functions in the finite-dimensional space of Equation (9), mapping the system input and output data in this high-dimensional space can obtain the time coefficients that characterize the system's non-linear time series.

[0014] It can be known from the orthogonality of the space basis functions that: (12) Step 104: Based on the space 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 corresponding fuzzy rules, and based on the fuzzy rules, establish a non-linear model to reconstruct the non-linear time dynamics of the system.

[0015] Based on the above-mentioned finite-dimensional space 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, corresponding fuzzy rules are established, and a non-linear model based on the fuzzy algorithm is proposed to reconstruct the non-linear time dynamics of the system.

[0016] According to the idea of space-time separation, projecting the elastic vibration data onto the kernel function can obtain the time coefficients that characterize the time dynamics of the system: (13) To facilitate the modeling of the time coefficients, let , and establish the time series variables as follows: (14) Among them, is used to characterize the time dynamics of the elastic body at 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 the input at d time moments, which is in line with the actual situation. Assume that represents the fuzzy set of the prior rule variable, and let , and establish the following fuzzy rules: Rule s: If is and is and … and is ; Then ; Among them, , represents the rule number; represents the non-linear time dynamics of the system at time moment, that is, the non-linear time series; represents the system at Input at a moment; and respectively represent the output of the previous moment and the coefficient of the input at this moment. Usually, the bias term , parameter and can be solved according to the Least Square method (LS).

[0017] Thus, the time coefficient model of elastic vibration can be constructed as follows: (15) where represents the membership degree of the s-th rule function; is the membership function; ; (16) represents the width parameter of the

[0018] th fuzzy set.

[0019] Step 106: Obtain the low-dimensional nonlinear spatio-temporal model of the elastic vibration of the aircraft according to the spatial basis function and the nonlinear model, and establish the vibration state equation of the elastic aircraft according to the nonlinear model and the low-dimensional nonlinear spatio-temporal model; improve the vibration state equation to obtain the improved vibration state equation. (17) From equations (15) and (17), the vibration state equation of the elastic aircraft can be established as follows: (18) It can be further transformed into: (19) where , ; However, considering the influence of complex uncertain factors such as the change of the aircraft's center of mass, data noise, and external disturbances, the parameters in model (19) will have a certain degree of perturbation. That is: (20) After arrangement, it is obtained: (21) where represents the sum of the internal uncertainty of the system and external disturbances.

[0020] Step 108: Establish a derivable control law based on 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.

[0021] Define the sliding surface , then there is (22) Based on the constant velocity reaching law , where T represents the sampling interval. Then there is: (23) Here, The value of can be predicted by the linear extrapolation method, that is . Usually, for vibration suppression control, The value of 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: (24) Here, since The upper bound of is unknown. Combining the adaptive idea, establish an Adaptive T-S fuzzy model of. Similarly, the T-S fuzzy model is built as follows: (25) Among them, Is the model estimated value of H , Represents the fuzzy variable 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: (26) Here, Is the membership function. For the sake of convenience of representation, the following variables are defined: , ; Among them, Is the adaptive fuzzy coefficient; Is the vector related to the fuzzy. M And N Are r-dimensional diagonal matrices, satisfying , ; Then, formula (25) is further transformed into: (27) For the above fuzzy model, taking the parameter as an example, its optimal value satisfies: (28) where , is the approximation error and there is . Let , there is: (29) Therefore, the control law can be further transformed into: (30) And design the adaptive control law as follows: .

[0022] By constructing a T-S fuzzy model, the uncertainties in the derivable control law are approximated and an adaptive control law is designed. The T-S fuzzy model can effectively approximate the system uncertainties, solve the robustness problems caused by the changes in the center of mass of the aircraft, parameter uncertainties, and external disturbances, etc. The adaptive control law can actively adjust the control strategy according to the changes in the system state and uncertainties, so as to achieve the active suppression of the elastic vibration of the aircraft, solve the robustness problems caused by the changes in the center of mass of the aircraft, parameter uncertainties, and external disturbances, etc., and overcome the deficiency that the conventional robust control methods can only passively adapt to the vibration change characteristics.

[0023] In the above data-driven vibration adaptive control method for elastomeric aircraft, this 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 elastomeric aircraft vibration, clarifies the main modes of vibration in the spatial dimension, and lays a foundation for subsequent establishment of 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. 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, thus providing a reliable basis for 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 elastomeric aircraft is established based on 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 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.

[0024] In one embodiment, the optimal dimension of the spatial vibration characteristics is determined through a threshold to obtain the spatial basis function as: ; Wherein, represents the spatial basis function of the i th feature, represents the spatial basis function of the j th feature.

