A coupling calibration and control method of a semi-physical fan thrust execution system

Abstract

This invention discloses a coupling calibration and control method for a semi-physical wind turbine thrust actuator system, belonging to the technical field of semi-physical real-time hybrid model testing for floating wind turbines. The specific steps include: collecting multiple sets of pulse width modulation signal combinations and corresponding generalized thrust output data as calibration samples; constructing a structured physical information feature containing first-order thrust terms, second-order nonlinear terms, adjacent coupling terms, and coaxial inverse competition terms through single-unit thrust mapping; obtaining a forward thrust calibration model through feature standardization and multi-output ridge regression training; constructing a control solution model with signal boundaries and reference constraints; deriving analytical Jacobian matrices to iteratively solve control commands; and driving each actuator to output the target thrust. This method can effectively characterize the aerodynamic coupling effect between multiple actuators, improve thrust calibration accuracy and control accuracy, and is suitable for semi-physical testing applications in floating wind turbine pools.

Description

Technical Field

[0001] This invention relates to the field of semi-physical real-time hybrid model testing technology for floating wind turbines, and in particular to a coupling calibration and control method for a semi-physical wind turbine thrust actuation system. Background Technology

[0002] In existing technologies, the thrust actuation system for semi-physical real-time hybrid model tests of floating wind turbines generally adopts a calibration and control method that combines single-unit static calibration with fixed geometric allocation: first, static calibration tests are carried out on each independent drive actuator to establish the correspondence between single-channel pulse width modulation signal and single-unit thrust output; then, a fixed load inverse solution allocation matrix is ​​constructed based on the spatial installation position, thrust direction, and lever arm parameters of each actuator, and the target generalized thrust is directly allocated to each independent drive actuator, thereby realizing the real-time loading of wind turbine aerodynamic loads onto the physical model.

[0003] However, such existing technical solutions have inherent performance limitations in practical applications: since each independent drive actuator is treated as an independent thrust output unit, system-level calibration is not carried out for multi-component combined operation conditions. Aerodynamic coupling and wake interference generated by spatially adjacent actuators will cause the actual thrust output to deviate from the single-machine calibration result. The thrust competition and dominance relationship between coaxially arranged actuators cannot be accurately reflected by fixed geometric allocation logic. At the same time, the linear mode based on single-machine calibration and fixed allocation is difficult to fully characterize the nonlinear output characteristics of the thrust system, which will lead to a large deviation between the target thrust and the actual loaded thrust. Furthermore, under the redundant mapping of multiple control inputs corresponding to few-dimensional thrust outputs, the existing solution method is difficult to simultaneously take into account thrust reproduction accuracy, control command continuity and real-time calculation efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a coupling calibration and control method for a semi-physical wind turbine thrust actuation system, thereby solving the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides a coupling calibration and control method for a semi-physical wind turbine thrust actuation system, comprising the following steps: S1, the semi-physical wind turbine thrust execution system includes seven independent drive execution elements, which are used to collect multiple sets of pulse width modulation signal combinations and corresponding actual generalized thrust output data to obtain multiple sets of calibration test samples; S2. Based on the pulse width modulation signal and single-machine thrust calibration relationship pre-established for each independent drive actuator, the single-machine thrust corresponding to each set of calibration test samples is obtained by mapping and converting the pulse width modulation signal in each set of calibration test samples. S3. Based on the spatial topology and steering relationship of the independent drive actuators, the physical information structure features of the single-machine thrust are obtained by constructing multi-dimensional physical information features, including first-order thrust terms, second-order thrust nonlinear terms, coupling terms of adjacent independent drive actuators, and competition terms of coaxial reverse independent drive actuators. S4. Based on the structured features of physical information and actual generalized thrust output data, a forward thrust calibration model of the thrust execution system is obtained through feature standardization and multi-output ridge regression training. S5. Based on the forward thrust calibration model, a pulse width modulation control signal solution model is constructed by introducing target thrust deviation optimization target, pulse width modulation signal boundary constraints and reference pulse width modulation signal constraints. S6. Based on the forward thrust calibration model, the analytical Jacobian matrix of the predicted thrust relative to the pulse width modulation signal is derived and iteratively solved to obtain the pulse width modulation control command for seven independent drive actuators. S7. Based on pulse width modulation control commands, the thrust execution system outputs an actual thrust corresponding to the target thrust by outputting corresponding control signals to each independent drive actuator.

[0006] Preferably, the specific steps of S1 are as follows: Based on the preset pulse width modulation signal operating range of seven independent drive actuators, multiple sets of seven-channel pulse width modulation signal combinations are generated by the Latin hypercube sampling method. The actual generalized thrust output data corresponding to each signal combination is measured synchronously to obtain multiple sets of calibration test samples that uniformly cover the operating range.

[0007] Preferably, the relationship between the pulse width modulation signal in S2 and the single-unit thrust calibration is established in the following way: Based on multiple pulse width modulation signals from a single independent drive actuator and corresponding measured thrust data of a single unit, a nonlinear fitting using a quadratic polynomial is performed to obtain the calibration relationship between the pulse width modulation signal and the thrust of the single unit. The calculation formula is as follows: ; in, For the first The thrust of a single drive actuator. For the first Pulse width modulation signal for each independent drive actuator, , , For the first Calibration coefficients for each independent drive actuator. .

