Decoupling control method for six-axis vibration table, and system

Abstract

A decoupling control method for a six-axis vibration table and a system for implementing the decoupling control method for a six-axis vibration table, capable of performing real-time adjustment on the vibration table according to specific conditions, thereby enhancing the robustness of the system, and achieving high reliability and good accuracy. The method comprises: acquiring data information of a target six-axis vibration table; representing a dynamic coupling model of the target six-axis vibration table in a global linearization manner to construct a koopman predictor; using a deep neural network to obtain a feature function and an operator matrix of the predictor; performing training to obtain a deep koopman estimator, and obtaining state information of the target six-axis vibration table; using the deep koopman estimator as a prediction model to design a multi-dimensional model prediction controller; using a fuzzy neural network to perform online tuning; and using the tuned multi-dimensional model prediction controller to control the target six-axis vibration table, so as to complete decoupling control over the target six-axis vibration table.

Description

Decoupling control method and system of six-axis vibration table TECHNICAL FIELD

[0001] The present application belongs to the field of real-time control, and particularly relates to a decoupling control method and system of a six-axis vibration table. BACKGROUND

[0002] Real-Time Hybrid Simulation (RTHS) is an important test method in the field of structural seismic resistance. In RTHS, a structure is divided into a physical substructure and a numerical substructure. The physical substructure contains parts of the structure that are difficult to model, have complex characteristics, or need to be tested, and the numerical substructure contains parts of the structure that are easy to model, are not convenient to test, or are mature in research. In the physical substructure, the loading signal is calculated in real time by the numerical substructure and loaded in real time by the vibration table; the numerical substructure calculates the loading signal at the next time point according to the feedback signal of the test piece. In specific implementation, the reproducibility accuracy of the vibration table for the loading signal, such as time delay, root mean square error, and peak error, greatly affects the stability and accuracy of RTHS.

[0003] For a single test piece or a single working condition, traditional PID control, three-parameter control, and model predictive control can achieve good results after special tuning. However, these schemes all assume that the control console is a linear time-invariant system, and the control scheme is tuned based on specific frequency, loading, and test piece assumptions, ignoring the uncertainty of the vibration table and the influence of the test piece on the characteristics of the vibration table. This makes it difficult to achieve good reliability and accuracy when controlling the vibration table in practice.

[0004] In addition, when loading waveforms of different frequency bands, the vibration table will exhibit different degrees of coupling effect, and the degree of coupling will increase with the increase of the frequency and amplitude of the waveform vibration. In the design process of traditional decoupling control schemes, complete modeling of the controlled object is required; however, complete modeling is difficult to achieve in practice. Therefore, existing decoupling control schemes cannot effectively solve these problems.

[0005] SUMMARY

[0006] One of the purposes of the present application is to provide a decoupling control method for a six-axis vibration table with high reliability and good accuracy.

[0007] The second purpose of the present application is to provide a system for implementing the decoupling control method of the six-axis vibration table.

[0008] The decoupling control method for a six-axis vibration table provided by the present application comprises the following steps:

[0009] S1. Obtain data information of a target six-axis vibration table;

[0010] S2. Based on the data information obtained in step S1, a koopman operator theory is used to globally linearize the dynamic coupling model of the target six-axis vibration table, so as to construct a koopman predictor;

[0011] S3. The characteristic function and operator matrix of the predictor constructed in step S2 are calculated by using a deep neural network;

[0012] S4. A deep koopman estimator is trained based on the position input data and output data of the target six-axis vibration table, and state information of the target six-axis vibration table is obtained through the obtained deep koopman estimator;

[0013] S5. A multi-dimensional model predictive controller is designed based on the deep koopman estimator obtained in step S4 as a prediction model;

[0014] S6. The parameters of the multi-dimensional model predictive controller designed in step S5 are adjusted online by using a fuzzy neural network;

[0015] S7. The target six-axis vibration table is controlled by using the adjusted multi-dimensional model predictive controller obtained in step S6, so as to complete the decoupling control of the target six-axis vibration table.

[0016] The step S2 comprises the following steps:

[0017] The position dynamics model of the target six-axis vibration table is set; in the position dynamics model, the koopman operator is introduced to construct a koopman predictor, which is used to upgrade the nonlinear model of the target six-axis vibration table to a linear space, and then a linear expression of the dynamics model of the target six-axis vibration table is obtained.

