Two-stage Adaptive Inverse Control Method and System Based on Fading Kalman Filter

Abstract

The present application relates to a two-stage adaptive inverse control method based on a fading Kalman filter, which includes: inputting a target displacement into an adaptive inverse controller based on a fading Kalman filter to obtain a first commanded displacement; inputting the first commanded displacement into an inverse controller to obtain a second commanded displacement; inputting the second commanded displacement into a controlled object to obtain a measured displacement; the inverse controller is an inverse model of the nominal model of the controlled object, and the controlled object is a system composed of a loading system and a physical substructure; the inverse controller and the controlled object form a new system, and the adaptive inverse controller is an adaptive inverse model of the new system. The present application uses the inverse controller as the primary control to eliminate most of the time delay and reduce the difficulty of parameter identification of the adaptive inverse controller; then uses the adaptive inverse controller based on the fading Kalman filter as the secondary control to achieve dynamic full compensation and effectively improve the accuracy and stability of real-time hybrid tests.

Description

Technical Field

[0001] The present invention relates to the field of engineering structure tests, and particularly to a two-stage adaptive inverse control method and system based on a fading Kalman filter. Background Art

[0002] The real-time hybrid test technology is an effective method for efficiently evaluating the dynamic performance of structures. In real-time hybrid tests, the overall dynamic structure is used as the test object and divided into a numerical substructure and a physical substructure. The former is numerically simulated in a computer, and the latter is physically loaded in a laboratory. The two are connected online through a servo loading system to ensure deformation coordination and force balance between them. This method gives full play to the respective advantages of physical tests and numerical simulations, completes large-scale or even full-scale tests, and greatly reduces test costs and time.

[0003] However, in actual real-time hybrid tests, due to the non-linear dynamic characteristics of the servo loading system, there are inevitably time delays and amplitude errors between the target displacement and the measured displacement. The closed-loop characteristics of real-time hybrid tests will cause the test errors to accumulate continuously, resulting in inaccurate test results, and even instability of the test system, affecting the accuracy and reliability of the test results.

[0004] To address this problem, related technologies adopt an adaptive time-delay compensation method to adapt to time-delay changes, but its performance depends to a large extent on the accuracy of the parameter estimation method. When the time delay is large or the target loading frequency is high, the adaptive time-delay compensation method in related technologies cannot guarantee the convergence of parameters, resulting in low test accuracy and poor stability. Summary of the Invention

[0005] This application provides a two-stage adaptive inverse control method and system based on a fading Kalman filter, which solves the technical problems in related technologies that when the time delay is large or the target loading frequency is high, the existing adaptive time-delay compensation method cannot guarantee the convergence of parameters, resulting in low test accuracy and poor stability.

[0006] In a first aspect, an embodiment of this application provides a two-stage adaptive inverse control method based on a fading Kalman filter, which includes:

[0007] The target displacement d is input into an adaptive inverse controller based on a fading Kalman filter to obtain a first command displacement d1;

[0008] The first command displacement d1 is input into an inverse controller to obtain a second command displacement d c ;

[0009] The second command displacement d c is input into a controlled object to obtain a measured displacement d m ;

[0010] Among them, the inverse controller is the inverse model of the nominal model of the controlled object, and the controlled object is a system composed of a loading system and a physical substructure; the inverse controller and the controlled object form a new system, and the adaptive inverse controller is the adaptive inverse model of the new system.

[0011] Combined with the first aspect, in an implementation manner, the adaptive inverse controller includes a first finite impulse response model connected to the inverse controller, a second finite impulse response model connected to the controlled object, and a fading Kalman filter located between the first finite impulse response model and the second finite impulse response model.

