Six-degree-of-freedom vibration table self-disturbance control method, system, terminal and medium

Abstract

The present invention discloses a six-degree-of-freedom vibration table auto-disturbance rejection control method, system, terminal and medium, wherein the method comprises: constructing a high-dimensional global linearized Koopman model of a six-degree-of-freedom vibration table system; considering the influence of disturbance on the output posture of the model, establishing an extended state system, and then constructing an extended state observer; designing an auto-disturbance rejection control law of the vibration table system based on the output disturbance observed by the extended state observer; establishing a nominal model without disturbance according to the auto-disturbance rejection control law; establishing an optimization problem of each degree-of-freedom posture of the vibration table system; solving the optimization problem of each degree-of-freedom posture of the vibration table system according to the predicted posture vector and reference posture vector of each degree of freedom, and obtaining an optimal control signal sequence; extracting the first control signal in the optimal control signal sequence, and correcting it using the auto-disturbance rejection control law, and using the corrected control signal as the final control signal. The present invention effectively improves reliability and control accuracy.

Description

Technical Field

[0001] The present invention relates to the field of engineering structure dynamic test, and in particular to a six-degree-of-freedom vibration table self-disturbance rejection control method, system, terminal and medium. Background Art

[0002] Real-time hybrid simulation (RTHS) is an important method for studying vibration tests of large structures. RTHS technology can simulate the vibration response of trains on bridges, the structural response of large building structures under earthquake motion, and the vibration effects of natural environments such as offshore wind turbines and tsunamis on structures. It can also provide simulation of real-time interactions between structures in complex dynamic systems, which has important guiding significance for the structural seismic performance of large building structures.

[0003] RTHS divides the test object into a numerical substructure and a test substructure. The test substructure is dynamically loaded on the loading device and interacts with the numerical substructure. Taking the seismic test of building structures as an example, RTHS measures the displacement, velocity, force and other signals of the house structure model in the earthquake simulation vibration table in real time, substitutes them into the numerical building structure model to calculate the expected response of the vibration table at the next moment in real time, and then excites the test substructure through the vibration table to form a closed loop. The accuracy of the earthquake simulation vibration table in reproducing seismic waves largely determines the stability and credibility of the real-time hybrid test. Compared with the single-degree-of-freedom vibration table, the six-degree-of-freedom vibration table can realize multi-degree-of-freedom response of structural vibration, which is suitable for more realistic seismic tests of building structures.

[0004] At present, the traditional control scheme for six-degree-of-freedom vibration tables over-relies on the mechanism model during the control process and does not fully consider the uncertainties and disturbances in the experimental process. As a result, the existing schemes still have problems of poor control reliability and low control accuracy during the control process. Summary of the invention

[0005] The present invention provides a six-degree-of-freedom vibration table self-disturbance rejection control method, system, terminal and medium to solve the problems of poor reliability and low control accuracy in existing control schemes.

[0006] In a first aspect, a six-degree-of-freedom vibration table self-disturbance rejection control method is provided, comprising the following steps:

[0007] S1: Construct the Koopman model of high-dimensional global linearization of the six-degree-of-freedom shaking table system;

[0008] S2: Based on the Koopman model, considering the influence of external disturbance and model identification deviation on the output posture of the Koopman model, an extended state system of the six-degree-of-freedom vibration table system is established, and then an extended state observer is constructed;

[0009] S3: Design the active disturbance rejection control law of the six-degree-of-freedom vibration table system based on the output disturbance observed by the extended state observer;

[0010] S4: Establish a Koopman nominal model without disturbance according to the active disturbance rejection control law;

[0011] S5: Establish the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system;

[0012] S6: According to the Koopman nominal model without disturbance, the predicted posture vector of each degree of freedom is obtained, and the reference posture vector of each degree of freedom is obtained, and the optimization problem of the posture of each degree of freedom of the six-degree-of-freedom vibration table system is solved to obtain the optimal control signal sequence;

[0013] S7: extract the first control signal in the optimal control signal sequence, and modify it using the anti-disturbance control law, and use the modified control signal as the control signal input to the six-degree-of-freedom vibration table system.

[0014] Furthermore, the Koopman model of the high-dimensional global linearization of the six-degree-of-freedom vibration table is expressed as follows:

[0015]

[0016] In the formula, , represents the linear state variables of the six-degree-of-freedom vibration table system in the increased-dimensional space, and the posture state , The six-degree-of-freedom vibration table system The pose vector at the moment, Respectively The vector formed by the first and second order differentials of the postures of each degree of freedom in , represents the dimension-raising function; , , Represents the system matrix of the Koopman model; Indicates the Koopman model for the pose state The predicted output value of express The control signal at the moment.

