Model-free integral sliding mode control method for grid-connected inverter system based on rbfnn estimator

Abstract

The application provides a grid-connected inverter system model-free integral sliding mode control method based on an RBFNN estimator, and comprises the following steps: firstly, regarding the related filter and grid-connected impedance parameters in the main circuit of a single-phase LCL grid-connected inverter as unknown quantities, an ultra-local model is established; secondly, an RBFNN estimator is designed to estimate the unknown part in the ultra-local model; thirdly, a control law is designed based on the RBFNN estimator and the integral sliding mode control method to enhance the robustness of the system, improve the dynamic response speed of the system and effectively suppress the chattering in the sliding mode control; finally, an online updating method for the neural network weight and center value of the estimator is designed. The application provides a model-free control strategy for the grid-connected inverter system, can enhance the robustness of the grid-connected inverter system in coping with uncertain disturbances in actual operation, ensures that the grid-connected current accurately tracks the reference value, and has significant engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic-based new energy power generation technology, and relates to a model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators. Background Technology

[0002] In recent years, research on photovoltaic-based new energy power generation technologies has become a focus both domestically and internationally. As a key interface device connecting photovoltaic arrays to the power grid, the performance of the photovoltaic grid-connected inverter directly affects the system's power quality, conversion efficiency, and operational stability.

[0003] Currently, the control methods used in existing grid-connected inverter systems include: backstepping control, PR control, and While the methods mentioned above can control the grid-connected current to track its reference value, they all rely on an accurate mathematical model of the grid-connected inverter's main circuit. However, photovoltaic grid-connected inverter systems face complex and variable operating conditions in actual operation, such as filter parameter perturbations, time-varying grid-connected impedance, and other unmodeled dynamic changes. These factors make it difficult to obtain an accurate system model.

[0004] Traditional controllers based on fixed models often exhibit significantly reduced control performance when faced with changes in system parameters and external disturbances. Although sliding mode control has attracted attention for its strong robustness to matching uncertainties and disturbances, its design usually requires a nominal system model, and the inherent high-frequency chattering problem still needs to be addressed. Furthermore, traditional sliding mode control has limited ability to directly handle modeling errors.

[0005] Therefore, developing an advanced control method that does not rely on precise mathematical models, can adaptively handle unknown dynamics and strong uncertainties in the system, and possesses both high-precision tracking capabilities and strong robustness is of urgent need and great significance for improving the operating performance of photovoltaic grid-connected inverters under various complex operating conditions. Summary of the Invention

[0006] To overcome the reliance on precise mathematical models, this invention provides a model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators. This method solves the problems of decreased control performance and weak error handling capability of traditional grid-connected inverter system control methods based on fixed model designs when dealing with filter perturbations, time-varying grid impedance, and other unmodeled dynamic factors in actual operation.

[0007] This invention treats all filter parameters, grid impedance, and unmodeled dynamics in a single-phase LCL grid-connected inverter system as nonlinear unknown dynamics, designs an RBFNN estimator, uses the RBFNN estimator to estimate the aforementioned nonlinear unknown dynamics online, and designs a grid-connected current controller by combining an integral sliding mode control method based on an improved reaching law. It proposes a method that deeply integrates the adaptive intelligent estimation capability of the RBFNN estimator with the strong robustness and high-precision tracking performance of integral sliding mode control, providing a high-performance, high-reliability model-free control method for photovoltaic grid-connected inverter systems.

[0008] Based on the above technical concept, the present invention specifically adopts the following technical solution:

[0009] A model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators includes the following steps:

[0010] Step 1: Establish the mathematical model of the main circuit of the single-phase LCL grid-connected inverter system, and its hyperlocal model; including:

[0011] (1)

[0012] In the formula, For the grid-connected inverter side inductor; For the output current of the grid-connected inverter; The current time; It is a control law, and ; Provide the DC input voltage for the grid-connected inverter; This refers to the capacitor voltage of the grid-connected inverter. For grid-connected inverter filter capacitors; This is the grid-connected current; For the grid-side inductor of the grid-connected inverter; For grid-connected inverters; This refers to the grid voltage.

