A control method for a two-degree-of-freedom electro-hydraulic position servo system

Abstract

The embodiment of the application discloses a control method of a two-degree-of-freedom electro-hydraulic position servo system, which comprises the following steps: obtaining historical operation data of the two-degree-of-freedom electro-hydraulic position servo system and performing normalization processing to obtain normalized data; iteratively training an initialized single-hidden-layer NARX neural network by using a position reference signal in the normalized data to obtain a preset neural network; obtaining a mean square error and a counter value of the preset neural network, and judging whether the preset neural network satisfies a second inequality condition according to the mean square error and the counter value; if the preset neural network does not satisfy the second inequality condition, updating Bayesian parameters of the preset neural network by using a data error, an effectiveness measurement index of the preset neural network and a control parameter of the preset neural network to obtain an updated neural network; and calculating driving data for the two-degree-of-freedom electro-hydraulic position servo system according to an actual position signal, the updated neural network and the normalized data.

Description

Technical Field

[0001] This invention relates to the field of electro-hydraulic position control technology, and in particular to a control method for a two-degree-of-freedom electro-hydraulic position servo system. Background Technology

[0002] The two-degree-of-freedom electro-hydraulic position servo system, as the core power drive and execution unit of the electro-hydraulic vibration table, directly determines the quality of reliability testing of large structural components. The electro-hydraulic vibration table is a key piece of equipment for reliability testing of large structural components, significantly improving the efficiency of vibration simulation testing and finding wide application in aerospace, civil engineering, and the automotive industry. The control accuracy of the two-degree-of-freedom electro-hydraulic position servo system directly affects the qualitative and quantitative evaluation of reliability experiments. Using the two-degree-of-freedom electro-hydraulic position servo system, position reference signals can be reproduced on the electro-hydraulic vibration table to test the dynamic response of the product under vibration conditions, thereby guiding the design of the product's vibration resistance performance.

[0003] A two-degree-of-freedom electro-hydraulic position servo system is a typical strongly coupled and highly nonlinear system. Existing controllers based on linearized models are only effective within the interval near the linearized operating point. When the two-degree-of-freedom electro-hydraulic position servo system operates at high speeds, the position output signal of the system will exhibit severe distortion compared to the position reference signal if a traditional controller is used. Controllers based on linearized models, because they do not consider the nonlinear factors in the system, are affected by the coupling effect between the degrees of freedom, resulting in excessively large peak time-domain errors between the position output signals of the two degrees of freedom and the reference signal, severely reducing the accuracy of reliability test evaluations. Summary of the Invention

[0004] The purpose of this invention is to propose a control method and related equipment for a two-degree-of-freedom electro-hydraulic position servo system, aiming to solve the problem of low evaluation accuracy in existing reliability experiments.

[0005] To achieve one, some, or all of the above objectives, or other objectives, in a first aspect, the present invention proposes a control method for a two-degree-of-freedom electro-hydraulic position servo system, the method comprising: Historical operating data of a two-degree-of-freedom electro-hydraulic position servo system is acquired, and the historical operating data is normalized to obtain normalized data. The position reference signal in the normalized data is used to iteratively train the initialized single-hidden-layer NARX neural network until the trained single-hidden-layer NARX neural network satisfies the first inequality condition, thus obtaining the preset neural network. Obtain the mean square error and counter value of the preset neural network, and determine whether the preset neural network satisfies the second inequality condition based on the mean square error and counter value. If the preset neural network does not satisfy the second inequality condition, then the data error of the preset neural network is calculated based on the output data of the preset neural network for the position reference signal; The Bayesian parameters of the preset neural network are updated based on the data error, validity measurement index and control parameters of the preset neural network until the updated preset neural network satisfies the first inequality condition and the second inequality condition, thus obtaining the updated neural network. Acquire the actual position signal, and calculate the drive data for the electro-hydraulic position servo system based on the actual position signal, the network parameters of the updated neural network, and the normalized data.

[0006] Optionally, the step of acquiring historical operating data of the two-degree-of-freedom electro-hydraulic position servo system and normalizing the historical operating data to obtain normalized data includes: Acquire historical operating data of the electro-hydraulic position servo system, the historical operating data including position input signals and position output signals; Based on the maximum value, minimum value, maximum value, and minimum value of the first input signal, the second input signal, the first output signal, the first output signal, the second output signal, and the second output signal, the historical operation data is normalized to obtain normalized data.