[0017] Furthermore, step S1 specifically includes:

[0018] Select pose state As the training set state of the Koopman model;

[0019] The original data set of the six-degree-of-freedom vibration table system is expressed as follows:

[0020]

[0021] In the formula, , , They represent the input posture state set, the output posture state set and the control signal set respectively;

[0022] The dimensionality-raising function is used to upgrade the posture state data of the six-degree-of-freedom vibration table system to a high dimension and is expressed as follows:

[0023]

[0024] In the formula, , Respectively , The dataset after dimensionality increase;

[0025] The system matrices of the Koopman model of the six-degree-of-freedom vibration table system obtained based on the EDMD method are:

[0026]

[0027] In the formula, the superscript represents pseudo-inverse operation;

[0028] Then according to the system matrix , , The Koopman model of high-dimensional global linearization of six-degree-of-freedom vibration table system is established.

[0029] Furthermore, step S2 specifically includes:

[0030] According to the Koopman model, we can get The pose vector of the six-degree-of-freedom vibration table system under the influence of disturbance at any moment The predicted output :

[0031]

[0032] In the formula, is the output matrix of the six-degree-of-freedom vibration table system; is the total disturbance including external disturbance and model identification error;

[0033] consider The impact on the posture of each degree of freedom of the system, the expansion state is defined as follows:

[0034]

[0035] Then the expanded state system of the six-degree-of-freedom vibration table system is:

[0036]

[0037] The extended state observer is established for the extended state system of the six-degree-of-freedom vibration table system, which is expressed as follows:

[0038]

[0039] In the formula, and The extended state observer is Always and Observed value of and is the system observation gain coefficient matrix, satisfying , , For the The observer gain corresponding to the degrees of freedom is , and satisfy:

[0040]

[0041] In the formula, is the real axis coefficient, is the imaginary axis coefficient.

[0042] Furthermore, in step S3, the active disturbance rejection control law is expressed as follows:

[0043]

[0044] In the formula, represents the optimal control quantity of the nominal model; , The corresponding postures are The output matrix of They are the position of the vibration table in the x-axis direction, the position in the y-axis direction, the position in the z-axis direction, the position rotated around the x-axis direction, the position rotated around the y-axis direction, and the position rotated around the z-axis direction.

[0045] Furthermore, by substituting the active disturbance rejection control law into the predicted output of the posture vector of the six-degree-of-freedom vibration table system under the influence of disturbance, the Koopman nominal model without disturbance in step S4 is finally obtained and expressed as follows:

[0046] .

[0047] Furthermore, in step S5, the optimization goal of the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system is to minimize the sum of the deviation between the predicted posture and the reference posture and the control signal in the entire prediction time domain, which is specifically expressed as follows:

[0048]

[0049] In the formula, For posture The cost function of , and Respectively represent the posture exist Predicted pose, reference pose and control signal at the moment; For the prediction time domain; The value is , , , , or ; and are the error weight matrix and the control weight matrix respectively.

[0050] In a second aspect, a six-degree-of-freedom vibration table self-disturbance rejection control system is provided, comprising:

[0051] Koopman model building module, used to build a high-dimensional global linear Koopman model of a six-degree-of-freedom shaker system;

[0052] The observer construction module is used to establish an extended state system of a six-degree-of-freedom vibration table system based on the Koopman model, considering the influence of external disturbances and model identification deviations on the output posture of the Koopman model, and then construct an extended state observer;

[0053] The active disturbance rejection control law building module is used to design the active disturbance rejection control law of the six-degree-of-freedom shaker system based on the output disturbance observed by the extended state observer;

[0054] The nominal model building module is used to build a Koopman nominal model without disturbance according to the active disturbance rejection control law;

[0055] Optimization problem building module, used to establish the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system;

[0056] The optimal control signal sequence acquisition module is used to obtain the predicted posture vector of each degree of freedom according to the Koopman nominal model without disturbance, and obtain the reference posture vector of each degree of freedom, solve the optimization problem of the posture of each degree of freedom of the six-degree-of-freedom vibration table system, and obtain the optimal control signal sequence;

[0057] The control signal generation module is used to extract the first control signal in the optimal control signal sequence, and to correct it using the anti-disturbance control law, and to use the corrected control signal as the control signal input to the six-degree-of-freedom vibration table system.