[0008] Preferably, the specific steps of S3 are as follows: Based on the single-machine thrust of seven independent drive actuators, by constructing basic contribution terms, nonlinear correction terms, adjacent aerodynamic interference terms, and coaxial reverse competition terms respectively, a twenty-three-dimensional physical information structured feature is obtained, consisting of seven first-order thrust terms, seven second-order thrust nonlinear terms, eight adjacent independent drive actuator coupling terms, and one coaxial reverse independent drive actuator competition term.

[0009] Preferably, the process for obtaining the competing items for coaxial reverse independent drive actuators is as follows: Based on the single-unit thrust of the second and seventh independent drive actuators, by introducing a preset small amount to avoid the denominator being zero and constructing a ratio term between the thrust difference and the absolute value of the thrust sum, the competition term of the coaxial reverse independent drive actuators is obtained, and the calculation formula is as follows: ; in, For coaxial reverse independent drive actuator competition item, For the single-machine thrust of the second independent drive actuator, For the single-machine thrust of the seventh independent drive actuator, The preset value is greater than zero; when the ratio is close to 1, it indicates that the thrust of the second independent drive actuator is dominant, and when the ratio is close to -1, it indicates that the thrust of the seventh independent drive actuator is dominant.

[0010] Preferably, the specific steps of S4 are as follows: Based on the physical information structured feature matrix and the actual generalized thrust output matrix corresponding to multiple sets of calibration test samples, the regression coefficient matrix of the forward thrust calibration model is obtained by standardizing the features, centering the output, and introducing Frobenius norm regularization term to constrain the magnitude of the regression coefficients, and using multi-output ridge regression for closed-form solution. The formula for the optimization objective of multi-output ridge regression is: ; in, For matrix To optimize the variables, find the optimal solution that minimizes the objective function; This is the centered actual generalized thrust output matrix; This is the standardized structured feature matrix of physical information; Here is the regression coefficient matrix to be solved; The ridge regression regularization coefficient has a value not less than 0. is the Frobenius norm, which is calculated by taking the square root of the sum of the squares of all elements of the matrix, and is used to represent the overall magnitude of the matrix. The formula for the closed-form solution of the regression coefficient matrix is: ; in, It is a 23×23 identity matrix; for The transpose of .

[0011] Preferably, the specific steps of S5 are as follows: Based on the deviation between the target thrust and the predicted thrust, and the deviation between the pulse width modulation signal and the reference pulse width modulation signal, a joint optimization objective is constructed by setting the thrust error weight matrix and regularization weight, and the upper and lower boundary constraints of the pulse width modulation signal are superimposed to construct a pulse width modulation control signal solution model. The formula for solving the optimization objective of the model is: ; in, For vectors To optimize the variables, find the optimal solution that minimizes the objective function; Let be the control vector composed of seven pulse width modulation signals, and be the optimization variables to be solved. This is the thrust error weighting matrix, used to weight and allocate the tracking errors of each generalized thrust component. The predicted generalized thrust vector output by the forward thrust calibration model is determined by the control vector. Obtained by mapping through the forward thrust calibration model; The target generalized thrust vector; It is the 2-norm of the vector; These are the regularization weight coefficients; The reference pulse width modulation signal vector is used to constrain the deviation between the control signal obtained from the solution and the reference value. , These are the upper and lower limits of operation for each pulse width modulation signal, used to normalize the deviation of the control signal; The constraints for solving the model are: .

[0012] Preferably, the process of acquiring the reference pulse width modulation signal in S5 is as follows: During the initial solution, the reference pulse width modulation signal is obtained by taking the midpoint of the interval based on the working range of the pulse width modulation signal. During continuous control, the reference pulse width modulation signal is obtained by taking the pulse width modulation control command of the previous cycle based on the output result of the previous control cycle.

[0013] Preferably, the process of obtaining the analytic Jacobian matrix in S6 is as follows: Based on the single-unit thrust calibration relationship, the structured feature construction relationship of physical information, the feature standardization relationship, and the ridge regression coefficient matrix, the analytical Jacobian matrix of the predicted thrust relative to the seven-channel pulse width modulation signal is derived layer by layer using the chain rule. The calculation formula is as follows: ; in, The analytical Jacobian matrix is ​​used to predict the generalized thrust relative to the seven-channel pulse width modulation signal, and is used to characterize the degree of influence of the pulse width modulation signal on the output thrust. To predict the generalized thrust vector Relative to pulse width modulation control vector The partial derivatives; It is a diagonal matrix composed of the standard deviations of each dimension of the structured features of physical information; The Jacobian matrix of the structured feature vectors of physical information relative to the seven-channel pulse width modulation signal; This indicates that the Jacobian matrix is ​​a real matrix with 4 rows and 7 columns.

[0014] Preferably, the iterative solution process in S6 is as follows: Based on the analytical Jacobian matrix and the augmented residual vector, the pulse width modulation signal is iteratively updated using the damped Gauss-Newton method until the infinity norm of the iteration increment is less than a preset threshold or the maximum number of iterations is reached, thus obtaining the final pulse width modulation control command. The formula for calculating the iterative increment of a pulse width modulation signal is: ; in, For the first The iteration increment vector of the seven pulse width modulation signals corresponding to the next iteration; This represents the number of iterations. For the first The augmented Jacobian matrix corresponding to the next iteration; To augment the Jacobian matrix The transpose of the matrix; For the first The damping coefficient of the next iteration is used to constrain the iteration step size and improve the numerical stability of the iterative solution; It is a 7th order identity matrix; For the first The augmented residual vector corresponding to the next iteration.