[0018] The step S2 specifically comprises the following steps:

[0019] The position dynamics model of the target six-axis vibration table is set as:

[0020] θ(k+1)=f(θ(k),U(k))

[0021] In the formula, θ(k+1) is the position vector at k+1 time; θ(k) is the position vector at k time; U(k) is the control vector at k time; f() is a nonlinear mapping function from state to state;

[0022] The expression of θ(k) is θ(k)=[X(k) Y(k) Z(k) α(k) β(k) γ(k)] Twherein X(k) is the pose of the X-axis direction of the target six-axis vibration table at time k, Y(k) is the pose of the Y-axis direction of the target six-axis vibration table at time k, Z(k) is the pose of the Z-axis direction of the target six-axis vibration table at time k, a(k) is the pose of the rotation of the target six-axis vibration table around the X direction at time k, b(k) is the pose of the rotation of the target six-axis vibration table around the Y direction at time k, and g(k) is the pose of the rotation of the target six-axis vibration table around the Z direction at time k;

[0023] The expression of U(k) is U(k)=[u x (k) u y (k) u z (k) u α (k) u β (k) u γ (k)] T wherein u x (k) is the control signal of the pose X(k) at time k, u y (k) is the control signal of the pose Y(k) at time k, u z (k) is the control signal of the pose Z(k) at time k, u α (k) is the control signal of the pose a(k) at time k, u β (k) is the control signal of the pose b(k) at time k, and u γ (k) is the control signal of the pose g(k) at time k.

[0024] The control signal of the prediction time step is obtained by calculation and is set to remain unchanged; the finite-dimensional koopman operator matrix K=[A B] and the observation function matrix G(0(k), U(k)) of the pose are defined, satisfying G(0(k+1), U(k))=AG(0(k), U(k))+BU(k) wherein G(0(k), U(k)) represents the observation function matrix of the pose at time k, and

[0025] G(0(k), U(k))=[g x (k) g y (k) g z (k) g α (k) g β (k) g γ (k)] T , g · (k) is the observation function of the pose ·(k) after dimensionality increase, g · (k) e H, H represents an infinite Hilbert space, and · takes values of x, y, z, a, b or g; A is the system matrix of the dimensionality increased system, and A=diag{A x ,A y ,A z ,Aα ,A β ,A γ},A · for g · (k) the corresponding system matrix; B is the input matrix of the lifted system, and B = diag{B x ,B y ,B z ,B α ,B β ,B γ},B · for g · (k) the corresponding input matrix;

[0026] The observation function matrix at time k and time k+1 evolves in H space through a finite-dimensional Koopman operator matrix K, the Koopman operator matrix K can lift the six-degree-of-freedom vibration table nonlinear model corresponding to the pose state θ to the H space, and the expression corresponding to the Koopman operator matrix K is K = [κ x κ y κ z κ α κ β κ γ ]In the formula, κ · is the Koopman operator corresponding to the pose·(k) after lifting.

[0027] The step S3 specifically comprises the following steps:

[0028] The observation function matrix G(θ(k), U(k)) and the operator matrix K are fitted through a deep neural network;

[0029] The first deep neural network Q1 is used to fit the pose observation function matrix G(θ(k), U(k)); the second deep neural network Q2 is used to fit the inverse function of the pose observation function matrix G(θ(k), U(k)), realize the lifting and the dimension reduction of the pose model, and determine the operator matrix K through a linear criterion; G(θ(k), U(k)) based on the deep neural network is expressed as G(θ(k), U(k)) = Q1(θ(k), U(k)) based on Q1, the nonlinear model of the pose is expressed in the form of the lifted linear state matrix G(θ(k), U(k)); the state after lifting evolves through K, and the estimated value of the state vector θ(k+1) at the next time is obtained based on the evolved state, the input and Q2 is expressed as:

[0030] In the formula, θ is the estimated value of the pose X(k+1) at time k+1; is the estimated value of the pose Y(k+1) at time k+1; is an estimated value of the pose Z(k+1) at the k+1 time; is an estimated value of the pose a(k+1) at the k+1 time; is an estimated value of the pose β(k+1) at the k+1 time; is an estimated value of the pose γ(k+1) at the k+1 time.

[0031] The step S4 specifically comprises the following steps:

[0032] Based on the pose input data and the output data of the target six-axis vibration table, Q1 and Q2 are trained to determine the mapping from the original state and the input to the koopman invariant subspace, the linear dynamic system G(θ(k+1), U(k)) = AG(θ(k), U(k)) + BU(k) and the mapping from the invariant subspace to the original state;

[0033] The criterion function for designing the network is:

[0034] ||Q1(θ(k+1), U(k+1))-KQ1(θ(k), U(k)), U(k))|| 2

[0035] ||Q2(Q1(θ(k), U(k)), U(k))-(θ(k), U(k))|| 2

[0036] ||(θ(k+1), U(k+1))-Q2(K(Q1(θ(k), U(k)), U(k)))|| 2

[0037] In the formula, || || represents the norm operation;

[0038] The input of the koopman predictor and the input of the deep neural network DNN are both six poses of the six-axis vibration table, and the output of Q2 is an estimated value of the six poses of the six-axis vibration table.