[0058] In a third aspect, an electronic terminal is provided, comprising:

[0059] a memory having a computer program stored thereon;

[0060] The processor is used to load and execute the computer program to implement the six-degree-of-freedom vibration table self-disturbance rejection control method as described above.

[0061] In a fourth aspect, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the six-degree-of-freedom vibration table self-disturbance rejection control method as described above is implemented.

[0062] The present invention proposes a six-degree-of-freedom vibration table self-disturbance rejection control method, system, terminal and medium, which have the following beneficial effects:

[0063] 1. The disturbance observer is based on data-driven design and does not require a detailed mechanism model of the six-degree-of-freedom vibration table system;

[0064] 2. The order and parameter tuning method of the disturbance observer are fixed and will not change with the data dimension or the dimension of the operator, which greatly simplifies the controller design;

[0065] 3. The disturbance of the high-dimensional model of the six-degree-of-freedom vibration table is reduced to low dimension and then eliminated through feedback control at the input end, which simplifies the disturbance suppression scheme of the controller designed based on the Koopman model. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0067] Figure 1 It is a flow chart of the six-degree-of-freedom vibration table self-disturbance rejection control method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0068] To make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described in detail below. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention.

[0069] The existing control scheme for the six-degree-of-freedom vibration table over-relies on the mechanism model during the control process and does not fully consider the uncertainty and disturbance in the experimental process, which makes the existing scheme still have the problems of poor control reliability and low control accuracy during the control process. Based on this, the present invention fully considers the uncertainty and disturbance in the experimental process, and proposes a six-degree-of-freedom vibration table self-disturbance control method, system, terminal and medium. The technical scheme of the present invention is specifically described in combination with specific embodiments below.

[0070] The embodiment of the present invention provides a six-degree-of-freedom vibration table self-disturbance rejection control method, such as Figure 1 As shown, the following steps are included:

[0071] S1: Construct the Koopman model of high-dimensional global linearization of the six-degree-of-freedom shaking table system;

[0072] S2: Based on the Koopman model, considering the influence of external disturbance and model identification deviation on the output posture of the Koopman model, an extended state system of the six-degree-of-freedom vibration table system is established, and then an extended state observer is constructed;

[0073] S3: Design the active disturbance rejection control law of the six-degree-of-freedom vibration table system based on the output disturbance observed by the extended state observer;

[0074] S4: Establish a Koopman nominal model without disturbance according to the active disturbance rejection control law;

[0075] S5: Establish the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system;

[0076] S6: According to the Koopman nominal model without disturbance, the predicted posture vector of each degree of freedom is obtained, and the reference posture vector of each degree of freedom is obtained, and the optimization problem of the posture of each degree of freedom of the six-degree-of-freedom vibration table system is solved to obtain the optimal control signal sequence;

[0077] S7: extract the first control signal in the optimal control signal sequence, and modify it using the anti-disturbance control law, and use the modified control signal as the control signal input to the six-degree-of-freedom vibration table system.

[0078] The following is a more specific description of the six-degree-of-freedom vibration table self-disturbance rejection control method provided in the above embodiment.

[0079] The model for a six-degree-of-freedom vibration table is expressed as follows:

[0080]

[0081] in, For a six-degree-of-freedom vibration table system The pose vector at the moment includes three translation poses and three rotation poses; The expression is ,in for Time vibration table The position in the axis direction, for Time vibration table The position in the axis direction, for Time vibration table The position in the axis direction, for Time vibration table around Direction rotation posture, for Time vibration table around Direction rotation posture, for Time vibration table around Direction rotation posture; is the nonlinear mapping function of the six-degree-of-freedom vibration table, represents external disturbance; express The control signal at the moment.

[0082] Since it is difficult to obtain an accurate multi-input and multi-output excitation model for a six-degree-of-freedom vibration table, this embodiment uses the Koopman operator to fit the system model. In order to improve the fitting accuracy of the Koopman operator, this embodiment uses the posture state As the Koopman training set state, Respectively The vector formed by the first and second order differentials of the posture of each degree of freedom in the 6-DOF vibration table system. In the 6-DOF vibration table system, the posture of each degree of freedom and the translational acceleration can be measured, and the translational velocity signal and the high-order signal of rotation can be obtained by Kalman filter, signal synthesis or tracking differentiator (TD). Taking TD as an example, TD is established by formula (1):

[0083] (1)

[0084] in, , , They are , , The reconstruction value of is the step length, is the gain matrix used to adjust the tracking speed.