[0007] Optionally, the step of iteratively training the initialized single-hidden-layer NARX neural network using the position reference signal in the normalized data until the trained single-hidden-layer NARX neural network satisfies the first inequality condition to obtain the preset neural network includes: The Jacobian matrix of the initialized single-hidden-layer NARX neural network is calculated based on the output data of the position reference signal. Calculate the approximate Hessian matrix based on the Jacobian matrix; The improved approximate Hessian matrix is ​​calculated based on the approximate Hessian matrix, and the parameter update gradient of the initialized single-hidden-layer NARX neural network is calculated based on the improved approximate Hessian matrix. Based on the parameter update gradient, the current parameters of the initialized single-hidden-layer NARX neural network are updated to obtain a candidate single-hidden-layer NARX neural network; Based on the data error of the NARX neural network in the hidden layer of the candidate list and the first inequality condition, identify whether the NARX neural network in the hidden layer of the candidate list satisfies the first inequality condition; If the candidate single-hidden-layer NARX neural network satisfies the first inequality condition, then the algorithm damping factor of the candidate single-hidden-layer NARX neural network is reduced by a first preset factor to obtain the preset neural network. If the candidate single-hidden-layer NARX neural network does not satisfy the first inequality condition, then the algorithm damping factor of the candidate single-hidden-layer NARX neural network is increased by a second preset factor. Based on the algorithm damping factor increased by the second preset factor, the steps of calculating the improved approximate Hessian matrix according to the approximate Hessian matrix and calculating the parameter update gradient of the initialized single-hidden-layer NARX neural network based on the improved approximate Hessian matrix are executed until a candidate single-hidden-layer NARX neural network that satisfies the first inequality condition is obtained, and the candidate single-hidden-layer NARX neural network is used as the preset neural network.

[0008] Optionally, the method further includes: If the preset neural network satisfies the second inequality condition, then the drive data for the electro-hydraulic position servo system is calculated based on the network parameters of the preset neural network, the maximum value vector in the normalized data, and the minimum value vector in the normalized data.

[0009] Optionally, the step of determining whether the preset neural network satisfies the second inequality condition based on the mean square error and the counter value includes: Based on the mean square error, determine whether the preset neural network satisfies the mean square error condition in the second inequality. Based on the counter value, determine whether the preset neural network satisfies the counting condition in the second inequality. If the preset neural network satisfies at least one of the mean square error condition and the counting condition, then it is determined that the preset neural network satisfies the second inequality condition.

[0010] Optionally, the step of acquiring the actual position signal and calculating the drive data for the electro-hydraulic position servo system based on the actual position signal, the network parameters of the updated neural network, and the normalized data includes: Based on the actual position signal, the maximum value of the first output signal in the normalized data, the minimum value of the first output signal in the normalized data, the maximum value of the second output signal in the normalized data, and the minimum value of the second output signal in the normalized data, the following is calculated using a first preset formula:

[0011] Calculate the first input signal, where, and This is the actual location signal. The minimum value of the first output signal. The maximum value of the first output signal. The minimum value of the second output signal. The maximum value of the second output signal. This is the first input signal; The first input signal is input into a single-hidden-layer NARX neural network using the network parameters of the updated neural network to obtain the second input signal. Based on the second input signal, the maximum value of the first input signal in the normalized data, the minimum value of the first input signal in the normalized data, the maximum value of the second input signal in the normalized data, and the minimum value of the second input signal in the normalized data, a second preset formula is used:

[0012] Calculate the drive data for the electro-hydraulic position servo system, where, and This is the second input signal. The maximum value of the first input signal in the normalized data, The minimum value of the first input signal in the normalized data, The maximum value of the second input signal in the normalized data, It is the minimum value of the second input signal in the normalized data.

[0013] Optionally, the mathematical representation of the first inequality condition is:

[0014] in, , For the first Bayesian parameters for the next iteration For the first Data error in the next iteration For the first The parameter vector to be updated in the next iteration For the first Data error in the next iteration For the first The parameter vector to be updated in the next iteration.