[0015] Therefore, the coupling calibration and control method of the semi-physical wind turbine thrust actuator system described above has the following beneficial effects: 1. By constructing a 23-dimensional physical information structured feature that includes a first-order thrust term, a second-order thrust nonlinear term, a coupling term between adjacent independent drive actuators, and a competition term between coaxial and reverse independent drive actuators, a system-level calibration of the combined working characteristics of seven independent drive actuators is achieved. This can accurately characterize the airflow interaction, second-order nonlinear effects, and thrust dominance relationship between adjacent actuators arranged in a coaxial and reverse manner, thereby improving the fitting accuracy of the thrust calibration model to the actual output characteristics and reducing the reproduction deviation of the target thrust.

[0016] 2. By adopting a modeling approach that combines feature standardization and output centering preprocessing with multi-output ridge regression, and introducing a Frobenius norm regularization term to constrain the overall amplitude of the regression coefficient matrix, the parameter fluctuation problem under highly correlated features is alleviated, and the generalization performance of the calibration model is improved. At the same time, the regression coefficients have closed-form analytical solutions, and the calculation process is efficient and stable. The forward thrust prediction model can be trained quickly based on the calibration samples, providing a high-precision, analytically differentiable forward mapping foundation for subsequent online control command solutions.

[0017] 3. Based on the single-machine thrust calibration relationship, structured feature construction relationship, feature standardization relationship and ridge regression coefficient matrix, the analytical Jacobian matrix of the predicted thrust relative to the seven-channel pulse width modulation signal is derived layer by layer through the chain rule. This avoids the truncation error and additional sampling calculation overhead caused by numerical difference, improves the accuracy and solution efficiency of gradient calculation, and provides accurate gradient information for the rapid iterative solution of control commands. It supports the real-time control requirements of semi-physical experiments from the underlying algorithm.

[0018] 4. By constructing a joint optimization objective that integrates the weighted error of thrust tracking and the deviation of the reference pulse width modulation signal, and superimposing upper and lower boundary constraints of the pulse width modulation signal, and using the damped Gauss-Newton method for iterative solution, it is ensured that the control command is always within the legal operating range, and the smoothness of the command during continuous control is guaranteed by the reference signal constraint. The damping term further improves the convergence stability of the iteration, and finally achieves the millisecond-level control command solution speed while maintaining extremely high thrust tracking accuracy, which can meet the real-time thrust loading requirements of the semi-physical real-time hybrid model test of floating wind turbine.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 A schematic diagram of the overall process for a coupling calibration and control method of a semi-physical wind turbine thrust actuator system provided by the present invention; Figure 2A schematic diagram of the spatial arrangement of independent drive actuators in a coupling calibration and control method for a semi-physical wind turbine thrust actuator system provided by the present invention; Figure 3 A schematic diagram illustrating the construction of the physical information structured features of the coupling calibration and control method for a semi-physical wind turbine thrust execution system provided by the present invention; Figure 4 A schematic diagram of the calibration results between the independent drive actuators PWM and thrust of a semi-physical wind turbine thrust actuator system provided by the present invention; Figure 5 A comparative schematic diagram of independent test verification results of the forward thrust calibration model for a coupled calibration and control method for a semi-physical wind turbine thrust actuation system provided by this invention; wherein, Figure 5 (a) in the figure represents the oscillation force. Comparison chart of predicted and measured values; Figure 5 (b) in the figure represents the vertical force. Comparison chart of predicted and measured values; Figure 5 (c) in the figure represents the rolling moment. Comparison chart of predicted and measured values; Figure 5 (d) in the figure represents the pitching moment. Comparison chart of predicted and measured values; Figure 6 A schematic diagram illustrating the comparison between target thrust and actual output thrust in the control method of a coupling calibration and control method for a semi-physical wind turbine thrust execution system provided by this invention; wherein, Figure 6 (a) in the figure represents the oscillation force. Comparison chart of target and achieved values; Figure 6 (b) in the figure represents the vertical force. Comparison chart of target and achieved values; Figure 6 (c) in the figure represents the rolling moment. Comparison chart of target and achieved values; Figure 6 (d) in the figure represents the pitching moment. A comparison chart of target and achieved values.

[0021] Figure Labels 1-1, First independent drive actuator; 1-2, Second independent drive actuator; 1-3, Third independent drive actuator; 1-4, Fourth independent drive actuator; 1-5, Fifth independent drive actuator; 1-6, Sixth independent drive actuator; 1-7, Seventh independent drive actuator; 11, Brushless motor; 12, Propeller; 2, Support rod; 3, Central mounting base; 4, Six-dimensional force sensor; 5, Tower connection part. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0023] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0024] The following is in conjunction with the appendix Figures 1-6 The embodiments of the present invention will be described in detail below.

[0025] Existing semi-physical wind turbine thrust actuation systems generally adopt a calibration and control scheme that combines single-unit static calibration with fixed geometric load inverse solution allocation. This scheme treats each independent drive actuator as an independent thrust output unit and does not conduct system-level calibration for multi-actuator combined operation conditions. It cannot accurately characterize the aerodynamic coupling and wake interference effects between spatially adjacent actuators, nor can it reflect the thrust competition and dominance relationship between coaxially arranged reverse actuators. At the same time, it is difficult to fully characterize the second-order nonlinear output characteristics of the system, resulting in a large deviation between the target thrust and the actual loaded thrust. In addition, under the redundant mapping characteristics of multiple control inputs corresponding to few-dimensional thrust outputs, the existing solution method cannot simultaneously guarantee thrust reproduction accuracy, continuous smoothness of control commands, and real-time calculation efficiency, making it difficult to adapt to the loading requirements of high-precision floating wind turbine semi-physical real-time hybrid model tests.