[0013] The mathematical model of the main circuit of the above grid-connected inverter system can be further written as follows:

[0014] (2)

[0015] In the formula, For grid-connected current The third derivative; For grid-connected current The first derivative; For grid voltage The second derivative; This is the first parameter to be estimated; The second unknown parameter;

[0016] Considering unknown disturbances Equation (2) can be written as:

[0017] (3)

[0018] In the formula:

[0019] (4)

[0020] make:

[0021] (5)

[0022] In the formula, The first unknown parameter; For unknown disturbances, and satisfying , For unknown disturbances The upper bound of is a positive real number;

[0023] The hyperlocal model of the main circuit of the grid-connected inverter system is obtained as follows:

[0024] (6)

[0025] Step 2: Based on the hyperlocal model of the main circuit of the grid-connected inverter system, design a first RBFNN estimator and a second RBFNN estimator; wherein, the first RBFNN estimator is used to estimate the first unknown parameter. The second RBFNN estimator is used to estimate the second unknown parameter. ;

[0026] Specifically, the first RBFNN estimator has 3 neurons in the input layer, 15 neurons in the hidden layer, and 1 neuron in the output layer; the second RBFNN estimator has the same structure as the first RBFNN estimator.

[0027] The input layer of the first RBFNN estimator is designed as follows:

[0028] (7)

[0029] in: ; ;

[0030] In the formula, This is the grid-connected current error vector; This refers to the grid-connected current error. For grid-connected current error The first derivative; For grid-connected current error The second derivative; This is the transpose of the matrix; The given value for the grid-connected current; Setpoint for grid-connected current The first derivative; Setpoint for grid-connected current The second derivative; For grid-connected current The second derivative; For grid-connected current Reference amplitude; For grid voltage angular frequency;

[0031] The input layer of the second RBFNN estimator is the same as that of the first RBFNN estimator.

[0032] The hidden layers of the first RBFNN estimator and the hidden layers of the second RBFNN estimator are designed as follows:

[0033] (8)

[0034] In the formula, Let be the first radial basis function, which serves as the first RBFNN estimator. The output of each hidden node; For exponentiation; For the first RBFNN estimator The radial basis function center vector of each hidden node; For the first RBFNN estimator The width of the radial basis function of each hidden node; These are the hidden nodes of the RBFNN estimator; The second radial basis function is used as the second RBFNN estimator. The output of each hidden node; For the second RBFNN estimator The radial basis function center vector of each hidden node; For the second RBFNN estimator The width of the radial basis function of each hidden node.

[0035] The output layers of the first RBFNN estimator and the second RBFNN estimator are designed as follows:

[0036] (9)

[0037] in:

[0038] (10)

[0039] In the formula, The first unknown parameter The estimated value; For the first RBFNN estimator The weights between each hidden node and the output; Here are the radial basis functions of the first RBFNN estimator; The transpose of the weight matrix connecting the hidden and output layers of the first RBFNN estimator; The hidden layer radial basis function matrix of the first RBFNN estimator; For the second unknown parameter The estimated value; For the second RBFNN estimator The weights between each hidden node and the output; The radial basis functions of the second RBFNN estimator; Transpose the weight matrix connecting the hidden and output layers of the second RBFNN estimator; The hidden layer radial basis function matrix of the second RBFNN estimator; The weight matrix connecting the hidden layer and the output layer for the first RBFNN estimator; The weight matrix connecting the hidden and output layers for the second RBFNN estimator.

[0040] Step 3: Based on the first RBFNN estimator, design the first online adaptive law for the weight matrix; based on the second RBFNN estimator, design the second online adaptive law for the weight matrix.

[0041] Specifically, the online adaptive law of the first weight matrix and the online adaptive law of the second weight matrix are both weight update rates of the RBFNN estimator. The update rate improves the estimator performance by continuously updating the weight matrix, thereby enabling the estimator to obtain more accurate estimates.