[0039] The step S5 specifically comprises the following steps:

[0040] The prediction problem of the multi-dimensional model predictive control preliminary model is described as the following optimization problem:

[0041] In the formula, J · (k) is a cost function of the pose ·, and · takes values of x, y, z, a, β or γ; N p and N c are the prediction time domain and the control time domain of the system, respectively; is a predicted value of the pose · at the k+s time; the norm of the weight P · ; ||| R· the norm of the weight R · ; · ref (k+s) is the reference input at k+s; Δu · (k+s) is the increment of the input signal at k+s; U min (k) is the lower limit of the control matrix; U max (k) is the upper limit of the control matrix;

[0042] In the optimization process, the control quantity outside the control time domain is set to remain unchanged; N p and N c of each optimization problem remain the same.

[0043] The step S6 comprises the following steps:

[0044] The parameters of the multi-dimensional model predictive control preliminary model designed in step S5 include N p , N c and P · ;

[0045] The parameters N p and N c are set by using an empirical method for calculation;

[0046] The parameter P · is set in real time by using a fuzzy neural network.

[0047] The parameter P · is set in real time by using a fuzzy neural network, and the method comprises the following steps:

[0048] The fuzzy neural network comprises an input layer, a membership function layer, a fuzzy rule fitness layer, a normalization layer and a network output layer;

[0049] The output ΔP · (k) of the network output layer is the increment of the parameter P · , and n is the number of rules of the fuzzy neural network; w ·kk is the output weight of the corresponding kth rule, and is the output corresponding to the normalization layer.

[0050] Then, the update rate of the gain P · (k+1) = P · (k) + ΔP · (k) is calculated.

[0051] The performance index function of the fuzzy neural network is set as

[0052] In the formula, E(k) is an expected value, r(k) is a target value at time k, and y(k) is an actual output value at time k.

[0053] Based on the performance index function, the gradient descent algorithm is used to update the related parameters of the fuzzy neural network, and the update process is represented as In the formula, sigma(t+1) is the value at time t+1, sigma(t) is the value at time t, eta is a learning rate, and a is a smoothing factor.

[0054] The application also provides a system for realizing the decoupling control method of the six-axis vibration table, which comprises a data acquisition module, a predictor construction module, a predictor calculation module, a state information calculation module, a model design module, a model training module and a decoupling control module; the data acquisition module is used to acquire data information of a target six-axis vibration table and upload the data information to the predictor construction module; the predictor construction module is used to, according to the received data information, acquire the data information, adopt the koopman operator theory, represent the dynamic coupling model of the target six-axis vibration table in a global linearization manner, thereby constructing a koopman predictor, and upload the data information to the predictor calculation module; the predictor calculation module is used to, according to the received data information, calculate the characteristic function and the operator matrix of the constructed predictor by using a deep neural network, and upload the data information to the state information calculation module; the state information calculation module is used to, according to the received data information, train a deep koopman estimator based on the position input data and the output data of the target six-axis vibration table, acquire the state information of the target six-axis vibration table by using the obtained deep koopman estimator, and upload the data information to the model design module; the model design module is used to, according to the received data information, design a multi-dimensional model predictive controller based on the obtained deep koopman estimator as a prediction model, and upload the data information to the model training module; the model training module is used to, according to the received data information, adopt a fuzzy neural network to perform online setting for parameters of the designed multi-dimensional model predictive controller, and upload the data information to the decoupling control module; and the decoupling control module is used to, according to the received data information, adopt the obtained set multi-dimensional model predictive controller to control the target six-axis vibration table, thereby completing the decoupling control of the target six-axis vibration table.

[0055] The decoupling control method and system of the six-axis vibration table disclosed by the application, through a deep learning algorithm fitting coupling characteristics, further separates different poses by an estimated pose signal, uses six model predictive controls to complete pose model predictive control of the six-axis vibration table, and finally, the application further adjusts weight parameters of the model predictive control in real time through a fuzzy neural network, so that the scheme can be adjusted in real time according to specific conditions, and the robustness of the system is enhanced; therefore, the reliability of the application is higher, and the accuracy is better. BRIEF DESCRIPTION OF DRAWINGS

[0056] Fig. 1 is a method flowchart of the method of the application.

[0057] Fig. 2 is a structural schematic diagram of a deep neural network DNN in the method of the application: Fig. 2(a) is a structural schematic diagram of a first deep neural network, and Fig. 2(b) is a structural schematic diagram of a second deep neural network.

[0058] Fig. 3 is a structural schematic diagram of a fuzzy neural network in the method of the application.