[0026] Based on the above analysis, the specific implementation details are designed, including: This embodiment provides a coupling calibration and control method for a semi-physical wind turbine thrust actuation system, which is applied to a floating wind turbine tank model test. The semi-physical wind turbine thrust actuator system includes seven independent drive actuators 1-1 to 1-7, a support rod 2, a central mounting base 3, a six-dimensional force sensor 4, and a tower connection part 5. Each independent drive actuator consists of a brushless motor 11, a propeller 12, and an electronic speed controller. The electronic speed controller receives pulse width modulation (PWM) control signals and drives the brushless motor to rotate the propeller, outputting thrust in the corresponding direction and amplitude. The tower connection part 5 serves as the mounting docking structure at the bottom of the system, used for fixed connection with the wind turbine tower model. The six-dimensional force sensor 4 is located between the tower connection part 5 and the support rod 2, used for real-time detection of the generalized thrust load output by the system. The support rod 2 is vertically arranged, with the central mounting base 3 fixedly mounted at its top. The central mounting base 3 serves as the bearing base for arranging the seven independent drive actuators 1-1 to 1-7. The support rod 2 includes three circumferentially spaced support rods, namely the first support rod, the second support rod, and the third support rod. (See [reference]). Figure 2 As shown, the first support rod extends upward at an angle, with the fifth independent drive actuator 1-5, the second independent drive actuator 1-2, and the seventh independent drive actuator 1-7 arranged sequentially along the rod body to output thrust components in different spatial orientations. The second independent drive actuator 1-2 and the seventh independent drive actuator 1-7 are arranged coaxially and in opposite directions. The second support rod extends horizontally laterally, with the first independent drive actuator 1-1 installed at its outer end, and the fourth independent drive actuator 1-4 suspended downwards in the middle of the arm body to provide lateral and vertical thrust inputs. The third support rod extends downward at an angle, with the sixth independent drive actuator 1-6 and the third independent drive actuator 1-3 arranged sequentially along the arm body. The first independent drive actuator 1-1 and the fourth independent drive actuator 1-7 are arranged coaxially and in opposite directions. 4. The second independent drive actuator 1-2 and the fifth independent drive actuator 1-5, the second independent drive actuator 1-2 and the seventh independent drive actuator 1-7, the fifth independent drive actuator 1-5 and the seventh independent drive actuator 1-7, the fourth independent drive actuator 1-4 and the fifth independent drive actuator 1-5, the fourth independent drive actuator 1-4 and the sixth independent drive actuator 1-6, the third independent drive actuator 1-3 and the sixth independent drive actuator 1-6, and the fifth independent drive actuator 1-5 and the sixth independent drive actuator 1-6 are adjacent actuator pairs with aerodynamic interactions. These seven independent drive actuators work together to synthesize a generalized thrust output including sway force, vertical force, roll moment, and pitch moment. The control vector composed of the seven pulse width modulation signals is: ; in, It is a control vector composed of seven pulse width modulation signals, which serves as the input control quantity for seven independent drive actuators; These correspond to the pulse width modulation signals of the first to seventh independently driven actuators, respectively. It is a 7-dimensional real vector space.

[0027] The generalized thrust output by the thrust actuation system includes sway force. , vertical force Rolling torque Pitch torque The generalized thrust vector is: ; in, For generalized thrust vector, it represents the equivalent aerodynamic load output by the thrust actuation system; It represents a 4-dimensional real vector space.

[0028] Specifically, the following steps are included: S1. Obtain calibration test samples: Based on the preset pulse width modulation signal working range of seven independent drive actuators, multiple sets of seven-channel pulse width modulation signal combinations are generated by the Latin hypercube sampling method. The actual generalized thrust output data corresponding to each signal combination is measured synchronously to obtain multiple sets of calibration test samples that uniformly cover the working range.

[0029] This embodiment generates a total of 5000 sets of calibration test samples, of which 4000 sets are used as the training set and 1000 sets are used as the independent test set. The group calibration test samples are represented as follows: ; in, The serial number of the test sample is used to determine its value, which is a positive integer. For the first The control vector of the seven pulse width modulation signals corresponding to the group calibration test samples; For the first The actual generalized thrust output vector corresponding to the calibration test sample.

[0030] S2. Conversion to obtain single-unit thrust: Based on the pre-established pulse width modulation signal and single-unit thrust calibration relationship between each independent drive actuator, the pulse width modulation signal in each set of calibration test samples is mapped and converted to obtain the single-unit thrust of the seven independent drive actuators corresponding to each set of samples.

[0031] The relationship between pulse width modulation (PWM) signals and single-unit thrust calibration is established as follows: Based on multiple sets of PWM signals and corresponding measured single-unit thrust data from a single independent drive actuator, a nonlinear fitting using a quadratic polynomial is performed to obtain the calibration relationship between PWM signals and single-unit thrust. The calculation formula is as follows: ; in, For the first The thrust of a single drive actuator. For the first Pulse width modulation signal for each independent drive actuator, , , For the first Calibration coefficients for each independent drive actuator. .

[0032] The derivative of the single-unit thrust with respect to the corresponding pulse width modulation signal is: ; This derivative is used for the subsequent construction of the analytical Jacobian matrix.

[0033] In this embodiment, the PWM-thrust quadratic fitting determination coefficient of a single independent drive actuator is... The accuracy can reach 0.9994, indicating high fitting precision.