[0015] The embodiments of the present invention have the following beneficial effects: By leveraging the nonlinear mapping capability of neural networks, the nonlinear dynamic behavior of a two-degree-of-freedom electro-hydraulic position servo system is reconstructed. Through a neural network controller, the time-domain peak values ​​of the two-degree-of-freedom position output signal and the position reference signal are reduced to less than 10%, significantly improving the waveform tracking accuracy of the position reference signal. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] in: Figure 1 This is a flowchart of a control method for a two-degree-of-freedom electro-hydraulic position servo system provided in an embodiment of this application. Detailed Implementation

[0018] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0019] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0020] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0021] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [the described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [the described condition or event] is detected," or "in response to detection of [the described condition or event]."

[0022] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0023] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0024] like Figure 1 As shown, the present invention provides a control method for a two-degree-of-freedom electro-hydraulic position servo system, the method comprising: S101. Obtain historical operating data of the two-degree-of-freedom electro-hydraulic position servo system, and normalize the historical operating data to obtain normalized data. In one possible implementation, the step of acquiring historical operating data of the two-degree-of-freedom electro-hydraulic position servo system and normalizing the historical operating data to obtain normalized data includes: Acquire historical operating data of the electro-hydraulic position servo system, the historical operating data including position input signals and position output signals; Based on the maximum value, minimum value, maximum value, minimum value of the first input signal, maximum value, minimum value of the second input signal, maximum value, minimum value of the second output signal, maximum value, minimum value of the first output signal, maximum value, minimum value of the second output signal, maximum value, and minimum value of the second output signal, the historical operation data is normalized to obtain normalized data.

[0025] For example, the position input signal of a two-degree-of-freedom electro-hydraulic position servo system is defined as follows: Define the position output signal of a two-degree-of-freedom electro-hydraulic position servo system as: ,collection and Both are 3D data matrix .

[0026] definition All vector elements are of 3D row vectors.

[0027] definition The maximum value is The minimum value is Construct vectors and ; definition The maximum value is The minimum value is Construct vectors and ; definition The maximum value is The minimum value is Construct vectors and ; definition The maximum value is The minimum value is Construct vectors and .

[0028] Normalization calculation and The calculation formula is:

[0029]

[0030]

[0031]

[0032] In the formula, This indicates that two vectors are divided element-wise.

[0033] and The expression is:

[0034] .

[0035] S102. The position reference signal in the normalized data is used to iteratively train the initialized single-hidden-layer NARX neural network until the trained single-hidden-layer NARX neural network satisfies the first inequality condition, and the preset neural network is obtained. For example, in a single-hidden-layer NARX neural network, the output signal of the neural network is defined as:

[0036] The calculation formula is:

[0037] In the formula, This is a counter for the number of iterations. ; The total number of training samples and .

[0038] Weights from hidden layer to output layer:

[0039] Weights input to the hidden layer:

[0040] The weights fed back to the hidden layer are:

[0041] Hidden layer bias:

[0042] Output layer bias:

[0043] Input delay sequence ; superscript Represents the transpose of a matrix or vector.

[0044] Feedback Delay Sequence ; Among them, sequence , , ; The hyperbolic tangent function is calculated using the following formula: ; definition For the first The parameter vector to be updated in the next iteration The expression is:

[0045] In the formula, , .

[0046] ; ; ; Define operators To round up, To take the remainder.

[0047] when hour: , ;like ,but ,in ; .like ,but ,make ,in ; .

[0048] when hour: , .

[0049] when hour: , , .

[0050] when hour: , .

[0051] For example, when initializing a single-hidden-layer NARX neural network, k=1. initialization , :

[0052] In the formula, ; For vectors Row vectors, and Each element in the dataset is a random number selected between [-0.5, 0.5]. It is the Euclidean norm.

[0053] initialization :set up Each element in Select a random number from the given range.

[0054] initialization :set up Each element in Select a random number from the given range.

[0055] initialization :set up .

[0056] definition For the first The algorithm damping factor for the next iteration is set to an initial value. .

[0057] Define initial data error , The calculation formula is:

[0058] definition For the first The effectiveness metrics for the next iteration parameters are set as follows: .

[0059] definition , For the first The Bayesian parameters for the next iteration are calculated initially. , : .