[0042] The expressions for the online adaptive law of the first weight matrix and the online adaptive law of the second weight matrix are as follows:

[0043] (11)

[0044] In the formula, Let be the coefficient of the first weighted adaptive law, and ; It is a sliding surface; This is the second parameter of the sliding surface; For the second weight adaptive law coefficients, and .

[0045] Step 4: Design a first online update method and a second online update method; wherein, the first online update method is used to update the radial basis function center value of the first RBFNN estimator, and the second online update method is used to estimate the radial basis function center value of the second RBFNN estimator.

[0046] Step 4 specifically includes the following steps:

[0047] set up For vectors With the first center vector The index value of the best match. For vectors With the second center vector The index value of the best match; where the first center vector For the first RBFNN estimator The center vector of the activation function at the nth iteration; the second center vector. For the second RBFNN estimator The center vector of each activation function at the nth iteration;

[0048] When the first center vector Second center vector When performing the nth iteration, the following can be calculated according to the Euclidean minimum distance criterion:

[0049] (12)

[0050] In the formula, Let be the index value corresponding to the minimum value of the arg min function with respect to f at time n; Let be the index value corresponding to the minimum value of the arg min function with respect to g at time n; Calculate the minimum value of the function; Let n be the grid-connected current error vector at time n;

[0051] Based on equation (12), the first online update method and the second online update method are designed respectively, and their expressions are as follows:

[0052] (13)

[0053] In the formula, For the first RBFNN estimator The center vector of each activation function in the (n+1)th iteration; For the first RBFNN estimator The center vector of each activation function at the nth iteration; Let f be the learning rate of the radial basis center value of the RBFNN estimator; For the second RBFNN estimator The center vector of each activation function in the (n+1)th iteration; For the second RBFNN estimator The center vector of each activation function at the nth iteration; Let g be the learning rate for the radial basis center values ​​of the RBFNN estimator. These are the hidden nodes of the RBFNN estimator.

[0054] Step 5: Based on the first RBFNN estimator and the second RBFNN estimator, design the control law for the grid-connected inverter system; including:

[0055] Select sliding surface as follows:

[0056] (14)

[0057] In the formula, All of these are parameters to be designed in the sliding surface, and all are positive numbers;

[0058] The state equation consisting of the grid-connected current tracking error and its derivative is expressed as:

[0059] (15)

[0060] In the formula, For grid-connected current error The first derivative; for The first derivative; for The first derivative; Setpoint for grid-connected current The third derivative;

[0061] To reduce chattering, the following approach law is chosen:

[0062] (16)

[0063] In the formula, For the approach law; For the gain of the approach law, it is a positive real number; Adjustable gain; It is a symbolic function;

[0064] Among them, the design allows for adjustable gain. for:

[0065] (17)

[0066] In the formula, The amplitude coefficient of the adjustable gain function; This is the width coefficient of the adjustable gain function; These are the center coefficients of the adjustable gain function; All are positive real numbers;

[0067] Therefore, the control law for the grid-connected inverter is:

[0068] (18)

[0069] Among them, the sign function The expression is as follows:

[0070]

[0071] Preferably, to further eliminate chattering in the grid-connected inverter system, the aforementioned sign function is... Replace with smoothing function :

[0072]

[0073] In the formula, This is a parameter for smoothness adjustment, and it is a positive number.

[0074] Compared to the initial sign function Improved smoothing function By adjusting the smoothness parameters, the step jump can be improved to a smooth state, thereby further reducing the chattering of the system output grid-connected current waveform.

[0075] The following is the process of proving the stability of the control law of the grid-connected inverter system of this invention.

[0076] In this technical field, the commonly used proof process in control theory includes: defining the Lyapunov function, taking its derivative, proving the negative definiteness of the derivative, and concluding that the control system is stable.