[0025] In one embodiment, based on the spatial basis function, the system input and output data are mapped in a high-dimensional space to obtain a nonlinear time series, including: Based on the spatial basis function, the system input and output data are mapped in a high-dimensional space to obtain a nonlinear time series as: ; Among them, represents the output of the sensor at moment, represents the spatial basis function of the i th feature.

[0026] In one embodiment, corresponding fuzzy rules are established according to the characteristics of the non-linear time series, and a non-linear model is established 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 variable as follows: ; Among them, is used to characterize the time dynamics of the elastomer at position, that is, the time coefficient; Assume that represents the fuzzy set of the prior rule variable, 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 ; Among them, , represents the rule number; represents the non-linear time series of the system at moment; represents the input of the system at moment; and respectively represent the coefficients of the output at the previous moment and the input at the current moment; Establish a non-linear model based on the fuzzy rule as: ; Among them, represents the membership degree of the sth rule function, represents the time coefficient.

[0027] In one embodiment, a low-dimensional non-linear spatio-temporal model of the elastic vibration of the aircraft is obtained according to the spatial basis function and the non-linear model, including: The low-dimensional non-linear spatio-temporal model of the elastic vibration of the aircraft obtained according to the spatial basis function and the non-linear model is: ; Among them, Denote the i spatial basis function of the M i

[0028] In one embodiment, the vibration state equation of the elastomeric aircraft is established according to the nonlinear model and the low-dimensional nonlinear spatio-temporal model, including: The vibration state equation of the elastomeric aircraft established according to the nonlinear model and the low-dimensional nonlinear spatio-temporal model is: ; where , , denotes the time series variable, denotes the membership degree of the and respectively denote the coefficients of the output at the previous moment and the input at the current moment, denotes the time coefficient, denotes the input of the system at the moment, denotes the i spatial basis function of the M i denotes the output of the sensor at the moment.

[0029] In one embodiment, the vibration state equation is improved to obtain the improved state equation, including: The vibration state equation is improved to obtain the improved state equation as: ; where denotes the desired elastic displacement at the moment, T denotes the sampling interval, denotes the sum of the internal uncertainty and external disturbance of the system, denotes the sliding mode surface at the moment,

[0030] In one embodiment, the derivable control law is established according to the improved vibration state equation, including: The derivable control law established according to the vibration state equation is: .

[0031] In one embodiment, the T-S fuzzy model is modeled as: ; where is the sum of the internal uncertainties and external disturbances of the system H is the model estimated value, represents a 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 squares method, is the prior coefficient of the fuzzy model, representing the membership degree of the sum of the internal uncertainties and external disturbances of the system for the p th rule.

[0032] In one of the embodiments, the adaptive control law is designed as: ; wherein, 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.

[0033] In a specific embodiment, the stability of the present application is proved: Define the Lyapunov function as follows: ; then there is: ; wherein, . Then the difference equation of the Lyapunov function satisfies: ; When the sampling period T is small enough, and the discrete sliding mode satisfies the existence and reachability conditions, that is: .

[0034] The present 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 effectively suppresses the elastic vibration under unknown terms and external disturbances in the control object.

[0035] It should be understood that although Figure 1The steps in the flowchart are shown sequentially according to the arrows, but these steps are not necessarily executed sequentially in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 at least some of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least some of the sub-steps or stages of other steps or other steps.

[0036] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as shown in Figure 3 . 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 a computer program. The internal memory provides an environment for the operation of the operating system and the computer program 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 implements a data-driven vibration adaptive control method for an elastomer aircraft. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device may be a touch layer covering the display screen, or a button, a trackball, or a touchpad provided on the outer shell of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0037] Those skilled in the art can understand that Figure 3 the structure shown in 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 a different component layout.

[0038] 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 to be within the scope described in this specification.

[0039] The above-described embodiments merely represent several implementation manners of the present application. The description thereof 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 the present application, several modifications and improvements can still be made, and these all fall within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims

1. A data-driven adaptive vibration control method for an elastic body aircraft, characterized in that: The method comprises: Distributing multiple sensors on the surface of the elastic body aircraft to collect vibration data, extracting spatial vibration features from the vibration data using a principal component analysis method, and obtaining a spatial basis function by determining an optimal dimension of the spatial vibration features through a threshold; Based on the spatial basis function, the input and output data of the system are mapped in a high-dimensional space to obtain a nonlinear time series, corresponding fuzzy rules are established according to the characteristics of the nonlinear time series, and a nonlinear model is established based on the fuzzy rules to reconstruct the nonlinear time dynamics of the system; A low-dimensional nonlinear space-time model of the elastic vibration of the aircraft is obtained according to the spatial basis function and the nonlinear model, and a vibration state equation of the elastic body aircraft is established according to the nonlinear model and the low-dimensional nonlinear space-time model; the vibration state equation is improved to obtain an improved vibration state equation; A derivable control law is established based on the improved vibration state equation, and the uncertainty in the derivable control law is approximated by constructing a TS fuzzy model and an adaptive control law is designed to actively suppress the elastic vibration of the aircraft.