[0085] After reconstructing the posture data of the six-degree-of-freedom vibration table, the original posture data set of the six-degree-of-freedom vibration table is expressed as formula (2):

[0086] (2)

[0087] In the formula, , , They represent the input pose state set, output pose state set and control signal set respectively.

[0088] Choose a set of basis dimensionality-raising functions Used for posture state dimension upgrade:

[0089] (3)

[0090] In the formula, Indicates dimensional function, subscript Indicates the serial number of the dimension-raising function.

[0091] Based on the dimension-raising function, the posture state data of the six-degree-of-freedom vibration table can be upgraded to a high dimension and expressed as follows:

[0092] (4)

[0093] In the formula, , Respectively , The dataset after dimensionality increase.

[0094] The system matrices of the Koopman model of the six-degree-of-freedom vibration table system obtained based on the EDMD method are:

[0095] (5)

[0096] In the formula, the superscript Represents a pseudo-inverse operation.

[0097] The Koopman model of high-dimensional global linearization of the six-degree-of-freedom vibration table can be established through equation (5) and expressed as follows:

[0098] (6)

[0099] In the formula, , represents the linear state variables of the six-degree-of-freedom vibration table system in the ascending dimensional space; , , Represents the system matrix of the Koopman model; Indicates the Koopman model for the pose state The predicted output value of . According to the above formula, we can get The pose vector of the six-degree-of-freedom vibration table system under the influence of disturbance at any moment The predicted output :

[0100] (7)

[0101] In the formula, is the output matrix of the six-degree-of-freedom vibration table system; is the total disturbance including external disturbance and model identification error.

[0102] consider The impact on the posture of each degree of freedom of the system, the expansion state is defined as follows:

[0103] (8)

[0104] Then the expanded state system of the six-degree-of-freedom vibration table system is:

[0105] (9)

[0106] The extended state observer is established for the extended state system of the six-degree-of-freedom vibration table system, which is expressed as follows:

[0107] (10)

[0108] In the formula, and The extended state observer is Always check the vibration table position and disturbance Observed value of and is the system observation gain coefficient matrix, satisfying , , For the The observer gain corresponding to the degrees of freedom is , and satisfy:

[0109] (11)

[0110] In the formula, is the real axis coefficient, is the imaginary axis coefficient. Based on the above formula, the system poles can be configured at To ensure system stability, the poles must satisfy .

[0111] The active disturbance rejection control law of the six-degree-of-freedom vibration table system is designed based on the disturbance observed by the extended state observer and is expressed as follows:

[0112] (12)

[0113] In the formula, represents the optimal control quantity of the standard model;

[0114] (13)

[0115] in, The corresponding postures are The output matrix of .

[0116] Substituting formula (12) into formula (9) yields:

[0117] (14)

[0118] Substituting equation (13) into equation (14), we have , represents the 4th-order unit matrix. Under the premise that the parameters are tuned to ensure the convergence of the observer, we have Therefore, equation (14) can be transformed into a nominal model without disturbance:

[0119] (15)

[0120] Based on the above model, control methods such as MPC (model predictive control), LQR (linear quadratic regulator), and state feedback control can be designed to further control the vibration table. The following takes MPC as an example to introduce the vibration table control under the data-driven six-degree-of-freedom vibration table self-disturbance rejection method. Based on the nominal model (15), the optimization problem of defining the posture of each degree of freedom of the six-degree-of-freedom vibration table system is expressed as follows:

[0121] (16)

[0122] In the formula, For posture The cost function of , and Respectively represent the posture exist Predicted pose, reference pose and control signal at the moment; For the prediction time domain, To control the time domain, there is ; The value is , , , , or ; and are the error weight matrix and the control weight matrix respectively. Assume that the control signal of the system outside the control time domain remains unchanged, that is, , .

[0123] By posture Taking as an example, the predicted pose vector, control signal vector and reference pose vector are defined as shown in equations (17), (18) and (19) respectively:

[0124] (17)

[0125] (18)

[0126] (19)

[0127] In the formula, , , Represent the predicted pose vector, control signal vector and reference pose vector respectively; represents the predicted position in the x-axis direction at time k+1, Indicates the control signal of the x-axis direction at the moment, Represents the reference pose in the x-axis direction at time k.