[0012] Combined with the first aspect, in an implementation manner, the target displacement d is input into the adaptive inverse controller based on the fading Kalman filter to obtain a first command displacement d1; it includes:

[0013] The target displacement d is input into the first finite impulse response model to obtain a first command displacement d1;

[0014] The measured displacement d m is input into the second finite impulse response model to obtain a third command displacement d3;

[0015] The first command displacement d1 and the third command displacement d3 are online identified through the fading Kalman filter to obtain model parameter estimation values;

[0016] The model parameter estimation values are respectively updated in real time to the first finite impulse response model and the second finite impulse response model.

[0017] Combined with the first aspect, in an implementation manner, the transfer function of the first finite impulse response model and / or the second finite impulse response model is:

[0018] Among them, d is the input signal of the model; is the estimated value of the model parameter; y is the output signal of the model; Δt is the sampling step; N is the order of the model; W is the model weight parameter vector; X is the input signal vector.

[0019] Combined with the first aspect, in an implementation manner, the state equation and the observation equation of the fading Kalman filter are respectively:

[0020] W i = W i-1 + h i-1 ;

[0021]

[0022] Among them, W is the model weight parameter vector; d 1,i is the first commanded displacement; X is the input signal vector; h is the process noise; ν is the measurement noise.

[0023] Combined with the first aspect, in one implementation, the calculation formula for the fading Kalman filter to perform online identification is:

[0024] P i / i-1 = λ -1 P i-1 + Q;

[0025]

[0026] Among them, the subscript i is the i-th discrete integration step number; λ is the forgetting factor; P is the covariance matrix; K is the Kalman gain; Q is the system noise covariance matrix; R is the measurement noise covariance matrix; I is the identity matrix; is the model identification parameter vector; d 1,i is the first commanded displacement.

[0027] Combined with the first aspect, in one implementation, the nominal model is a zero-free transfer function identified offline based on the input-output data of the controlled object.

[0028] Combined with the first aspect, in one implementation, the order of the nominal model is three or four.

[0029] In the second aspect, an embodiment of the present application provides a two-stage adaptive inverse control system based on a fading Kalman filter, which includes:

[0030] An adaptive inverse control module, configured to: input the target displacement d into an adaptive inverse controller based on a fading Kalman filter to obtain a first commanded displacement d1;

[0031] An inverse control module, configured to: input the first commanded displacement d1 into an inverse controller to obtain a second commanded displacement d c ;

[0032] A control module, configured to: input the second commanded displacement d c into the controlled object to obtain a measured displacement d m ;

[0033] Among them, the inverse controller is the inverse model of the nominal model of the controlled object, and the controlled object is a system composed of a loading system and a physical substructure; the inverse controller and the controlled object form a new system, and the adaptive inverse controller is the adaptive inverse model of the new system.

[0034] In combination with the second aspect, in one embodiment, the adaptive inverse controller includes a first finite impulse response model connected to the inverse controller, a second finite impulse response model connected to the controlled object, and a fading Kalman filter located between the first finite impulse response model and the second finite impulse response model.

[0035] The beneficial effects brought by the technical solutions provided in the embodiments of the present application include:

[0036] The present application provides a two-stage adaptive inverse control method based on a fading Kalman filter. When the time delay is large or the target loading frequency is high, this method uses the inverse controller as the primary control to effectively cancel most of the dynamic characteristics of the controlled object, eliminate most of the time delay, and reduce the parameter identification difficulty of the adaptive inverse controller; then use the adaptive inverse controller based on the fading Kalman filter as the secondary control. The controlled object and the inverse controller form a new system, and the adaptive inverse controller optimizes the overall dynamic response of the new system in an adaptive adjustment manner to achieve dynamic full compensation, effectively improving the accuracy and stability of the real-time hybrid test, and having strong robustness and good control performance. Description of the Drawings

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0038] Figure 1 It is a schematic flowchart of a two-stage adaptive inverse control method based on a fading Kalman filter in an embodiment of the present invention.

[0039] Figure 2 It is a schematic block diagram of a two-stage adaptive inverse control method based on a fading Kalman filter in an embodiment of the present invention.

[0040] Figure 3 It is a schematic diagram of the principle of a real-time hybrid test in an embodiment of the present invention.