[0077] To facilitate the subsequent stability proof, the following variables are defined first:

[0078] Suppose there exist ideal weights such that the following equation holds:

[0079] (19)

[0080] in: ;

[0081] In the formula, The output of the first ideal RBFNN estimator; This is the transpose of the first optimal weight vector; Let be the approximation error of the first ideal RBFNN estimator, with an upper bound of . , It is a positive real number and satisfies ; The output of the second ideal RBFNN estimator; This is the transpose of the second optimal weight vector; The approximation error of the second ideal RBFNN estimator is given by the upper bound as follows: , It is a positive real number and satisfies .

[0082] The differences between the weight matrix and the estimated weight matrix of the first ideal RBFNN estimator, and the differences between the weight matrix and the estimated weight matrix of the second ideal RBFNN estimator are defined respectively, and their expressions are as follows:

[0083] (20)

[0084] In the formula, The weight bias of the first RBFNN estimator; The ideal weights are those of the first RBFNN estimator; The actual weights of the first RBFNN estimator; The weight bias of the second RBFNN estimator; The ideal weights are for the second RBFNN estimator; The actual weights of the second RBFNN estimator;

[0085] Define the output error of the first ideal RBFNN estimator respectively. The output error of the second ideal RBFNN estimator The expressions for both are as follows:

[0086] (twenty one)

[0087] In the formula, This is the transpose of the actual weights of the first RBFNN estimator; This is the transpose of the ideal weights of the first RBFNN estimator; The transpose of the weight bias of the second RBFNN estimator; Estimate the value for the second RBFNN estimator; This is the transpose of the actual weights of the second RBFNN estimator; This is the transpose of the ideal weights of the second RBFNN estimator; The weight bias of the second RBFNN estimator.

[0088] After defining the above variables, we will now begin to elaborate on the proof process.

[0089] First, define the Lyapunov function. Its expression is:

[0090] (twenty two)

[0091] Next, the Lyapunov function is calculated. The first derivative with respect to time, and prove its negative definiteness:

[0092] (twenty three)

[0093] Sliding surface The calculation process for the first derivative with respect to time is as follows:

[0094] (twenty four)

[0095] Substituting equation (23) into equation (22), we get:

[0096] (25)

[0097] Since the approximation error can be limited to a sufficiently small value, if we take... Then we can obtain .

[0098] Therefore, it exists. , , making .

[0099] The above analysis shows that the grid-connected inverter sliding mode control method based on RBFNN estimator proposed in this invention can guarantee the stability of the system.

[0100] The beneficial effects of this invention are as follows:

[0101] 1. This invention provides a control method based on a hyperlocal model, which is essentially a model-free control method. By utilizing the RBFNN estimator to estimate the nonlinear dynamic part containing system parameters online, as well as the modeling uncertainty part when the filter parameters are disturbed in actual operation, this invention can enhance the robustness of the grid-connected inverter system to unknown disturbances in actual operation without knowing the actual parameters of the grid-connected inverter system or the disturbances it experiences in actual operation. This ensures that the grid-connected current accurately tracks its reference value and has significant engineering practical value.

[0102] 2. This invention does not require obtaining sample data, thus eliminating the offline training process. The online training process of the RBFNN estimator used in this invention can be achieved through the weight adaptive law and the center value update method.

[0103] 3. By combining an integral sliding mode control method based on an improved reaching law, this invention can significantly reduce steady-state error and suppress chattering, thereby giving the grid-connected inverter system strong robustness, enhancing its ability to cope with interference, and significantly improving the dynamic and steady-state performance of the grid-connected inverter system. Attached Figure Description

[0104] Figure 1 For the first unknown parameter in this embodiment Schematic diagram of the RBFNN estimator;

[0105] Figure 2 Regarding the second unknown parameter in this embodiment Schematic diagram of the RBFNN estimator;

[0106] Figure 3 This is the control block diagram of the grid-connected inverter based on the RBFNN estimator in this embodiment;

[0107] Figure 4 The waveforms of grid-connected current and grid voltage under two control methods are shown.