[0060] In one possible implementation, the step of iteratively training an initialized single-hidden-layer NARX neural network using the position reference signal in the normalized data until the trained single-hidden-layer NARX neural network satisfies the first inequality condition to obtain a preset neural network includes: The Jacobian matrix of the initialized single-hidden-layer NARX neural network is calculated based on the output data of the position reference signal. Calculate the approximate Hessian matrix based on the Jacobian matrix; The improved approximate Hessian matrix is ​​calculated based on the approximate Hessian matrix, and the parameter update gradient of the initialized single-hidden-layer NARX neural network is calculated based on the improved approximate Hessian matrix. Based on the parameter update gradient, the current parameters of the initialized single-hidden-layer NARX neural network are updated to obtain a candidate single-hidden-layer NARX neural network; Based on the data error of the NARX neural network in the hidden layer of the candidate list and the first inequality condition, identify whether the NARX neural network in the hidden layer of the candidate list satisfies the first inequality condition; If the candidate single-hidden-layer NARX neural network satisfies the first inequality condition, then the algorithm damping factor of the candidate single-hidden-layer NARX neural network is reduced by a first preset factor to obtain the preset neural network. If the candidate single-hidden-layer NARX neural network does not satisfy the first inequality condition, then the algorithm damping factor of the candidate single-hidden-layer NARX neural network is increased by a second preset factor. Based on the algorithm damping factor increased by the second preset factor, the steps of calculating the improved approximate Hessian matrix according to the approximate Hessian matrix and calculating the parameter update gradient of the initialized single-hidden-layer NARX neural network based on the improved approximate Hessian matrix are executed until a candidate single-hidden-layer NARX neural network that satisfies the first inequality condition is obtained, and the candidate single-hidden-layer NARX neural network is used as the preset neural network.

[0061] In one possible implementation, the first inequality condition is mathematically represented as:

[0062] in, , For the first Bayesian parameters for the next iteration For the first Data error in the next iteration For the first The parameter vector to be updated in the next iteration For the first Data error in the next iteration For the first The parameter vector to be updated in the next iteration.

[0063] For example, calculating the Jacobian matrix

[0064] for A 3D matrix, expressed as:

[0065] The formulas for calculating each element are as follows:

[0066]

[0067] In the formula,

[0068]

[0069] Calculate the approximate Hessian matrix :

[0070] In the formula, for An identity matrix of order.

[0071] Calculate the improved approximate Hessian matrix :

[0072] definition For the first The gradient for updating parameters in the next iteration is calculated using the following formula:

[0073] Update network parameters:

[0074] Calculate the new network output The calculation formula is:

[0075]

[0076] Calculate the data error after updating the network parameter variables. The calculation formula is:

[0077] Calculate the following inequalities:

[0078] If the inequality does not hold, let Perform the steps of calculating the improved approximate Hessian matrix based on the approximate Hessian matrix, and calculating the parameter update gradient of the initialized single-hidden-layer NARX neural network based on the improved approximate Hessian matrix. If the inequality holds, let Based on the mean square error and the counter value, it is determined whether the preset neural network satisfies the second inequality condition.

[0079] S103. Obtain the mean square error and counter value of the preset neural network, and determine whether the preset neural network satisfies the second inequality condition based on the mean square error and counter value. S104. If the preset neural network does not satisfy the second inequality condition, then calculate the data error of the preset neural network based on the output data of the preset neural network for the position reference signal. S105. Update the Bayesian parameters of the preset neural network according to the data error, validity measurement index and control parameters of the preset neural network until the updated preset neural network satisfies the first inequality condition and the second inequality condition, and obtain the updated neural network. In one possible implementation, the step of determining whether the preset neural network satisfies the second inequality condition based on the mean square error and the counter value includes: Based on the mean square error, determine whether the preset neural network satisfies the mean square error condition in the second inequality. Based on the counter value, determine whether the preset neural network satisfies the counting condition in the second inequality. If the preset neural network satisfies at least one of the mean square error condition and the counting condition, then it is determined that the preset neural network satisfies the second inequality condition.

[0080] For example, calculation :

[0081] In the formula, The trace of a matrix is ​​the sum of the elements on its main diagonal.

[0082] Update counter

[0083] Calculate the mean square error

[0084] When satisfied and Output any one of the following: These parameters serve as the optimal parameters for the neural network controller; otherwise, training continues and the Bayesian parameters are updated.