[0041] Figure 4 It is a scatter plot of the target displacement - measured displacement of the real-time hybrid test under different control conditions in an embodiment of the present invention.

[0042] In the figure: 1. Controlled object; 10. Numerical substructure; 11. Loading system; 12. Physical substructure; 2. Inverse controller; 3. Adaptive inverse controller; 31. First finite impulse response model; 32. Second finite impulse response model; 33. Fading Kalman filter. Detailed Embodiments

[0043] To enable those skilled in the art to better understand the solution of this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this application.

[0044] The embodiments of this application provide a two - stage adaptive inverse control method and system based on a fading Kalman filter, which can solve the technical problem that in the related art, when the time delay is large or the target loading frequency is high, the existing adaptive time - delay compensation method cannot ensure the convergence of parameters, resulting in low control accuracy of the experiment, and is applicable to the fields of civil engineering, vehicle, bridge, aerospace, etc.

[0045] Referring to Figure 1 and Figure 2 , where Figure 1 is a schematic flowchart of a two - stage adaptive inverse control method based on a fading Kalman filter in an embodiment of the present invention. Figure 2 is a schematic block diagram of a two - stage adaptive inverse control method based on a fading Kalman filter in an embodiment of the present invention.

[0046] This embodiment provides a two - stage adaptive inverse control method based on a fading Kalman filter, including the following steps:

[0047] Step S1: The target displacement d is input into the adaptive inverse controller 3 based on the fading Kalman filter 33 to obtain the first command displacement d1;

[0048] Step S2: The first command displacement d1 is input into the inverse controller 2 to obtain the second command displacement d c ;

[0049] Step S3: The second command displacement d c is input into the controlled object 1 to obtain the measured displacement d m ;

[0050] Among them, the inverse controller 2 is the inverse model of the nominal model of the controlled object 1, and the controlled object 1 is a system composed of a loading system 11 and a physical sub - structure 12; the inverse controller 2 and the controlled object 1 form a new system, and the adaptive inverse controller 3 is the adaptive inverse model of the new system.

[0051] This embodiment provides a two - stage adaptive inverse control method based on a fading Kalman filter. When the time delay is large or the target loading frequency is high, this method uses the inverse controller as the primary control to effectively cancel most of the dynamic characteristics of the controlled object, eliminate most of the time delay, and reduce the difficulty of parameter identification of the adaptive inverse controller. Then, the adaptive inverse controller based on the fading Kalman filter is used as the secondary control. The controlled object and the inverse controller form a new system, and the adaptive inverse controller optimizes the overall dynamic response of the new system in an adaptive adjustment manner to achieve dynamic full compensation, effectively improving the accuracy and stability of real - time hybrid tests, and having strong robustness and good control performance.

[0052] The following elaborates on each step in detail.

[0053] As Figure 2 shown, in one embodiment, the adaptive inverse controller 3 includes a first finite impulse response model 31 connected to the inverse controller 2, a second finite impulse response model 32 connected to the controlled object 1, and a fading Kalman filter 33 located between the first finite impulse response model 31 and the second finite impulse response model 32.

[0054] Through the above - mentioned scheme, an adaptive inverse model is established according to the new system (i.e., the system jointly composed of the controlled object 1 and the inverse controller 2), and the adaptive inverse controller 3 is connected in series to the input end of the new system to further control the dynamic characteristics of the controlled object 1.

[0055] The first finite impulse response model 31 and the second finite impulse response model 32 adopt finite impulse response (Finite Impulse Response, abbreviated as FIR), that is, the FIR model.

[0056] In one embodiment, the transfer function of the first finite impulse response model 31 and / or the second finite impulse response model 32 is:

[0057] where d is the input signal of the model; is the estimated value of the model parameters; y is the output signal of the model; Δt is the sampling step; N is the order of the model; W is the model weight parameter vector; X is the input signal vector.