[0108] Figure 5 This is a schematic diagram comparing the grid-connected current tracking error under two control methods;

[0109] Figure 6 When the grid-connected current reference amplitude is The grid-connected current waveforms under the two control methods when the current is reduced from 15A to 10A;

[0110] Figure 7 When the inverter-side filter inductor is Time Reduced to 0.7 The grid-connected current waveforms under the two control methods are shown below.

[0111] Figure 8 For the filter capacitor in Time Increased to 1.1 The grid-connected current waveforms under the two control methods are shown below.

[0112] Figure 9 For the grid-side filter inductor in Time Reduced to 0.7 The grid-connected current waveforms under the two control methods are shown below.

[0113] Figure 10 This is the first unknown parameter in this embodiment. A schematic diagram comparing the waveforms of the estimated and actual values;

[0114] Figure 11 The second unknown parameter in this embodiment A diagram showing the comparison of the estimated and actual waveforms. Detailed Implementation

[0115] The technical solution of the present invention will be described below with reference to the accompanying drawings and implementation methods.

[0116] Example

[0117] A model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators includes the following steps:

[0118] Step 1: Establish the mathematical model of the main circuit of the single-phase LCL grid-connected inverter system, and its hyperlocal model; including:

[0119] The mathematical model of the main circuit of the grid-connected inverter system is as follows:

[0120]

[0121] The hyperlocal model of the main circuit of the grid-connected inverter system is as follows:

[0122]

[0123] Step 2: Based on the hyperlocal model of the main circuit of the grid-connected inverter system, design a first RBFNN estimator and a second RBFNN estimator; wherein, the first RBFNN estimator is used to estimate the first unknown parameter. The second RBFNN estimator is used to estimate the second unknown parameter. ;

[0124] Specifically, the first RBFNN estimator has 3 neurons in the input layer, 15 neurons in the hidden layer, and 1 neuron in the output layer; the second RBFNN estimator has the same structure as the first RBFNN estimator.

[0125] The input layer of the first RBFNN estimator is designed as follows:

[0126]

[0127] in: ; ;

[0128] In the formula, This is the reference amplitude for the grid-connected current. The angular frequency of the grid voltage;

[0129] The input layer of the second RBFNN estimator is the same as that of the first RBFNN estimator.

[0130] The expressions for the hidden layers of the first RBFNN estimator and the second RBFNN estimator are as follows:

[0131]

[0132] The expressions for the output layers of the first and second RBFNN estimators are designed as follows:

[0133]

[0134] in:

[0135]

[0136] Step 3: Based on the first RBFNN estimator, design the first online adaptive law for the weight matrix; based on the second RBFNN estimator, design the second online adaptive law for the weight matrix.

[0137] The expressions for the online adaptive law of the first weight matrix and the online adaptive law of the second weight matrix are as follows:

[0138]

[0139] Step 4: Design a first online update method and a second online update method; wherein, the first online update method is used to update the radial basis function center value of the first RBFNN estimator, and the second online update method is used to estimate the radial basis function center value of the second RBFNN estimator;

[0140] The expressions for the first online update method and the second online update method are as follows:

[0141]

[0142] Step 5: Based on the first RBFNN estimator and the second RBFNN estimator, design the control law for the grid-connected inverter system. Its expression is as follows:

[0143]

[0144] in:

[0145]

[0146] In the formula, This is a parameter for smoothness adjustment, and it is a positive number.

[0147] To verify the effectiveness and feasibility of the method proposed in this invention, a first control method and a second control method were compared. The first control method adopted integral sliding mode control (ISMC), and the second control method adopted the model-free integral sliding mode control method (ISMC&RBF) for grid-connected inverter systems based on the RBFNN estimator provided in this invention.

[0148] Two single-phase grid-connected inverter simulation models were built on the MATLAB / Simulink platform. The main parameters involved are shown in Table 1.