[0059] Fig. 4 is a functional module schematic diagram of the system of the application. DETAILED DESCRIPTION

[0060] As shown in Fig. 1, which is a method flowchart of the method of the application: the decoupling control method of the six-axis vibration table disclosed by the application comprises the following steps:

[0061] S1. Obtain data information of a target six-axis vibration table;

[0062] S2. According to the data information obtained in step S1, adopt a koopman operator theory, express a dynamic coupling model of the target six-axis vibration table in a global linearization manner, and thereby construct a koopman predictor; comprising the following steps:

[0063] Set a pose dynamic model of the target six-axis vibration table; in the pose dynamic model, introduce a koopman operator, and construct a koopman predictor, which is used to upgrade a nonlinear model of the target six-axis vibration table to a linear space, and thereby obtain a linearization expression of the dynamic model of the target six-axis vibration table;

[0064] In specific implementation, the following steps are specifically included:

[0065] Set the pose dynamic model of the target six-axis vibration table as: θ(k+1)=f(θ(k),U(k)) wherein θ(k+1) is a pose vector at k+1 time; θ(k) is a pose vector at k time; U(k) is a control vector at k time; f() is a nonlinear mapping function from state to state;

[0066] The expression of θ(k) is θ(k) = [X(k) Y(k) Z(k) α(k) β(k) γ(k)] T where X(k) is the pose of the target six-axis vibration table in the X-axis direction at time k, Y(k) is the pose of the target six-axis vibration table in the Y-axis direction at time k, Z(k) is the pose of the target six-axis vibration table in the Z-axis direction at time k, α(k) is the pose of the target six-axis vibration table rotating around the X direction at time k, β(k) is the pose of the target six-axis vibration table rotating around the Y direction at time k, and γ(k) is the pose of the target six-axis vibration table rotating around the Z direction at time k;

[0067] The expression of U(k) is U(k) = [u x (k) u y (k) u z (k) u α (k) u β (k) u γ (k)] T where u x (k) is the control signal of the pose X(k) at time k, u y (k) is the control signal of the pose Y(k) at time k, u z (k) is the control signal of the pose Z(k) at time k, u α (k) is the control signal of the pose α(k) at time k, u β (k) is the control signal of the pose β(k) at time k, and u γ (k) is the control signal of the pose γ(k) at time k;

[0068] The control signal of the prediction step is calculated and set to remain unchanged; define the finite-dimensional koopman operator matrix K = [A B] and the observation function matrix G(θ(k), U(k)) of the pose, which satisfies G(θ(k+1), U(k)) = AG(θ(k), U(k)) + BU(k) In the formula, G(θ(k), U(k)) represents the pose observation function matrix at time k, and

[0069] G(θ(k), U(k)) = [g x (k) g y (k) g z (k) g α (k) g β (k) g γ (k)] T , g · (k) is the observation function of the pose ·(k) after dimensionality increase, g ·(k) e H, H denotes an infinite Hilbert space, · takes value of x, y, z, a, b or g; A is a system matrix of the lifted system, and A = diag{A x ,A y ,A z ,A α ,A β ,A γ}, A · is the corresponding system matrix of g · (k) ; B is an input matrix of the lifted system, and B = diag{B x ,B y ,B z ,B α ,B β ,B γ}, B · is the corresponding input matrix of g · (k) ; the observation function matrix at time k and k + 1 evolves in H space through a finite-dimensional Koopman operator matrix K, the Koopman operator matrix K can lift the six-degree-of-freedom shaker nonlinear model corresponding to the pose state θ to H space, the expression corresponding to the Koopman operator matrix K is K = [kappa x kappa y kappa z kappa α kappa β kappa γ ], wherein kappa · is the Koopman operator corresponding to the pose · (k) after lifting;

[0070] S3. Calculate the feature function and the operator matrix of the predictor constructed in step S2 by using a deep neural network; specifically including the following steps:

[0071] Fit the pose observation function matrix G (θ (k), U (k) ) and the operator matrix K through a deep neural network DNN (structure as shown in FIG. 2) ;

[0072] The deep neural network DNN is realized based on a TensorFlow framework;

[0073] wherein the first deep neural network Q1 is used for fitting the pose observation function G (θ (k), U (k) ) ; the second deep neural network Q2 is used for fitting the inverse function of the observation pose function matrix G (θ (k), U (k) ), realizing lifting and descending of the pose model, and determining the operator matrix K through a linear criterion;

[0074] Q1 and Q2 both include 5 hidden layers, and each hidden layer includes 120 nodes;

[0075] G(θ(k), U(k)) based on the deep neural network, denoted as G(θ(k), U(k)) = Q1(θ(k), U(k)) represents a nonlinear model of the pose in a linear state matrix G(θ(k), U(k)) of dimensionality promotion based on Q1; the state after dimensionality promotion evolves through K, and based on the evolved state, the input, and Q2, an estimated value of the state vector θ(k+1) at the next moment is obtained denoted as: is an estimated value of the pose X(k+1) at the k+1 moment; is an estimated value of the pose Y(k+1) at the k+1 moment; is an estimated value of the pose Z(k+1) at the k+1 moment; is an estimated value of the pose α(k+1) at the k+1 moment; is an estimated value of the pose β(k+1) at the k+1 moment; is an estimated value of the pose γ(k+1) at the k+1 moment;

[0076] S4. Based on the pose input data and the output data of the target six-axis vibration table, a deep koopman estimator is trained, and state information of the target six-axis vibration table is obtained through the obtained deep koopman estimator; specifically, the following steps are included:

[0077] Based on the pose input data, the control signal, and the output data of the target six-axis vibration table, Q1 and Q2 are trained, so as to determine the mapping from the original state and the input to the koopman invariant subspace, the linear dynamic system G(θ(k+1), U(k)) = AG(θ(k), U(k))+BU(k), and the mapping from the invariant subspace to the original state;

[0078] The criterion function for designing the network is:

[0079] ||Q1(θ(k+1), U(k+1))-K(Q1(θ(k), U(k)), U(k))|| 2

[0080] ||Q2(Q1(θ(k), U(k)), U(k))-(θ(k), U(k))|| 2

[0081] ||(θ(k+1), U(k+1))-Q2(K(Q1(θ(k), ux(k)), U(k)))|| 2

[0082] In the formula, || || represents the norm operation;

[0083] ​The first criterion function is used to ensure the linear restriction of the original system after network mapping, which is reflected in the linear evolution of the system variables in the koopman invariant subspace; the second criterion function represents the reconstruction error of the mapped original system, which is used to ensure that there is no much information loss of the system state under the mapping of the DNN; the third criterion function is the core constraint of the koopman operator, which is used to represent the prediction of the future state, and this constraint further reflects the linearity of the system state in the koopman subspace and ensures the stability of Q1 and Q2;

[0084] The input of the koopman predictor and the input of the deep neural network DNN are both six poses of the six-axis vibration table, and the output of Q2 is the estimated value of the six poses of the six-axis vibration table, rather than the output of a single pose, which fully considers the coupling effect between the degrees of freedom, so that the deep koopman predictor can adapt to the coupling effect of the six-axis vibration table in practice;

[0085] S5. Based on the deep koopman estimator obtained in step S4, a multi-dimensional model predictive controller is designed as a prediction model, which specifically includes the following steps:

[0086] The prediction problem of the multi-dimensional model predictive control preliminary model is described as the following six optimization problems:

[0087] In the formula, J · (k) is the cost function of the pose ·, and · takes the value of x, y, z, α, β or γ; N p and N c are the prediction time domain and the control time domain of the system, respectively; is the predicted value of the pose · at k+s time; is the sign of the norm with weight P·; || || R· is the sign of the norm with weight R · ·; ref (k+s) is the reference input of the pose · at k+s time; Δu · (k+s) is the increment of the input signal of the pose · at k+s time; U min (k) is the lower limit of the control matrix; U max (k) is the upper limit of the control matrix; in the specific implementation, R · =1 is generally set, and only the error weight needs to be adjusted, and the value of P · / R · can be changed;

[0088] In the optimization process, the control amount outside the control time domain is set to remain unchanged; N p and N c of each optimization problem remain the same;

[0089] The above optimization problem divides the six-axis vibration table dynamics model into six separate optimization problems, simplifies the design of the controller, avoids the coupling of the controller parameter setting, and reduces the difficulty of parameter setting; after solving the above six optimization problems, the six control quantity increments obtained are applied to the system to realize the model predictive control of the six-axis vibration table;

[0090] S6. The parameters of the multi-dimensional model predictive controller designed in step S5 are adjusted online using a fuzzy neural network; including the following steps:

[0091] The parameters of the preliminary model of the multi-dimensional model predictive control designed in step S5 include N p , N c and P · ;

[0092] For parameters N p and N c , the empirical method is used for setting calculation;

[0093] For parameter P · , it is closely related to the control accuracy, and it is difficult to set by the empirical method, and the control accuracy is not guaranteed, so a fuzzy neural network is used for real-time setting; specifically including the following steps:

[0094] The fuzzy neural network used (structure as shown in Figure 3) includes five layers: input layer, membership function layer, fuzzy rule fitness layer, normalization layer and network output layer;

[0095] The first layer is the input layer: the input is the deviation e of the reference signal and the actual output and the differential The output of the first layer network is the output o ii of the first layer network, ii takes the value of 1 or 2, and

[0096] The second layer is the membership function layer: a Gaussian membership function is used as the membership function of the fuzzy neural network, the input is the output o ii of the first layer, and the output is the membership degree of o ii , e and each corresponds to jj membership functions, so the number of nodes of the second layer is 2×jj; the processing process of the second layer is represented as Where c iijj is the center value of the membership function, and σ iijj is the width of the membership function;

[0097] The third layer is the fuzzy rule fitness layer: the input is the output of the second layer, and the output is oii The cross product of membership functions; In fuzzy control, the number of nodes l corresponds to the fuzzy rule and is 4 × jj. 2 The processing procedure of the third layer is represented as follows: For the jj1-th membership function corresponding to the first layer output o1, This is the jj2th membership function corresponding to the first layer output o2;

[0098] The fourth layer is a normalization layer, and its input is the output of the third layer. Output The normalization of the values ​​in the third layer; the processing procedure in the fourth layer is represented as follows:

[0099] The fifth layer is the network output layer, and its input is the output ΔP of the fourth layer. · (k) is the parameter P · The increment, and Where n is the number of rules in the fuzzy neural network; w ·kk Let k be the output weight of the k-th rule corresponding to the pose. This is the output corresponding to the normalization layer;

[0100] Then, the update rate of the gain is calculated as P. · (k+1)=P · (k)+ΔP · (k);

[0101] The parameters to be updated in the fuzzy neural network are w of the network output layer. mkk Membership function layer c iijj and the σ of the membership function layer iijj Based on the performance index function, the gradient descent algorithm is used to update the relevant parameters of the fuzzy neural network; the performance index function of the fuzzy neural network is set as follows: In the formula, E(k) is the desired value, r(k) is the target value at time k, and y(k) is the actual output value at time k. In order for the actual output y(k) to approximate the target value r(k) as much as possible, E(k) needs to be as small as possible.

[0102] The gradient descent algorithm is used to update the parameter w using the following formula. mkk c iijj and σ iijj Update;

[0103] In the formula, sigma (t+1) is the value of parameter at time t+1; sigma (t) is the value of parameter at time t; eta is a learning rate, and a is a smoothing factor; the parameters to be updated of the fuzzy neural network are w of the network output layer mkk , c of the membership function layer iijj , and sigma of the membership function layer iijj The three parameters can be updated by using the above formula.

[0104] S7. The tuned multi-dimensional model predictive controller obtained in step S6 is used to control the target six-axis vibration table, so that the decoupling control of the target six-axis vibration table is completed.

[0105] In the application, the pose prediction value of the six-axis vibration table is obtained through a deep koopman estimator, and the koopman estimator is trained through the input and output of the six-axis vibration table and the control quantity. Since the training process considers the pose output theta of the vibration table under coupling and the corresponding control quantity U, the deep koopman estimator can predict the accurate pose output of the vibration table at a future time according to the current pose of the vibration table and the control quantity under the consideration of coupling. Compared with the single-degree-of-freedom model identification method which cannot consider the coupling effect and the system dynamics modeling method which is difficult to accurately obtain the dynamic characteristics of the coupling term, the method directly obtains the vibration table pose prediction value under coupling based on the vibration table operation data, and the accuracy, reliability and practicability are greatly improved.

[0106] The model predictive controller designed based on the deep koopman estimator obtains the control quantity U of the system by solving six separate optimization problems, which simplifies the design of the controller while considering the coupling characteristics of the vibration table, so that the system pose output accurately tracks the reference pose theta ref The six weight parameters of the model predictive control are realized by six fuzzy neural networks for real-time adjustment, so that the performance of the controller can remain stable under different working conditions, and the robustness of the system is enhanced. The fuzzy neural network obtains the increment AR · of the weight R · by the error of the pose tracking and its differential, wherein · x, y, z, alpha, beta or gamma are taken.

[0107] As shown in Figure 4 is a functional module diagram of the system of the application: the system for realizing the decoupling control method of the six-axis vibration table disclosed in the application comprises a data acquisition module, a predictor construction module, a predictor calculation module, a state information calculation module, a model design module, a model training module and a decoupling control module; the data acquisition module is used for acquiring data information of the target six-axis vibration table and uploading the data information to the predictor construction module; the predictor construction module is used for, according to the received data information, according to the acquired data information, adopting the koopman operator theory, representing the dynamic coupling model of the target six-axis vibration table in a global linearization manner, thereby constructing a koopman predictor, and uploading the data information to the predictor calculation module; the predictor calculation module is used for, according to the received data information, calculating the characteristic function and the operator matrix of the constructed predictor by using a deep neural network, and uploading the data information to the state information calculation module; the state information calculation module is used for, according to the received data information, training a deep koopman estimator based on the pose input data and the output data of the target six-axis vibration table, obtaining the state information of the target six-axis vibration table through the obtained deep koopman estimator, and uploading the data information to the model design module; the model design module is used for, according to the received data information, designing a multi-dimensional model predictive controller based on the obtained deep koopman estimator as a prediction model, and uploading the data information to the model training module; the model training module is used for, according to the received data information, adopting a fuzzy neural network to perform online setting of the parameters of the designed multi-dimensional model predictive controller, and uploading the data information to the decoupling control module; the decoupling control module is used for, according to the received data information, adopting the obtained set multi-dimensional model predictive controller to control the target six-axis vibration table, thereby completing the decoupling control of the target six-axis vibration table.