[0058] Through the above - mentioned scheme, where N represents the order of the model and also represents the number of parameters. By using the FIR model, more parameters (such as 10) can be taken, the model is more accurate, and a better effect of eliminating time delay can be obtained.

[0059] In one embodiment, step S1: The target displacement d is input into the adaptive inverse controller 3 based on the fading Kalman filter 33 to obtain the first command displacement d1, including:

[0060] Step S11: The target displacement d is input into the first finite impulse response model 31 to obtain the first command displacement d1.

[0061] Step S12: The measured displacement d m is input into the second finite impulse response model 32 to obtain the third command displacement d3.

[0062] Step S13: The first command displacement d1 and the third command displacement d3 are online identified by the fading Kalman filter 33 to obtain the model parameter estimation values.

[0063] Step S14: The model parameter estimation values are respectively updated in real time to the first finite impulse response model 31 and the second finite impulse response model 32.

[0064] Through the above scheme, an adaptive inverse model is established according to the new system (i.e., the system jointly composed of the controlled object 1 and the inverse controller 2), and the adaptive inverse controller 3 is connected in series to the input end of the new system to further control the dynamic characteristics of the controlled object 1. Based on the fading Kalman filter 33 for online identification and continuously updating the model parameter estimation values in real time, and repeating in a cycle, further eliminating the remaining time delay of the system and achieving dynamic full compensation.

[0065] In one embodiment, the state equation and the observation equation of the fading Kalman filter 33 are respectively:

[0066] W i = W i-1 + h i-1 ;

[0067]

[0068] where W is the model weight parameter vector; d 1,i is the first command displacement; X is the input signal vector; h is the process noise; ν is the measurement noise.

[0069] Through the above scheme, the state equation and the observation equation are respectively used to describe the change process of the system state and the relationship between the observed quantity and the system state.

[0070] In one embodiment, the calculation formula for the online identification of the fading Kalman filter 33 is:

[0071] P i / i-1 = λ -1 P i-1 + Q;

[0072]

[0073] Wherein, the subscript i is the i-th discrete integration step number; λ is the forgetting factor, and its value range is 0.95 < λ < 1; P is the covariance matrix; Q is the system noise covariance matrix; X is the input signal vector; R is the measurement noise covariance matrix; K is the Kalman gain; I is the identity matrix; is the model identification parameter vector; d 1,i is the first command displacement.

[0074] When performing online identification through the fading Kalman filter 33, it specifically includes the following steps:

[0075] 1. Directly set the values of the system noise covariance matrix Q, the measurement noise covariance matrix R, the forgetting factor λ, as well as the initial values of the covariance matrix P and the model identification parameter vector ;

[0076] 2. Input a set of input signal vectors X (i.e., the measured displacement vector) at the i-th step, the first-order command displacement d1, and the model identification parameter vector at the (i - 1)-th step (i.e., the third-order command displacement d3); calculate the model identification parameter vector and the covariance matrix P at the i-th step according to the above formula;

[0077] 3. The calculated model identification parameter vector at the i-th step is used to update the model parameter estimation value of the adaptive inverse controller 3, that is, the model weight parameter vector W.

[0078] 4. Based on the model identification parameter vector and the covariance matrix P at the i-th step, as well as a set of input signal vectors X (i.e., the measured displacement vector) and the first-order command displacement d1 output at the (i + 1)-th step, calculate the model identification parameter vector and the covariance matrix P at the (i + 1)-th step, form a closed loop, and repeat the cycle throughout the entire real-time hybrid test process.

[0079] Through the above solution, the adopted fading Kalman filter adjusts the forgetting factor, increases the prediction error covariance matrix, increases the utilization weight of new observation data, improves the modeling accuracy of the adaptive inverse controller 3 (i.e., the adaptive inverse model), and then realizes the dynamic full compensation effect and also avoids model divergence.

[0080] In step S2, the first command displacement d1 is input into the inverse controller 2 to obtain the second command displacement d c .