[0149] Table 1 Electrical and Control Parameters

[0150]

[0151] Depend on Figure 4 It can be seen that the phase of the grid-connected current corresponding to both control methods is the same as the voltage at the point of common coupling. Since the phases are consistent, the grid-connected current phase can accurately track the phase of the common coupling point voltage under both control strategies.

[0152] Depend on Figure 5 As shown in Table 2, compared with the first control method, the grid-connected current tracking error and total harmonic distortion rate of this embodiment are significantly reduced.

[0153] Table 2 Comparison of Total Harmonic Distortion Rate of Grid-Connected Current

[0154]

[0155] Depend on Figure 6 It can be seen that when the inverter input power changes, that is, under the conditions of light and temperature changes, both of the above control methods can make the grid-connected current track its reference value. However, according to the enlarged part of the diagram, compared with the first control method, this embodiment can make the grid-connected current have less jitter and better tracking effect. That is, the grid-connected inverter system under this embodiment can better adapt to changes in light and temperature.

[0156] Depend on Figure 7 It can be seen that when the inverter-side filter inductor changes abruptly at 0.1s, both control methods can make the grid-connected current track its reference value. However, according to the enlarged view, compared with the first control method, this embodiment makes the grid-connected current have less chattering and better tracking effect, indicating that this embodiment has stronger robustness to changes in the inverter-side filter inductor parameters.

[0157] Depend on Figure 8It can be seen that when the filter capacitor changes by 0.1s, both control methods can make the grid-connected current track its reference value. However, according to the enlarged view, compared with the first control method, this embodiment makes the grid-connected current have less chattering and better tracking effect, indicating that this embodiment has stronger robustness to changes in the filter capacitor parameters.

[0158] Depend on Figure 9 It can be seen that when the grid-side filter inductor changes abruptly at 0.1s, both control methods can make the grid-connected current track its reference value. However, according to the enlarged view, compared with the first control method, this embodiment can make the grid-connected current have less chattering and better tracking effect, indicating that this embodiment has stronger robustness to changes in grid-side inductor parameters.

[0159] Depend on Figure 10 and Figure 11 It can be seen that the first unknown parameter estimated in this embodiment... Second unknown parameter The fact that it can completely track its actual value indicates that the estimator in this embodiment has a good estimation effect and high feasibility.

Claims

1. A model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators, characterized in that, Includes the following steps: Design a mathematical model based on the main circuit of a grid-connected inverter system, and its hyperlocal model; Based on the hyperlocal model of the main circuit of the grid-connected inverter system, a first RBFNN estimator and a second RBFNN estimator are designed; wherein, the first RBFNN estimator is used to estimate the first unknown parameter. The second RBFNN estimator is used to estimate the second unknown parameter. ; Design a first online update method and a second online update method; wherein, the first online update method is used to update the radial basis function center value of the first RBFNN estimator, and the second online update method is used to estimate the radial basis function center value of the second RBFNN estimator; Based on the first RBFNN estimator, an online adaptive law for the first weight matrix is ​​designed. Based on the second RBFNN estimator, an online adaptive law for the second weight matrix is ​​designed. Design a control law for a grid-connected inverter system based on the first RBFNN estimator and the second RBFNN estimator; The mathematical model of the main circuit of the grid-connected inverter system is as follows: ； In the formula, For the grid-connected inverter side inductor; For the output current of the grid-connected inverter; The current time; It is a control law, and ; Provide the DC input voltage for the grid-connected inverter; This refers to the capacitor voltage of the grid-connected inverter. For grid-connected inverter filter capacitors; This is the grid-connected current; For the grid-side inductor of the grid-connected inverter; For grid-connected inverters; This refers to the grid voltage. The hyperlocal model of the main circuit of the grid-connected inverter system is as follows: ； In the formula, The first unknown parameter; This is the second unknown parameter.

2. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 1, characterized in that, The first RBFNN estimator has 3 neurons in the input layer, 10-20 neurons in the hidden layer, and 1 neuron in the output layer; The second RBFNN estimator has the same structure as the first RBFNN estimator.

3. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 2, characterized in that, The input layer of the first RBFNN estimator is: ； in: ; ; In the formula, This is the grid-connected current error vector; This refers to the grid-connected current error. This is the first derivative of the grid-connected current error; This is the second derivative of the grid-connected current error; This is the transpose of the matrix; The given value for the grid-connected current; The first derivative of the given value of the grid-connected current; For grid-connected current The first derivative; The second derivative of the given value of the grid-connected current; For grid-connected current The second derivative; This is the reference amplitude for the grid-connected current. This is the angular frequency of the grid voltage.

4. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 2, characterized in that, The hidden layer of the first RBFNN estimator is: ； In the formula, Let be the first radial basis function, which serves as the first RBFNN estimator. The output of each hidden node; For exponentiation; For the first RBFNN estimator The radial basis function center vector of each hidden node; For the first RBFNN estimator The width of the radial basis function of each hidden node; These are hidden nodes in the RBFNN estimator; The second radial basis function is used as the second RBFNN estimator. The output of each hidden node; For the second RBFNN estimator The radial basis function center vector of each hidden node; For the second RBFNN estimator The width of the radial basis function of each hidden node.

5. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 2, characterized in that, The output layer of the first RBFNN estimator is: ； in: ； In the formula, The first unknown parameter The estimated value; For the first RBFNN estimator The weights between each hidden node and the output; Here are the radial basis functions of the first RBFNN estimator; The transpose of the weight matrix connecting the hidden and output layers of the first RBFNN estimator; The hidden layer radial basis function matrix of the first RBFNN estimator; For the second unknown parameter The estimated value; For the second RBFNN estimator The weights between each hidden node and the output; The radial basis functions of the second RBFNN estimator; Transpose of the weight matrix connecting the hidden and output layers of the second RBFNN estimator; is the radial basis function matrix of the hidden layer of the second RBFNN estimator.

6. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 1, characterized in that, The expressions for the online adaptive law of the first weight matrix and the online adaptive law of the second weight matrix are as follows: ； In the formula, The weight matrix connecting the hidden layer and the output layer for the first RBFNN estimator; The coefficients of the first weighted adaptive law; It is a sliding surface; This is the second parameter of the sliding surface; The weight matrix connecting the hidden layer and the output layer for the second RBFNN estimator; These are the coefficients of the second weighted adaptive law; The hidden layer radial basis function matrix of the first RBFNN estimator; The hidden layer radial basis function matrix of the second RBFNN estimator; This is a control law.

7. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 1, characterized in that, The expressions for the first online update method and the second online update method are as follows: ； in: ； In the formula, For the first RBFNN estimator The center vector of each activation function in the (n+1)th iteration; For the first RBFNN estimator The center vector of each activation function at the nth iteration; The learning rate is the radial basis center value of the first RBFNN estimator; Let n be the grid-connected current error vector at time n; Let f be the index value at time n when the argmin function with respect to f reaches its minimum value. For the second RBFNN estimator The center vector of each activation function in the (n+1)th iteration; For the second RBFNN estimator The center vector of each activation function at the nth iteration; The learning rate is the radial basis center value of the second RBFNN estimator; Let be the index value corresponding to the minimum value of the arg min function with respect to g at time n; These are the hidden nodes of the RBFNN estimator.

8. The model-free integral sliding mode control method for grid-connected inverter systems based on RBFNN estimators according to claim 1, characterized in that, The expression for the control law of the grid-connected inverter system is: ； in: ； In the formula, Setpoint for grid-connected current The third derivative; This is the third parameter of the sliding surface; This is the first parameter of the sliding surface; For the gain of the reaching law; Adjustable gain; It is a smoothing function; This is a parameter for smoothness adjustment, and it is a positive number. For control laws; This is the second parameter of the sliding surface; This refers to the grid-connected current error. This is the first derivative of the grid-connected current error; This is the second derivative of the grid-connected current error; For the second unknown parameter The estimated value; The first unknown parameter The estimated value; It is a sliding surface.

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