[0085] make And recalculate the Jacobian matrix. .

[0086] S106. Obtain the actual position signal, and calculate the driving data for the electro-hydraulic position servo system based on the actual position signal, the network parameters of the updated neural network, and the normalized data.

[0087] In one possible implementation, the step of acquiring the actual position signal and calculating the drive data for the electro-hydraulic position servo system based on the actual position signal, the network parameters of the updated neural network, and the normalized data includes: Based on the actual position signal, the maximum value of the first output signal in the normalized data, the minimum value of the first output signal in the normalized data, the maximum value of the second output signal in the normalized data, and the minimum value of the second output signal in the normalized data, the following is calculated using a first preset formula:

[0088] Calculate the first input signal, where, and This is the actual location signal. The minimum value of the first output signal. The maximum value of the first output signal. The minimum value of the second output signal. The maximum value of the second output signal. This is the first input signal; The first input signal is input into a single-hidden-layer NARX neural network using the network parameters of the updated neural network to obtain the second input signal. Based on the second input signal, the maximum value of the first input signal in the normalized data, the minimum value of the first input signal in the normalized data, the maximum value of the second input signal in the normalized data, and the minimum value of the second input signal in the normalized data, a second preset formula is used:

[0089] Calculate the drive data for the electro-hydraulic position servo system, where, and This is the second input signal. The maximum value of the first input signal in the normalized data, The minimum value of the first input signal in the normalized data, The maximum value of the second input signal in the normalized data, It is the minimum value of the second input signal in the normalized data.

[0090] For example, the position reference signal is defined as , for 3D data matrix It is a positive integer greater than 20. The reference signal... As the first input signal, calculate the corresponding output signal. The calculation formula is:

[0091] Will As the input signal to the neural network controller, using optimal parameters Calculate the output signal of the neural network controller The calculation formula is:

[0092]

[0093] ; The total number of valid outputs of the network, and ; ; And sequence , , ; Will As the second input signal, calculate the corresponding output signal. The calculation formula is:

[0094] Will The signal is used as a drive signal to drive the electro-hydraulic position servo system.

[0095] In one possible implementation, the method further includes: If the preset neural network satisfies the second inequality condition, then the drive data for the electro-hydraulic position servo system is calculated based on the network parameters of the preset neural network, the maximum value vector in the normalized data, and the minimum value vector in the normalized data.

[0096] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computing device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0097] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

[0098] The above description discloses only preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Therefore, equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A control method for a two-degree-of-freedom electro-hydraulic position servo system, characterized in that, The method includes: Historical operating data of a two-degree-of-freedom electro-hydraulic position servo system is acquired, and the historical operating data is normalized to obtain normalized data. The position reference signal in the normalized data is used to iteratively train the initialized single-hidden-layer NARX neural network until the trained single-hidden-layer NARX neural network satisfies the first inequality condition, thus obtaining the preset neural network. Obtain the mean square error and counter value of the preset neural network, and determine whether the preset neural network satisfies the second inequality condition based on the mean square error and counter value. If the preset neural network does not satisfy the second inequality condition, then the data error of the preset neural network is calculated based on the output data of the preset neural network for the position reference signal; The Bayesian parameters of the preset neural network are updated based on the data error, validity measurement index and control parameters of the preset neural network until the updated preset neural network satisfies the first inequality condition and the second inequality condition, thus obtaining the updated neural network. Acquire the actual position signal, and calculate the drive data for the electro-hydraulic position servo system based on the actual position signal, the network parameters of the updated neural network, and the normalized data.

2. The control method for a two-degree-of-freedom electro-hydraulic position servo system according to claim 1, characterized in that, The step of acquiring historical operating data of a two-degree-of-freedom electro-hydraulic position servo system and normalizing the historical operating data to obtain normalized data includes: Acquire historical operating data of the electro-hydraulic position servo system, the historical operating data including position input signals and position output signals; Based on the maximum value, minimum value, maximum value, and minimum value of the first input signal, the second input signal, the first output signal, the first output signal, the second output signal, and the second output signal, the historical operation data is normalized to obtain normalized data.