[0081] The inverse controller 2 is the inverse model of the nominal model of the controlled object 1.

[0082] In one embodiment, the nominal model is a zero-free transfer function identified offline according to the input-output data of the controlled object 1.

[0083] In one embodiment, the order of the nominal model is three or four.

[0084] Through the above solution, an inverse model of a higher order is established, enabling the system to have a higher frequency bandwidth, thereby realizing the compensation of higher frequency signals.

[0085] As Figure 3 shown, Figure 3 is a schematic diagram of the principle of real-time hybrid testing in one embodiment of the present invention.

[0086] In one embodiment, a high-speed train is used as the test object for real-time hybrid testing, which is divided into a numerical substructure 10 and a physical substructure 12. Among them, the physical substructure 12 is the test piece, specifically an anti-hunting damper of the front bogie of the high-speed train. The physical loading is carried out by an actuator as the loading system 11. The system composed of the loading system 11 and the physical substructure 12 is defined as the controlled object 1; the remaining car body system is used as the numerical substructure 10 for numerical simulation by computer modeling.

[0087] In real-time hybrid testing, the excitation input is the track irregularity in the Wuhan-Guangzhou line direction, and the numerical substructure 10 performs simulation calculations to obtain the target displacement d at the i-th step.

[0088] According to the method provided in the embodiments of the present application:

[0089] Step S1: The target displacement d is input into the adaptive inverse controller 3 based on the fading Kalman filter 33 to obtain the first command displacement d1.

[0090] Among them, the transfer function form of the FIR model of the adaptive inverse controller 3 is:

[0091]

[0092] Step S2: The first command displacement d1 is input into the inverse controller 2 to obtain the second command displacement d c .

[0093] Among them, the inverse controller 2 is the inverse model of the nominal model of the controlled object 1.

[0094] Specifically, a swept-frequency signal with a frequency of 0-20 Hz, an amplitude of 5 mm, and a duration of 60 s is used as the input data of the controlled object 1 to obtain the measured displacement of the physical substructure 12. Based on the target displacement and the measured displacement, offline identification is performed using the MATLAB toolbox to obtain the fourth-order nominal model G0 of the controlled object 1:

[0095]

[0096] Among them, b = 4.7942×10 8, a1 = 560.7883, a2 = 1.5536×10 5 , a3 = 1.1288×10 7 , a4 = 5.0814×10 8 ; s is the Laplace operator.

[0097] The inverse model corresponding to the nominal model is:

[0098]

[0099] where u is the input signal of the inverse controller; y is the output signal of the inverse controller, and u (j) is the j-th discrete derivative of u.

[0100] Step S3. The second commanded displacement d c is input into the controller of the loading system 11 of the controlled object 1. The controller of the loading system 11 drives the loading system 11 to load the physical substructure 12 to implement this command;

[0101] The measured displacement d is collected in real time through a collection device (such as a sensor) m and the measured force f m ; The measured force f m is fed back to the numerical substructure 10 for the operation of the next integration step to solve the target displacement d at the (i + 1)-th step; The measured displacement d m is input into the adaptive inverse controller 3 for parameter estimation.

[0102] As Figure 4 shown, Figure 4 This is the scatter plot of the target displacement - measured displacement under different control conditions in an embodiment of the present invention for real-time hybrid testing.

[0103] All use high-speed trains as the test objects for real-time hybrid testing. The physical substructure 12 is specifically an anti-hunting damper of the front bogie of a high-speed train. Physical loading is carried out by an actuator as the loading system 11. The system composed of the loading system 11 and the physical substructure 12 is defined as the controlled object 1; The running speed of the high-speed train is set to 500 km / h.

[0104] The first control condition is: the inverse control method (Inverse Control, abbreviated as the IC method).

[0105] The specific process is: After the target displacement d is input into the inverse controller and then into the controlled object, the measured displacement is obtained. The inverse controller 2 is the inverse model of the nominal model of the controlled object 1.