[0034] S3. Constructing Physical Information Structured Features: Based on the spatial topology and steering relationships of the independent drive actuators, construct multi-dimensional physical information features for the thrust of a single unit, resulting in twenty-three-dimensional physical information structured features that include first-order thrust terms, second-order thrust nonlinear terms, coupling terms of adjacent independent drive actuators, and competition terms of coaxial reverse independent drive actuators.

[0035] Specifically, based on the single-machine thrust of seven independently driven actuators, a basic contribution term, a nonlinear correction term, an adjacent aerodynamic interference term, and a coaxial reverse competition term are constructed respectively, ultimately yielding a 23-dimensional physical information structured feature vector. : ; in, For the reason The physical information structured features of the group calibration test samples are stacked in rows to form a feature matrix; They are respectively the 1st, 2nd, ... The 23-dimensional physical information structured feature row vectors corresponding to each group of samples; This is the eigenmatrix corresponding to the first-order thrust term, which has 7 dimensions and represents the basic independent thrust contribution of each independent drive actuator. It is the eigenmatrix corresponding to the second-order thrust nonlinearity term, which has 7 dimensions and characterizes the second-order nonlinear output characteristics of single-engine thrust. The feature submatrix corresponding to the coupling terms of adjacent independent drive actuators is 8-dimensional and characterizes the aerodynamic coupling and wake interference effects of spatially adjacent actuators. This is a feature submatrix corresponding to the competition terms of coaxial reverse independent drive actuators. It has one dimension and represents the thrust competition and dominance relationship of coaxial reverse-arranged actuators.

[0036] First-order thrust characteristic (7 dimensions): Represents the basic independent thrust contribution of each independent drive actuator, as shown in the formula: ; Second-order thrust nonlinearity (7 dimensions): Represents the second-order nonlinear effect of individual independent drive actuators during combined operation, consisting of the square terms of the thrust of each individual actuator, expressed as: ; Coupling characteristics of adjacent independent drive actuators (8-dimensional): This represents the aerodynamic coupling and wake interference between spatially adjacent independent drive actuators, and is composed of the product of the single-machine thrust of two actuators with adjacent topological relationships. The formula is as follows: ; Competition term for coaxial reverse independent drive actuators (1D): Based on the single-machine thrust of the second and seventh independent drive actuators, it is obtained by introducing a preset small amount to avoid the denominator being zero and constructing a ratio term between the thrust difference and the absolute value of the thrust sum. The calculation formula is as follows: ; in, For coaxial reverse independent drive actuator competition item, For the single-machine thrust of the second independent drive actuator, For the single-machine thrust of the seventh independent drive actuator, The preset value is greater than zero; when the ratio is close to 1, it indicates that the thrust of the second independent drive actuator is dominant, and when the ratio is close to -1, it indicates that the thrust of the seventh independent drive actuator is dominant.

[0037] S4. Training to obtain the forward thrust calibration model: Based on the structured features of physical information and the actual generalized thrust output data, the forward thrust calibration model of the thrust execution system is obtained through feature standardization and multi-output ridge regression training.

[0038] The specific steps are as follows: Structure the physical information features corresponding to the 4000 sets of training samples into a feature matrix. The corresponding actual generalized thrust is used to form the output matrix. First, the features are standardized and the output is centered. Then, the Frobenius norm regularization term is introduced to constrain the magnitude of the regression coefficients. Multi-output ridge regression is used for closed-form solution to obtain the regression coefficient matrix of the forward thrust calibration model.

[0039] S401, Feature Standardization and Output Centralization: Calculate the mean vector of each feature dimension in the training set. and standard deviation vector Standardize the feature matrix: ; in, The standardized physical information structured feature matrix is ​​the result of the original features after mean zeroing and variance normalization. It is the characteristic matrix, and ; The training set consists of 23 dimensional mean vectors for each dimension of the structured features of the physical information, with each element corresponding to the sample mean of a one-dimensional feature. Let be a diagonal matrix composed of the standard deviations of each dimension of the training set features, where It is a 23-dimensional feature standard deviation vector. As a diagonalization operator, it places vector elements on the main diagonal of the matrix.

[0040] Calculate the mean vector of the output matrix and center the output matrix accordingly: ; in, This is the centered actual generalized thrust output matrix; The output matrix is ​​composed of the actual generalized thrust, and ; Let be the mean vector of the output matrix, and .

[0041] S402, Multi-output Ridge Regression Training: The formula for calculating the optimization objective of multi-output ridge regression is: ; in, For matrix To optimize the variables, find the optimal solution that minimizes the objective function; This is the centered actual generalized thrust output matrix; This is the standardized structured feature matrix of physical information; Here is the regression coefficient matrix to be solved; The ridge regression regularization coefficient has a value not less than 0. It is the Frobenius norm, which is calculated by taking the square root of the sum of the squares of all elements of the matrix, and is used to represent the overall magnitude of the matrix.

[0042] The closed-form solution to the regression coefficient matrix is: ; in, It is a 23×23 identity matrix; for The transpose of .

[0043] S403, Model Validation Results: For any input PWM control vector After single-engine thrust conversion, structured feature construction, and standardization, the predicted thrust output by the forward thrust calibration model is: ; in, The predicted generalized thrust vector output by the forward thrust calibration model is the input PWM control vector. Predicted output load obtained through model mapping; The standardized feature vector; The transpose of the regression coefficient matrix A obtained from the multi-output ridge regression is used to establish a linear mapping relationship between standardized features and output.