3. The control method for a two-degree-of-freedom electro-hydraulic position servo system according to claim 1, characterized in that, The step of iteratively training an initialized single-hidden-layer NARX neural network using the position reference signal in the normalized data until the trained single-hidden-layer NARX neural network satisfies the first inequality condition to obtain the preset neural network includes: The Jacobian matrix of the initialized single-hidden-layer NARX neural network is calculated based on the output data of the position reference signal. Calculate the approximate Hessian matrix based on the Jacobian matrix; The improved approximate Hessian matrix is ​​calculated based on the approximate Hessian matrix, and the parameter update gradient of the initialized single-hidden-layer NARX neural network is calculated based on the improved approximate Hessian matrix. Based on the parameter update gradient, the current parameters of the initialized single-hidden-layer NARX neural network are updated to obtain a candidate single-hidden-layer NARX neural network; Based on the data error of the NARX neural network in the hidden layer of the candidate list and the first inequality condition, identify whether the NARX neural network in the hidden layer of the candidate list satisfies the first inequality condition; If the candidate single-hidden-layer NARX neural network satisfies the first inequality condition, then the algorithm damping factor of the candidate single-hidden-layer NARX neural network is reduced by a first preset factor to obtain the preset neural network. If the candidate single-hidden-layer NARX neural network does not satisfy the first inequality condition, then the algorithm damping factor of the candidate single-hidden-layer NARX neural network is increased by a second preset factor. Based on the algorithm damping factor increased by the second preset factor, the steps of calculating the improved approximate Hessian matrix according to the approximate Hessian matrix and calculating the parameter update gradient of the initialized single-hidden-layer NARX neural network based on the improved approximate Hessian matrix are executed until a candidate single-hidden-layer NARX neural network that satisfies the first inequality condition is obtained, and the candidate single-hidden-layer NARX neural network is used as the preset neural network.

4. The control method for a two-degree-of-freedom electro-hydraulic position servo system according to claim 1, characterized in that, The method further includes: If the preset neural network satisfies the second inequality condition, then the drive data for the electro-hydraulic position servo system is calculated based on the network parameters of the preset neural network, the maximum value vector in the normalized data, and the minimum value vector in the normalized data.

5. The control method for a two-degree-of-freedom electro-hydraulic position servo system according to claim 1, characterized in that, The step of determining whether the preset neural network satisfies the second inequality condition based on the mean square error and the counter value includes: Based on the mean square error, determine whether the preset neural network satisfies the mean square error condition in the second inequality. Based on the counter value, determine whether the preset neural network satisfies the counting condition in the second inequality. If the preset neural network satisfies at least one of the mean square error condition and the counting condition, then it is determined that the preset neural network satisfies the second inequality condition.

6. The control method for a two-degree-of-freedom electro-hydraulic position servo system according to claim 1, characterized in that, The steps of acquiring the actual position signal and calculating the drive data for the electro-hydraulic position servo system based on the actual position signal, the network parameters of the updated neural network, and the normalized data include: Based on the actual position signal, the maximum value of the first output signal in the normalized data, the minimum value of the first output signal in the normalized data, the maximum value of the second output signal in the normalized data, and the minimum value of the second output signal in the normalized data, the following is calculated using a first preset formula: Calculate the first input signal, where, and This is the actual location signal. The minimum value of the first output signal. The maximum value of the first output signal. The minimum value of the second output signal. The maximum value of the second output signal. This is the first input signal; The first input signal is input into a single-hidden-layer NARX neural network using the network parameters of the updated neural network to obtain the second input signal. Based on the second input signal, the maximum value of the first input signal in the normalized data, the minimum value of the first input signal in the normalized data, the maximum value of the second input signal in the normalized data, and the minimum value of the second input signal in the normalized data, a second preset formula is used: Calculate the drive data for the electro-hydraulic position servo system, where, and This is the second input signal. The maximum value of the first input signal in the normalized data, The minimum value of the first input signal in the normalized data, The maximum value of the second input signal in the normalized data, It is the minimum value of the second input signal in the normalized data.

7. The control method for a two-degree-of-freedom electro-hydraulic position servo system according to claim 1, characterized in that, The mathematical representation of the first inequality condition is: in, , For the first Bayesian parameters for the next iteration For the first Data error in the next iteration For the first The parameter vector to be updated in the next iteration For the first Data error in the next iteration For the first The parameter vector to be updated in the next iteration.

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