[0106] The second control condition is: the Fading Kalman Filter-based Two-stage Adaptive Inverse Control method (FKF-TAIC method for short) provided by the embodiments of the present application.

[0107] As Figure 4 shown, compared with the IC method, the scatter plot of the target displacement and the measured displacement of the real-time hybrid test obtained by the FKF-TAIC method provided by the embodiments of the present application is closer to the "diagonal line", which indicates that the method provided by the embodiments of the present application has more excellent control performance, higher accuracy and better stability in the real-time hybrid test, and has strong robustness.

[0108] In a second aspect, the embodiments of the present application provide a two-stage adaptive inverse control system based on a fading Kalman filter, which includes:

[0109] An adaptive inverse control module, configured to: input the target displacement d into the adaptive inverse controller 3 based on the fading Kalman filter 33 to obtain the first command displacement d1;

[0110] An inverse control module, configured to: input the first command displacement d1 into the inverse controller 2 to obtain the second command displacement d c ;

[0111] A control module, configured to: input the second command displacement d c into the controlled object 1 to obtain the measured displacement d m ;

[0112] Wherein, the inverse controller 2 is the inverse model of the nominal model of the controlled object 1, and the controlled object 1 is a system composed of a loading system 11 and a physical substructure 12; the inverse controller 2 and the controlled object 1 form a new system, and the adaptive inverse controller 3 is the adaptive inverse model of the new system.

[0113] In one embodiment, the adaptive inverse controller 3 includes a first finite impulse response model 31 connected to the inverse controller 2, a second finite impulse response model 32 connected to the controlled object 1, and a fading Kalman filter 33 located between the first finite impulse response model 31 and the second finite impulse response model 32.

[0114] Wherein, the function implementation of each module in the above two-stage adaptive inverse control system based on a fading Kalman filter corresponds to each step in the embodiment of the above two-stage adaptive inverse control method based on a fading Kalman filter, and its function and implementation process will not be elaborated here one by one.

[0115] It should be noted that the serial numbers of the embodiments of the present application above are only for description and do not represent the superiority or inferiority of the embodiments. The terms "including" and "having" and any variations thereof in the description of the specification, claims and drawings of the present application are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes steps or units not listed, or optionally further includes other steps or units inherent to these processes, methods, products or devices. The descriptions with terms such as "first", "second" and "third" are used to distinguish different objects, etc., and do not represent the order of precedence, nor do they limit that "first", "second" and "third" are different types.

[0116] In the description of the embodiments of the present application, "exemplary", "for example" or "for instance" are used to indicate examples, illustrations or explanations. Any embodiment or design solution described as "exemplary", "for example" or "for instance" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary", "for example" or "for instance" is intended to present the relevant concepts in a specific manner.

[0117] In the description of the embodiments of the present application, unless otherwise specified, " / " means "or". For example, A / B may mean A or B; "and / or" in the text is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of the present application, "a plurality of" means two or more than two.

[0118] In some processes described in the embodiments of the present application, there are multiple operations or steps that appear in a specific order. However, it should be understood that these operations or steps may not be executed in the order in which they appear in the embodiments of the present application or may be executed in parallel. The serial numbers of the operations are only used to distinguish different operations, and the serial numbers themselves do not represent any order of execution. In addition, these processes may include more or fewer operations, and these operations or steps may be executed in order or in parallel, and these operations or steps can be combined.

[0119] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product is stored in a storage medium as described above (such as ROM / RAM, magnetic disk, optical disk), and includes several instructions for causing a terminal device to execute the methods described in the various embodiments of the present application.

[0120] The above are only the preferred embodiments of the present application, and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, is similarly included in the patent protection scope of the present application.