[0128] From formula (15), we can know that the prediction equation based on the Koopman model is:

[0129] (20)

[0130] in,

[0131] (twenty one)

[0132] In the formula, .

[0133] Based on the above prediction equation and reference pose vector, the optimal control sequence can be obtained by solving the optimization problem:

[0134] (twenty two)

[0135] Take the first control signal in the optimal control signal sequence, then:

[0136] (twenty three)

[0137] The control signal is corrected using the anti-disturbance control law of formula (12), and the corrected control signal is used as the control signal input to the six-degree-of-freedom vibration table system to achieve data-based anti-disturbance control at the posture end.

[0138] The above embodiment provides a six-degree-of-freedom vibration table self-disturbance rejection control method, which has the following advantages: the disturbance observer is based on data-driven design and does not require a detailed mechanism model of the six-degree-of-freedom vibration table system; the order and parameter setting method of the disturbance observer are fixed and will not change with the data dimension or the dimension increase of the operator, which greatly simplifies the controller design; the disturbance of the high-dimensional model of the six-degree-of-freedom vibration table is reduced to a low dimension and then eliminated through feedback control at the input end, which simplifies the disturbance suppression scheme of the controller designed based on the Koopman model.

[0139] The embodiment of the present invention further provides a six-degree-of-freedom vibration table self-disturbance rejection control system, comprising:

[0140] Koopman model building module, used to build a high-dimensional global linear Koopman model of a six-degree-of-freedom shaker system;

[0141] Observer building block for considering external disturbances based on the Koopman model The influence of each degree of freedom posture of the six-degree-of-freedom vibration table system is established, and the extended state system of the six-degree-of-freedom vibration table system is established, and then the extended state observer is constructed;

[0142] An automatic disturbance rejection control law building module for designing the automatic disturbance rejection control law of a six-degree-of-freedom shaker system based on disturbances observed by an extended state observer;

[0143] A nominal model building module is used to build a disturbance-free nominal model according to the active disturbance rejection control law;

[0144] Optimization problem building module, used to establish the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system;

[0145] The optimal control signal sequence acquisition module is used to obtain the predicted posture vector of each degree of freedom according to the nominal model without disturbance, and obtain the reference posture vector of each degree of freedom, solve the optimization problem of the posture of each degree of freedom of the six-degree-of-freedom vibration table system, and obtain the optimal control signal sequence;

[0146] The control signal generation module is used to extract the first control signal in the optimal control signal sequence, and to modify it using the anti-disturbance control law, and to use the modified control signal as the control signal input to the vibration table system.

[0147] It should be understood that the functional unit modules in various embodiments of the present invention may be concentrated in one processing unit, or each unit module may exist physically separately, or two or more unit modules may be integrated in one unit module, and may be implemented in the form of hardware or software.

[0148] An embodiment of the present invention further provides an electronic terminal, including:

[0149] a memory having a computer program stored thereon;

[0150] The processor is used to load and execute the computer program to implement the six-degree-of-freedom vibration table self-disturbance rejection control method described in the above embodiment.

[0151] An embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the six-degree-of-freedom vibration table self-disturbance rejection control method described in the above embodiment is implemented.

[0152] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0153] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0154] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0155] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0156] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0157] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A six-degree-of-freedom vibration table auto-disturbance rejection control method, characterized in that: The steps include: S1: Construct the Koopman model of high-dimensional global linearization of the six-degree-of-freedom shaking table system; S2: Based on the Koopman model, considering the influence of external disturbance and model identification deviation on the output posture of the Koopman model, an extended state system of the six-degree-of-freedom vibration table system is established, and then an extended state observer is constructed; S3: Design the active disturbance rejection control law of the six-degree-of-freedom vibration table system based on the output disturbance observed by the extended state observer; S4: Establish a Koopman nominal model without disturbance according to the active disturbance rejection control law; S5: Establish the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system; S6: According to the Koopman nominal model without disturbance, the predicted posture vector of each degree of freedom is obtained, and the reference posture vector of each degree of freedom is obtained, and the optimization problem of the posture of each degree of freedom of the six-degree-of-freedom vibration table system is solved to obtain the optimal control signal sequence; S7: extract the first control signal in the optimal control signal sequence, and modify it using the anti-disturbance control law, and use the modified control signal as the control signal input to the six-degree-of-freedom vibration table system.