[0044] This embodiment uses 1000 sets of independent test samples for verification, and the results show that: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] , vertical force Rolling torque Pitch torque coefficient of determination The values ​​were 0.99114, 0.98123, 0.98994 and 0.99382, respectively, all greater than 0.98; the corresponding normalized root mean square errors were 1.4352%, 2.6370%, 1.8756% and 1.3114%, respectively, all less than 3%, indicating excellent model fitting accuracy and generalization performance.

[0045] S5. Constructing a solution model for pulse width modulation control signals: Based on the forward thrust calibration model, a solution model for pulse width modulation control signals is constructed by introducing target thrust deviation optimization target, pulse width modulation signal boundary constraints and reference pulse width modulation signal constraints.

[0046] Specifically, based on the deviation between the target thrust and the predicted thrust, and the deviation between the pulse width modulation signal and the reference pulse width modulation signal, a joint optimization objective is constructed by setting the thrust error weight matrix and regularization weight, and the upper and lower boundary constraints of the pulse width modulation signal are superimposed to construct a solution model.

[0047] The optimization objective formula for solving the model is: ; in, For vectors To optimize the variables, find the optimal solution that minimizes the objective function; Let be the control vector composed of seven pulse width modulation signals, and be the optimization variables to be solved. This is the thrust error weighting matrix, used to weight and allocate the tracking errors of each generalized thrust component. , To determine the sample standard deviation of the sway force component in the training set calibration samples; To determine the sample standard deviation corresponding to the vertical force components in the training set calibration samples; To determine the sample standard deviation of the roll moment component in the training set calibration samples; To determine the sample standard deviation of the pitch torque component in the training set calibration samples; The predicted generalized thrust vector output by the forward thrust calibration model is determined by the control vector. Obtained by mapping through the forward thrust calibration model; Let be the target generalized thrust vector, and , The target sway force corresponds to the target thrust component along the x-axis. The vertical force of the target corresponds to the target thrust component along the z-axis. The target roll moment corresponds to the target moment component about the x-axis; The target pitching moment corresponds to the target moment component about the y-axis; It is the 2-norm of the vector; These are the regularization weight coefficients; The reference pulse width modulation signal vector is used to constrain the deviation between the control signal obtained from the solution and the reference value. , These are the upper and lower limits of operation for each pulse width modulation signal, used to normalize the deviation of the control signal.

[0048] The formula for solving the constraint conditions of the model is: .

[0049] The rules for obtaining the reference pulse width modulation signal are as follows: during the first solution, the median value of the interval is taken as the reference pulse width modulation signal based on the working range of the pulse width modulation signal; during the continuous control process, the pulse width modulation control command of the previous cycle is taken as the reference signal based on the output result of the previous control cycle, so as to reduce the sudden change of the control signal between adjacent cycles.

[0050] S6. Iterative solution to obtain pulse width modulation control commands: Based on the forward thrust calibration model, the analytical Jacobian matrix of the predicted thrust relative to the pulse width modulation signal is derived and iteratively solved to obtain the pulse width modulation control commands of seven independent drive actuators.

[0051] Constructing the Jacobian matrix: Based on the single-unit thrust calibration relationship, the structured feature construction relationship of physical information, the feature standardization relationship, and the ridge regression coefficient matrix, the analytical Jacobian matrix of the predicted thrust relative to the seven-channel pulse width modulation signal is derived layer by layer using the chain rule. The calculation formula is as follows: ; in, The analytical Jacobian matrix is ​​used to predict the generalized thrust relative to the seven-channel pulse width modulation signal, and is used to characterize the degree of influence of the pulse width modulation signal on the output thrust. To predict the generalized thrust vector Relative to pulse width modulation control vector The partial derivatives; It is a diagonal matrix composed of the standard deviations of each dimension of the structured features of physical information; Let be the Jacobian matrix of the structured eigenvectors of physical information relative to the seven pulse width modulation signals, and , Structured feature vectors of physical information Relative to pulse width modulation control vector The partial derivatives; This indicates that the Jacobian matrix is ​​a real matrix with 4 rows and 7 columns.

[0052] The derivatives of the second-order thrust nonlinearity and adjacent coupling terms can be obtained analytically from the first-order thrust derivative, as shown in the following formula: ; ; in, For the first The thrust of a single drive actuator. In order to be with the first The sequence number of another actuator that forms an adjacent coupling pair.

[0053] Regarding the coaxial reverse competition feature, it has the following characteristics: and The partial derivatives are as follows: ; ; in, The partial derivative of the competition term of the coaxial reverse independent drive actuator with respect to the second pulse width modulation signal; This is the partial derivative of the competition term of the coaxial reverse independent drive actuator with respect to the seventh pulse width modulation signal.

[0054] Damped Gauss-Newton iterative solution: Based on the analytical Jacobian matrix and the augmented residual vector, the pulse width modulation signal is iteratively updated using the damped Gauss-Newton method until the infinity norm of the iteration increment is less than a preset threshold or the maximum number of iterations is reached, thus obtaining the final pulse width modulation control command.

[0055] In the k-th iteration, construct the augmented residual vector: ; in, For the first The seven-path pulse width modulation control vector corresponding to the next iteration step; The square root of the regularization weighting coefficient is used to scale the control signal deviation term, making it compatible with the thrust error term in terms of unified optimization dimensions, thus forming the regularized deviation component of the augmented residual.

[0056] The corresponding augmented Jacobian matrix is: ; in, For the first The predicted generalized thrust analytical Jacobian matrix corresponding to the next iteration step is the current control vector. The gradient calculation results at the given location.