Claims

1. A two-stage adaptive inverse control method based on a fading Kalman filter, characterized in that: It includes: The target displacement d is input into an adaptive inverse controller (3) based on a fading Kalman filter (33) to obtain a first command displacement d1; The first command displacement d1 is input into the inverse controller (2) to obtain the second command displacement d c ; The second command displacement d c Input the controlled object (1) to obtain the measured displacement d m ; The inverse controller (2) is an inverse model of a nominal model of a controlled object (1), and the controlled object (1) is a system composed of a loading system (11) and a physical substructure (12); the inverse controller (2) and the controlled object (1) form a new system, and the adaptive inverse controller (3) is an adaptive inverse model of the new system; The adaptive inverse controller (3) comprises a first finite impulse response model (31) connected to the inverse controller (2), a second finite impulse response model (32) connected to the controlled object (1), and a fading Kalman filter (33) located between the first finite impulse response model (31) and the second finite impulse response model (32).

2. The two-stage adaptive inverse control method based on the fading Kalman filter according to claim 1, characterized in that: The target displacement d is input into an adaptive inverse controller (3) based on a fading Kalman filter (33) to obtain a first command displacement d1; comprising: The target displacement d is input into the first finite impulse response model (31) to obtain a first command displacement d1; The measured displacement d m Inputting the second finite impulse response model (32) to obtain a third command displacement d3; The first command displacement d1 and the third command displacement d3 are identified online by the fading Kalman filter (33) to obtain model parameter estimation values; The model parameter estimation values ​​are updated in real time to the first finite impulse response model (31) and the second finite impulse response model (32).

3. The two-stage adaptive inverse control method based on the fading Kalman filter according to claim 1, characterized in that: The transfer function of the first finite impulse response model (31) and / or the second finite impulse response model (32) is: Among them, d is the input signal of the model; is the estimated value of the model parameters; y is the output signal of the model; Δt is the sampling step; N is the order of the model; W is the model weight parameter vector; X is the input signal vector.

4. The two-stage adaptive inverse control method based on the fading Kalman filter according to claim 2, characterized in that: The state equation and observation equation of the fading Kalman filter (33) are respectively: W i =W i-1 +h i-1 ; Where W is the model weight parameter vector; d 1,i is the first command displacement; X is the input signal vector; h is the process noise; ν is the measurement noise.

5. The two-stage adaptive inverse control method based on the fading Kalman filter according to claim 4, characterized in that: The calculation formula for online identification by the fading Kalman filter (33) is: P ii-1 =λ -1 P i-1 +Q; Wherein, the subscript i is the number of the ith discrete integration step; λ is the forgetting factor; P is the covariance matrix; K is the Kalman gain; Q is the system noise covariance matrix; R is the measurement noise covariance matrix; I is the identity matrix; is the model identification parameter vector; d 1,i is the first command displacement.

6. The two-stage adaptive inverse control method based on the fading Kalman filter according to claim 1, characterized in that: The nominal model is a transfer function without zero points identified offline based on the input and output data of the controlled object (1).

7. The two-stage adaptive inverse control method based on the fading Kalman filter according to claim 6, characterized in that: The order of the nominal model is third order or fourth order.

8. A two-stage adaptive inverse control system based on a fading Kalman filter, characterized in that: It includes: The adaptive inverse control module is configured to: input the target displacement d into an adaptive inverse controller (3) based on a fading Kalman filter (33) to obtain a first command displacement d1; The inverse control module is configured to: input the first command displacement d1 into the inverse controller (2) to obtain the second command displacement d c ; The control module is configured to: the second command displacement d c Input the controlled object (1) to obtain the measured displacement d m ; The inverse controller (2) is an inverse model of a nominal model of a controlled object (1), and the controlled object (1) is a system composed of a loading system (11) and a physical substructure (12); the inverse controller (2) and the controlled object (1) form a new system, and the adaptive inverse controller (3) is an adaptive inverse model of the new system; The adaptive inverse controller (3) comprises a first finite impulse response model (31) connected to the inverse controller (2), a second finite impulse response model (32) connected to the controlled object (1), and a fading Kalman filter (33) located between the first finite impulse response model (31) and the second finite impulse response model (32).

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