Claims

1. A decoupling control method of a six-axis vibration table, characterized by It comprises the following steps: S1. Obtain the data information of the target six-axis vibration table; S2. According to the data information obtained in step S1, using the koopman operator theory, the dynamic coupling model of the target six-axis vibration table is expressed in a global linearization manner, so as to construct a koopman predictor; S3. The characteristic function and operator matrix of the predictor constructed in step S2 are calculated by using a deep neural network; S4. Based on the pose input data and output data of the target six-axis vibration table, a deep koopman estimator is trained, and the state information of the target six-axis vibration table is obtained through the obtained deep koopman estimator; S5. Based on the deep koopman estimator obtained in step S4 as a prediction model, a multi-dimensional model predictive controller is designed; S6. The parameters of the multi-dimensional model predictive controller designed in step S5 are adjusted online by using a fuzzy neural network; S7. The adjusted multi-dimensional model predictive controller obtained in step S6 is used to control the target six-axis vibration table, so as to complete the decoupling control of the target six-axis vibration table.

2. The decoupling control method of a six-axis shaker according to claim 1, wherein The step S2 comprises the following steps: The pose dynamics model of the target six-axis vibration table is set; In the pose dynamics model, the koopman operator is introduced, and the koopman predictor is constructed to upgrade the nonlinear model of the target six-axis vibration table to a linear space, and then the linear expression of the dynamics model of the target six-axis vibration table is obtained.

3. The decoupling control method of a six-axis shaker according to claim 2, characterized in that The step S2 specifically comprises the following steps: The pose dynamics model of the target six-axis vibration table is set as: θ(k+1)=f(θ(k),U(k)) In the formula, θ(k+1) is the pose vector at k+1 time; θ(k) is the pose vector at k time; U(k) is the control vector at k time; f() is a nonlinear mapping function from state to state; The expression of θ(k) is θ(k) = [X(k) Y(k) Z(k) α(k) β(k) γ(k)] T wherein X(k) is the pose of the X-axis direction of the target six-axis vibration table at time k, Y(k) is the pose of the Y-axis direction of the target six-axis vibration table at time k, Z(k) is the pose of the Z-axis direction of the target six-axis vibration table at time k, α(k) is the pose of the rotation of the target six-axis vibration table around the X direction at time k, β(k) is the pose of the rotation of the target six-axis vibration table around the Y direction at time k, and γ(k) is the pose of the rotation of the target six-axis vibration table around the Z direction at time k. The expression of U(k) is U(k) = [u x (k) u y (k) u z (k) u α (k) u β (k) u γ (k)] T where u x (k) is the control signal of the pose X(k) at the k time, u y (k) is the control signal of the pose Y(k) at the k time, and u z (k) u(k) is the control signal for the pose Z(k) at time k α u(k) is the control signal for the pose a(k) at time k β u(k) is the control signal for the pose β(k) at time k γ u(k) is the control signal for the pose γ(k) at time k The control signal of the prediction time step is calculated and set to remain unchanged; define the finite-dimensional Koopman operator matrix K = [A B] and the pose observation function matrix G(θ(k), U(k)), which satisfies G(θ(k+1), U(k)) = AG(θ(k), U(k)) + BU(k) In the formula, G(θ(k), U(k)) represents the pose observation function matrix at time k, and G(θ(k), U(k)) = [g x (k) g y (k) g z (k) g α (k) g β (k) g γ (k)] T , g · (k) is an observation function representing the pose ·(k) after dimensionality increase, g · (k) ∈ H, H represents an infinite Hilbert space, and · takes values of x, y, z, α, β or γ; A is a system matrix of the dimensionality-increased system, and A = diag{A x ,A y ,A z ,A α ,A β ,A γ}, A · is a system matrix corresponding to g · (k); B is an input matrix of the dimensionality-increased system, and B = diag{B x ,B y ,B z ,B α ,B β ,B γ}, B · is an input matrix corresponding to g · (k). The observation function matrices at time k and time k+1 evolve in the H space through a finite-dimensional Koopman operator matrix K, which can upgrade the six-degree-of-freedom vibration table nonlinear model corresponding to the pose state θ to the H space, and the expression corresponding to the Koopman operator matrix K is K=[κ x κ y κ z κ α κ β κ γ ]In the formula, κ · is the Koopman operator corresponding to the pose·(k) after upgrading.

4. The decoupling control method of a six-axis shaker according to claim 3, wherein The step S3 specifically comprises the following steps: The observation function matrix G(θ(k),U(k)) and the operator matrix K are fitted by the deep neural network; wherein the first deep neural network Q1 is configured to fit the pose observation function matrix G(0(k), U(k)); the second deep neural network Q2 is configured to fit an inverse function of the pose observation function matrix G(0(k), U(k)), to realize dimensionality increasing and dimensionality decreasing of the pose model, and to determine the operator matrix K through a linear criterion; the G(0(k), U(k)) based on the deep neural network is represented as G(0(k), U(k)) = Q1(0(k), U(k)) based on Q1, the nonlinear model of the pose is represented in a dimensionality-increased linear state matrix G(0(k), U(k)); the dimensionality-increased state evolves through K, and based on the evolved state, the input, and Q2, an estimated value of the state vector 0(k+1) at the next time is obtained denoted as: In the formulae an estimate of the pose X(k+1) at time k+1; Y(k+1) is an estimate of the pose Y(k+1) at time k+1; Z(k+1) is an estimate of the pose at time k+1; The pose α(k+1) is in the estimated value at time k+1; β(k+1) is an estimated value of the pose β(k+1) at the time k+1; The pose γ(k+1) is the estimated value at k+1 time.