[0057] The formula for calculating the iterative increment of a pulse width modulation signal is: ; in, For the first The iteration increment vector of the seven pulse width modulation signals corresponding to the next iteration; This represents the number of iterations. For the first The augmented Jacobian matrix corresponding to the next iteration; To augment the Jacobian matrix The transpose of the matrix; For the first The damping coefficient of the next iteration is used to constrain the iteration step size and improve the numerical stability of the iterative solution; It is a 7th order identity matrix; For the first The augmented residual vector corresponding to the next iteration.

[0058] The formula for updating the pulse width modulation signal is: in, For the first The seven-channel pulse width modulation control vector obtained after the next iteration update This is a vector truncation operation used to constrain the elements of an input vector to a specified upper and lower bound. Elements that exceed the boundaries are truncated to their corresponding boundary values.

[0059] The results are then limited to the PWM operating range. The iteration stops when the infinity norm of the iteration increment is less than a preset threshold, or when the preset maximum number of iterations is reached, and the current control vector is output.

[0060] In this embodiment, the average solution time for the control commands of 100 sets of target thrust is 0.46868ms, the solution time for the 95th percentile is 0.7587ms, the maximum solution time is 1.3526ms, and the average number of iterations is 5.8, which can meet the control cycle requirements of real-time testing.

[0061] S7. Output control commands and execute thrust loading: Based on the pulse width modulation control commands obtained by solving, the thrust execution system outputs the actual thrust corresponding to the target thrust by outputting corresponding control signals to each independent drive actuator.

[0062] This embodiment selects 100 sets of target thrust for control verification. The results show that the target thrust and the actual output thrust have a high degree of consistency: sway force , vertical force Rolling torque Pitch torque The corresponding average relative errors are 0.08777%, 0.01098%, 0.00898% and 0.05965%, respectively, demonstrating excellent thrust reproduction accuracy.

[0063] In summary, this invention achieves system-level coupling calibration for multi-actuator combined operation conditions by constructing a structured physical information feature that integrates first-order thrust terms, second-order thrust nonlinear terms, adjacent coupling terms, and coaxial reverse competition terms. This effectively solves the problem that single-machine calibration cannot characterize aerodynamic coupling, wake interference, and nonlinear characteristics. By combining multi-output ridge regression to establish a high-precision forward calibration model, and by using analytical Jacobian matrix and constrained damped Gauss-Newton iteration to achieve rapid solution of control commands, this invention meets real-time control requirements while ensuring thrust reproduction accuracy. It can significantly improve the thrust loading accuracy and stability of the semi-physical real-time hybrid model test of floating wind turbines.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A coupling calibration and control method for a semi-physical wind turbine thrust actuation system, characterized in that, Includes the following steps: S1, the semi-physical wind turbine thrust execution system includes seven independent drive execution elements, which are used to collect multiple sets of pulse width modulation signal combinations and corresponding actual generalized thrust output data to obtain multiple sets of calibration test samples; S2. Based on the pulse width modulation signal and single-machine thrust calibration relationship pre-established for each independent drive actuator, the single-machine thrust corresponding to each set of calibration test samples is obtained by mapping and converting the pulse width modulation signal in each set of calibration test samples. S3. Based on the spatial topology and steering relationship of the independent drive actuators, the physical information structure features of the single-machine thrust are obtained by constructing multi-dimensional physical information features, including first-order thrust terms, second-order thrust nonlinear terms, coupling terms of adjacent independent drive actuators, and competition terms of coaxial reverse independent drive actuators. S4. Based on the structured features of physical information and actual generalized thrust output data, a forward thrust calibration model of the thrust execution system is obtained through feature standardization and multi-output ridge regression training. S5. Based on the forward thrust calibration model, a pulse width modulation control signal solution model is constructed by introducing target thrust deviation optimization target, pulse width modulation signal boundary constraints and reference pulse width modulation signal constraints. S6. Based on the forward thrust calibration model, the analytical Jacobian matrix of the predicted thrust relative to the pulse width modulation signal is derived and iteratively solved to obtain the pulse width modulation control command for seven independent drive actuators. S7. Based on pulse width modulation control commands, by outputting corresponding control signals to each independent drive actuator, the thrust execution system is controlled to output the actual thrust corresponding to the target thrust.

2. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 1, characterized in that: The specific steps of S1 are as follows: Based on the preset pulse width modulation signal operating range of seven independent drive actuators, multiple sets of seven-channel pulse width modulation signal combinations are generated by the Latin hypercube sampling method. The actual generalized thrust output data corresponding to each signal combination is measured synchronously to obtain multiple sets of calibration test samples that uniformly cover the operating range.

3. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 1, characterized in that: The relationship between the pulse width modulation signal in S2 and the single-unit thrust calibration is established in the following way: Based on multiple pulse width modulation signals from a single independent drive actuator and corresponding measured thrust data of a single unit, a nonlinear fitting using a quadratic polynomial is performed to obtain the calibration relationship between the pulse width modulation signal and the thrust of the single unit. The calculation formula is as follows: ； in, For the first The thrust of a single drive actuator. For the first Pulse width modulation signal for each independent drive actuator, , , For the first Calibration coefficients for each independent drive actuator. .

4. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 1, characterized in that: The specific steps for S3 are as follows: Based on the single-machine thrust of seven independent drive actuators, by constructing basic contribution terms, nonlinear correction terms, adjacent aerodynamic interference terms, and coaxial reverse competition terms respectively, a twenty-three-dimensional physical information structured feature is obtained, consisting of seven first-order thrust terms, seven second-order thrust nonlinear terms, eight adjacent independent drive actuator coupling terms, and one coaxial reverse independent drive actuator competition term.

5. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 4, characterized in that: The process for obtaining the competition item for coaxial reverse independent drive actuators is as follows: Based on the single-unit thrust of the second and seventh independent drive actuators, by introducing a preset small amount to avoid the denominator being zero and constructing a ratio term between the thrust difference and the absolute value of the thrust sum, the competition term of the coaxial reverse independent drive actuators is obtained, and the calculation formula is as follows: ； in, For coaxial reverse independent drive actuator competition item, For the single-machine thrust of the second independent drive actuator, For the single-machine thrust of the seventh independent drive actuator, The preset value is greater than zero; when the ratio is close to 1, it indicates that the thrust of the second independent drive actuator is dominant, and when the ratio is close to -1, it indicates that the thrust of the seventh independent drive actuator is dominant.

6. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 1, characterized in that: The specific steps of S4 are as follows: Based on the physical information structured feature matrix and the actual generalized thrust output matrix corresponding to multiple sets of calibration test samples, the regression coefficient matrix of the forward thrust calibration model is obtained by standardizing the features, centering the output, and introducing Frobenius norm regularization term to constrain the magnitude of the regression coefficients, and using multi-output ridge regression for closed-form solution. The formula for the optimization objective of multi-output ridge regression is: ； in, For matrix To optimize the variables, find the optimal solution that minimizes the objective function; This is the centered actual generalized thrust output matrix; This is the standardized structured feature matrix of physical information; Here is the regression coefficient matrix to be solved; is the ridge regression regularization coefficient, and its value is not less than 0; is the Frobenius norm, which is calculated by taking the square root of the sum of the squares of all elements of the matrix, and is used to represent the overall magnitude of the matrix. The formula for the closed-form solution of the regression coefficient matrix is: ； in, It is a 23×23 identity matrix.

7. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 1, characterized in that: The specific steps of S5 are as follows: Based on the deviation between the target thrust and the predicted thrust, and the deviation between the pulse width modulation signal and the reference pulse width modulation signal, a joint optimization objective is constructed by setting the thrust error weight matrix and regularization weight, and the upper and lower boundary constraints of the pulse width modulation signal are superimposed to construct a pulse width modulation control signal solution model. The formula for solving the optimization objective of the model is: ； in, For vectors To optimize the variables, find the optimal solution that minimizes the objective function; Let be the control vector composed of seven pulse width modulation signals, and be the optimization variables to be solved. This is the thrust error weighting matrix, used to weight and allocate the tracking errors of each generalized thrust component. The predicted generalized thrust vector output by the forward thrust calibration model is determined by the control vector. Obtained by mapping through the forward thrust calibration model; The target generalized thrust vector; It is the 2-norm of the vector; These are the regularization weight coefficients; The reference pulse width modulation signal vector is used to constrain the deviation between the control signal obtained from the solution and the reference value. , These are the upper and lower limits of operation for each pulse width modulation signal, used to normalize the deviation of the control signal; The constraints for solving the model are: 。 8. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 7, characterized in that: The process of acquiring the reference pulse width modulation signal in S5 is as follows: During the initial solution, the reference pulse width modulation signal is obtained by taking the midpoint of the interval based on the working range of the pulse width modulation signal. During continuous control, the reference pulse width modulation signal is obtained by taking the pulse width modulation control command of the previous cycle based on the output result of the previous control cycle.

9. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 1, characterized in that: The process of obtaining the analytic Jacobian matrix in S6 is as follows: Based on the single-unit thrust calibration relationship, the structured feature construction relationship of physical information, the feature standardization relationship, and the ridge regression coefficient matrix, the analytical Jacobian matrix of the predicted thrust relative to the seven-channel pulse width modulation signal is derived layer by layer using the chain rule. The calculation formula is as follows: ； in, The analytical Jacobian matrix is ​​used to predict the generalized thrust relative to the seven-channel pulse width modulation signal, and is used to characterize the degree of influence of the pulse width modulation signal on the output thrust. To predict the generalized thrust vector Relative to pulse width modulation control vector The partial derivatives; It is a diagonal matrix composed of the standard deviations of each dimension of the structured features of physical information; The Jacobian matrix of the structured feature vectors of physical information relative to the seven-channel pulse width modulation signal; This indicates that the Jacobian matrix is ​​a real matrix with 4 rows and 7 columns.

10. The coupling calibration and control method for a semi-physical wind turbine thrust actuator system according to claim 9, characterized in that: The specific iterative solution process in S6 is as follows: Based on the analytical Jacobian matrix and the augmented residual vector, the pulse width modulation signal is iteratively updated using the damped Gauss-Newton method until the infinity norm of the iteration increment is less than a preset threshold or the maximum number of iterations is reached, thus obtaining the final pulse width modulation control command. The formula for calculating the iterative increment of a pulse width modulation signal is: ； in, For the first The iteration increment vector of the seven pulse width modulation signals corresponding to the next iteration; This represents the number of iterations. For the first The augmented Jacobian matrix corresponding to the next iteration; To augment the Jacobian matrix The transpose of the matrix; For the first The damping coefficient of the next iteration is used to constrain the iteration step size and improve the numerical stability of the iterative solution; It is a 7th order identity matrix; For the first The augmented residual vector corresponding to the next iteration.

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