2. The six-degree-of-freedom vibration table auto-disturbance rejection control method according to claim 1, characterized in that: The Koopman model of high-dimensional global linearization of a six-degree-of-freedom vibration table is expressed as follows: ； In the formula, , represents the linear state variables of the six-degree-of-freedom vibration table system in the increased-dimensional space, and the posture state , The six-degree-of-freedom vibration table system The pose vector at the moment, Respectively The vector formed by the first and second order differentials of the postures of each degree of freedom in , represents the dimension-raising function; , , The system matrix representing the Koopman model; Indicates the Koopman model for the pose state The predicted output value of express The control signal at the moment.

3. The six-degree-of-freedom vibration table auto-disturbance rejection control method according to claim 2, characterized in that: Step S1 specifically includes: Select pose state As the training set state of the Koopman model, the system matrix of the Koopman model of the six-degree-of-freedom vibration table system is obtained based on the EDMD method. , , , and then establish the Koopman model of high-dimensional global linearization of the six-degree-of-freedom vibration table system.

4. The six-degree-of-freedom vibration table auto-disturbance rejection control method according to claim 2, characterized in that: Step S2 specifically includes: According to the Koopman model, we can get The pose vector of the six-degree-of-freedom vibration table system under the influence of disturbance at any moment The predicted output : ； In the formula, is the output matrix of the six-degree-of-freedom vibration table system; is the total disturbance including external disturbance and model identification error; consider The impact on the posture of each degree of freedom of the system defines the expansion state: , ; The extended state observer is established for the extended state of the six-degree-of-freedom vibration table system, which is expressed as follows: ； In the formula, and The extended state observer is Always and Observed value of and is the system observation gain coefficient matrix.

5. The six-degree-of-freedom vibration table auto-disturbance rejection control method according to claim 4, characterized in that: In step S3, the active disturbance rejection control law is expressed as follows: ； In the formula, represents the optimal control quantity of the nominal model; , The corresponding postures are The output matrix of They are the position of the vibration table in the x-axis direction, the position in the y-axis direction, the position in the z-axis direction, the position rotated around the x-axis direction, the position rotated around the y-axis direction, and the position rotated around the z-axis direction.

6. The six-degree-of-freedom vibration table auto-disturbance rejection control method according to claim 5, characterized in that: By substituting the self-disturbance rejection control law of claim 5 into the predicted output of the posture vector of the six-degree-of-freedom vibration table system under the influence of disturbance of claim 4, the Koopman nominal model without disturbance in step S4 is finally obtained.

7. The six-degree-of-freedom vibration table auto-disturbance rejection control method according to claim 1, characterized in that: In step S5, the optimization goal of the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system is to minimize the sum of the deviation between the predicted posture and the reference posture and the control signal in the entire prediction time domain.

8. A six-degree-of-freedom vibration table anti-disturbance control system, characterized in that: include: Koopman model building module, used to build a high-dimensional global linear Koopman model of a six-degree-of-freedom shaker system; The observer construction module is used to establish an extended state system of a six-degree-of-freedom vibration table system based on the Koopman model, considering the influence of external disturbances and model identification deviations on the output posture of the Koopman model, and then construct an extended state observer; The active disturbance rejection control law building module is used to design the active disturbance rejection control law of the six-degree-of-freedom shaker system based on the output disturbance observed by the extended state observer; The nominal model building module is used to build a Koopman nominal model without disturbance according to the active disturbance rejection control law; Optimization problem building module, used to establish the optimization problem of each degree of freedom posture of the six-degree-of-freedom vibration table system; The optimal control signal sequence acquisition module is used to obtain the predicted posture vector of each degree of freedom according to the Koopman nominal model without disturbance, and obtain the reference posture vector of each degree of freedom, solve the optimization problem of the posture of each degree of freedom of the six-degree-of-freedom vibration table system, and obtain the optimal control signal sequence; The control signal generation module is used to extract the first control signal in the optimal control signal sequence, and to correct it using the anti-disturbance control law, and to use the corrected control signal as the control signal input to the six-degree-of-freedom vibration table system.

9. An electronic terminal, characterized in that: include: a memory having a computer program stored thereon; A processor is used to load and execute the computer program to implement the six-degree-of-freedom vibration table self-disturbance rejection control method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the six-degree-of-freedom vibration table auto-disturbance rejection control method according to any one of claims 1 to 7 is implemented.

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