5. The decoupling control method of a six-axis shaker according to claim 4, wherein The step S4 specifically comprises the following steps: Based on the pose input data, control signal and output data of the target six-axis vibration table, Q1 and Q2 are trained to determine the mapping from the original state and input to the koopman invariant subspace, the linear dynamic system G(θ(k+1),U(k))=AG(θ(k),U(k))+BU(k) and the mapping from the invariant subspace to the original state; The criterion function of the network is designed as: ||Q1(θ(k+1),U(k+1))-KQ1(θ(k),U(k)),U(k)|| 2 ||Q2(Q1(θ(k),U(k)),U(k)) - (θ(k),U(k))| 2 || (θ(k+1), U(k+1)) - Q2(θ(k), U(k))| x (k)), U(k))| 2 In the formula, || || represents the norm operation; The input of the koopman predictor and the input of the deep neural network are six poses of the six-axis vibration table, and the output of Q2 is the estimated value of the six poses of the six-axis vibration table.

6. The decoupling control method of a six-axis shaker according to claim 5, wherein The step S5 specifically comprises the following steps: The prediction problem of the preliminary model of the multi-dimensional model predictive control is described as the following optimization problem: where J · (k) is a cost function for the pose x, y, z, a, b, or g; N p and N c are the systems a prediction horizon and a control horizon; for the pose at the time k + s of the prediction; For the norm of the weight P · the sign; R · the sign of the norm of the weight R ref (k+s) is the reference input at time k+s; Δu · (k+s) is the increment of the input signal at time k+s; U min (k) is the lower bound of the control matrix; U max (k) is the upper bound of the control matrix; In the optimization process, the control variables outside the control horizon are kept constant; N p and N c are kept the same for each optimization problem.

7. The decoupling control method of a six-axis shaker according to claim 6, characterized in that The step S6 comprises the following steps: The parameters of the preliminary model predicted by the multi-dimensional model predictive control designed in step S5 include N p , N c , and P · ; For parameter N p and N c , the empirical method is used for setting calculation; For parameter P · , a fuzzy neural network is used for real-time setting.

8. The decoupling control method of a six-axis shaker according to claim 7, wherein For parameter P · , a fuzzy neural network is used for real-time setting, specifically including the following steps: The fuzzy neural network comprises an input layer, a membership function layer, a fuzzy rule fitness layer, a normalization layer and a network output layer; the output ΔP of the network output layer · (k) is the increment of the parameter P · and n is the number of rules of the fuzzy neural network; w ·kk is the output weight of the kth rule corresponding to the pose, The output corresponding to the normalization layer is. Then, the update rate of the gain is calculated as P · (k+1) = P · (k) + ΔP · (k); The performance index function of the fuzzy neural network is set as In the formula, E(k) is an expected value, r(k) is a target value at k moment; y(k) is an actual output value at k moment; Based on the performance index function, the gradient descent algorithm is used to update the related parameters of the fuzzy neural network; the update process is represented as In the formula, σ(t+1) is a value of parameter at t+1 moment; σ(t) is a value of parameter at t moment; η is a learning rate, and a is a smoothing factor.

9. A system for implementing the decoupling control method of a six-axis shaker according to one of claims 1 to 8, characterized in that The data acquisition module is configured to acquire data information of the target six-axis vibration table and upload the data information to the predictor construction module; the predictor construction module is configured to, according to the received data information, according to the acquired data information, adopt a koopman operator theory, represent a dynamic coupling model of the target six-axis vibration table in a global linearization manner, thereby construct a koopman predictor, and upload the data information to the predictor calculation module; the predictor calculation module is configured to, according to the received data information, adopt a deep neural network to calculate a characteristic function and an operator matrix of the constructed predictor, and upload the data information to the state information calculation module; the state information calculation module is configured to, according to the received data information, based on pose input data and output data of the target six-axis vibration table, train a deep koopman estimator, acquire state information of the target six-axis vibration table through the obtained deep koopman estimator, and upload the data information to the model design module; The model design module is configured to, according to the received data information, based on the obtained deep koopman estimator as a prediction model, design a multi-dimensional model predictive controller, and upload the data information to the model training module; The model training module is configured to, according to the received data information, adopt a fuzzy neural network to perform online setting on parameters of the designed multi-dimensional model predictive controller, and upload the data information to the decoupling control module; The decoupling control module is configured to, according to the received data information, adopt the obtained set multi-dimensional model predictive controller to control the target six-axis vibration table, thereby completing decoupling control of the target six-axis vibration table.

Images