2. The method according to claim 1, characterized in that Determining the optimal dimension of the spatial vibration feature through a threshold value to obtain a spatial basis function includes: determining the optimal dimension of the spatial vibration feature through a threshold value to obtain a spatial basis function as: in, Indicates i The spatial basis functions of the features, Indicates j The spatial basis functions of the features.

3. The method according to claim 1, characterized in that Based on the spatial basis function, the system input and output data are mapped in high-dimensional space to obtain nonlinear time series, including: Based on the spatial basis function, the system input and output data are mapped in high-dimensional space, and the nonlinear time series is obtained as follows: in, Indicates that the sensor is Output at the moment, Indicates i The spatial basis functions of the features.

4. The method according to any one of claims 1 to 3, characterized in that: According to the characteristics of the nonlinear time series, corresponding fuzzy rules are established, and based on the fuzzy rules, a nonlinear model is established to reconstruct the nonlinear time dynamics of the system, including: To facilitate modeling of the time coefficient, let , and establish the time series variables as follows: in, For characterization of elastomers the temporal dynamics of the position, i.e. the temporal coefficient; Assumptions Represents the fuzzy set of prior rule variables, let According to the characteristics of the nonlinear time series, the corresponding fuzzy rules are established as follows: Belongs to the collection , Belongs to the collection ,……, Belongs to the collection ,So ;in, , Indicates the rule number; Indicates that the system is Nonlinear time series of moments; Indicates that the system is Input of time; and Respectively represent the coefficients of the output at the previous moment and the input at the current moment; The nonlinear model based on fuzzy rules is: in, represents the membership of the sth rule function, Represents the time coefficient.

5. The method according to claim 4, characterized in that According to the spatial basis function and nonlinear model, a low-dimensional nonlinear space-time model of the elastic vibration of the aircraft is obtained, including: According to the spatial basis function and nonlinear model, the low-dimensional nonlinear space-time model of the elastic vibration of the aircraft is obtained as follows: in, Indicates i The spatial basis functions of the features, M Indicates the number of features.

6. The method according to claim 1, characterized in that The vibration state equation of the elastic body aircraft is established according to the nonlinear model and the low-dimensional nonlinear space-time model, including: The vibration state equation of the elastic body aircraft is established based on the nonlinear model and the low-dimensional nonlinear space-time model: in, , , represents a time series variable, represents the membership of the sth rule function, and Respectively represent the coefficients of the output at the previous moment and the input at the current moment, represents the time coefficient, Indicates that the system is Input at the moment, Indicates i The spatial basis functions of the features, M represents the number of features, Indicates that the sensor is Output at the moment.

7. The method according to claim 6, characterized in that The vibration state equation is improved to obtain an improved state equation, including: The vibration state equation is improved to obtain the improved state equation: in, express The expected elastic displacement at time, T represents the sampling interval, represents the sum of the internal uncertainty and external disturbance of the system, express The sliding surface at time, is a constant representing the coefficient of the exponential approach term.

8. The method according to claim 7, characterized in that According to the improved vibration state equation, a derivable control law is established, including: According to the vibration state equation, the control law can be derived as follows: 。 9. The method according to claim 1, characterized in that: Modeling TS fuzzy model is: in, It is the sum of the internal uncertainty of the system and the external disturbance H The model estimate of represents a fuzzy variable and , R represents the number of rules, and there are ; represents the fuzzy posterior coefficient, obtained using the least squares method, is the prior coefficient of the fuzzy model, which represents the sum of the internal uncertainty and external disturbance of the system. p The membership degree of a rule.

10. The method according to claim 1, characterized in that The designed adaptive control law is: in, is the adaptive fuzzy coefficient, Indicates i The spatial basis functions of the features, M represents the number of features, , is the prior coefficient of the fuzzy model, represents the fuzzy variable, express The sliding surface at time, Represents the gain coefficient for adjusting the adaptive control law.

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