Electric fuel pump active disturbance rejection control method based on radial basis function neural network

Abstract

The invention belongs to the technical field of aero-engine control, and discloses an electric fuel pump active-disturbance-rejection control method based on a radial basis function neural network. According to the method, an intelligent control system is constructed through a radial basis function neural network, an active-disturbance-rejection controller with a nonlinear state error feedback control law as a core is designed, a control strategy is adjusted in real time according to the current state of the system, the complexity of controller parameter setting is reduced, and the stability and response speed of the system are improved. Through verification, the electric fuel pump control system obtained through the design can achieve the stable and rapid control effect under all working conditions, and is high in practicability, good in system robustness and high in anti-interference capacity.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engine control, and particularly to an active disturbance rejection control method for an electric fuel pump based on a radial basis neural network. Background Art

[0002] Artificial neural networks have powerful self-learning ability and adaptability. They can automatically extract features from a large amount of data for prediction or classification, and are especially good at dealing with non-linear and high-dimensional data problems. In recent years, they have been widely used in many aspects such as computer vision, natural language processing, and speech recognition. In the field of controller design, artificial neural networks provide new ideas and technical means for modern engineering control. By using the self-learning characteristics of neural networks, intelligent control systems can be constructed, which can adjust control strategies in real time according to environmental changes, thereby improving the stability and response speed of the system. Controllers based on artificial neural networks can also handle complex non-linear dynamic systems and provide more flexible and effective solutions than traditional control methods.

[0003] In a multi-electric aero-engine, there is an electric fuel pump as an actuator, which is responsible for the regulation of main fuel, afterburner fuel, etc. to meet the fuel supply requirements of the aero-engine under different working conditions. Compared with PID control, active disturbance rejection control has stronger robustness, better non-linear processing ability and the ability to suppress external disturbances, and at the same time reduces the dependence on accurate models and fine parameter adjustment. However, according to patents CN113726240B and CN114687899B, active disturbance rejection control needs to adjust multiple parameters including the bandwidth of the extended state observer, controller gain, and disturbance compensation gain, etc., which is extremely complex in parameter tuning. Based on the problems existing in the traditional control method of the electric fuel pump, the present invention proposes an active disturbance rejection control scheme for the electric fuel pump combined with a radial basis neural network to avoid the above disadvantages. Summary of the Invention

[0004] The present invention proposes an active disturbance rejection control scheme for the electric fuel pump based on a radial basis neural network: using the non-linear processing ability of the neural network to tune the parameters of the non-linear state error feedback control law in active disturbance rejection control, reducing the complexity of controller parameter tuning. Update the controller parameters in real time according to the current state of the system, so that the electric fuel pump system can achieve more accurate and rapid control effects under the whole working conditions.

[0005] The technical solution of the present invention is as follows:

[0006] An auto-disturbance rejection control method for an electric fuel pump based on a radial basis neural network is realized based on an electric fuel pump control system; the electric fuel pump control system is a speed-current double-closed-loop control system, which consists of a controller, a driver, a permanent magnet synchronous motor and a gear pump; the permanent magnet synchronous motor is coaxially connected to the gear pump, and the gear pump load is driven by the permanent magnet synchronous motor. There is a linear relationship between the output flow of the gear pump and the rotational speed of the gear pump; the controller consists of a nonlinear state error feedback control law, a tracking differentiator, a linear extended state observer and a radial basis neural network. The tracking differentiator gives the differential process of the expected value. The linear extended state observer gives an estimated value of the system state based on the actual output and control input of the system. The nonlinear state error feedback control law calculates the control quantity according to the error between the expected value and the actual state and the system disturbance value. The radial basis neural network updates the controller parameters in real time based on the gradient descent method according to the difference between the system expectation and the estimated value of the system state to achieve higher performance control of the system; the driver modulates the control quantity output by the controller into three-phase voltage to drive the operation of the electric fuel pump system.

[0007] The specific implementation steps of the neural network auto-disturbance rejection control of the electric fuel pump are as follows;

[0008] Step 1: Perform simulation modeling on the above electric fuel pump system.

[0009] Step 1.1: Model the permanent magnet synchronous motor. By coordinate transformation, the equations of each group of the permanent magnet synchronous motor are decoupled and reduced in order. The permanent magnet synchronous motor model after coordinate transformation is as follows:

[0010]

[0011] where: u d 、u q 、i d 、i q 、L d 、L q 、Ψ d 、Ψ q and respectively represent the equivalent voltage, equivalent current, equivalent inductance and equivalent magnetic flux in the two-phase rotating d-q coordinate system; R s represents the stator phase resistance, Ψ f is the main pole magnetic flux, p n represents the number of pole pairs; T e 、T L 、J、ω r 、ω e respectively represent the electromagnetic torque of the motor, the externally applied load torque, the rotational inertia of the system, the mechanical angular velocity and the electrical angular velocity; B is the friction coefficient.

[0012] Step 1.2: Modeling of the gear pump. The structure of the gear pump is an external meshing gear pump with the same size specifications for the driving and driven wheels. It is a positive displacement pump. When the displacement displ and rotational speed n of the gear pump are known and flow leakage is ignored, the output flow Q of the gear pump is Q = displ·n, and the load torque T of the gear pump L = displ·Δp, where Δp is the pressure difference before and after the gear pump.

[0013] Step 1.3: Design the controller of the electric fuel pump using the active disturbance rejection method. Take the second derivative of ω r to obtain the second-order mathematical model of the speed loop:

[0014]

[0015] Where: is the second derivative of ω r , is the first derivative of ω r , b is the control gain, and w(t) is the total disturbance of the fuel pump system. Based on this, take ω r as the state variable x1, and take as the state variable x2 to establish the state-space expression of the system:

[0016]

[0017] Where f(·) represents a function containing the state variables x1 and x2, and y represents the system output.

[0018] Design the differential tracker of the system as:

[0019]

[0020] Where v1 is the transition process arranged by the differential tracker according to the desired , v2 is the differential of the signal v1, r0 is the speed factor, h is the system sampling step, and the superscript k represents the k-th moment of the system operation.

[0021] According to the state-space expression of the system, design the third-order linear extended state observer of the system:

[0022]

[0023] Where e represents the estimation error of the state x1, and z1, z2, z3 represent the estimated values of the states x1, x2, x3; β 01 , β 02 , β 03 represent the observer gain coefficients.

[0024] Perform nonlinear combination on the error link:

[0025] u0 = β1fal(e1, a1, δ) + β2fal(e2, a2, δ)

[0026] Wherein, u0 represents the output control quantity of the nonlinear state error feedback control law, e1 represents the difference between the desired value v1 and the estimated value z1, and e2 represents the difference between the differential signal v2 and the estimated value z2; fal(·) represents a nonlinear function, a1 and a2 are constants between 0 and 1, which affect the nonlinear degree of the fal(·) function, and δ represents the width of the nonlinear interval; β1 and β2 represent the control law gain coefficients.

[0027] Finally, to compensate for the disturbance, the actual control quantity u is taken as:

[0028]

[0029] Step 2: Improve the control law of the active disturbance rejection controller based on the radial basis neural network. Specifically: The radial basis neural network is used to perform real-time optimal control on the parameters β1 and β2 of the nonlinear state error feedback control law in Step 1.3 to improve the tracking performance and disturbance rejection performance of the controller.

[0030] Step 2.1: Neural network structure design. The number of neuron nodes in the input layer is set to n RBF , and the input vector The Gaussian function is used as the activation function of the hidden layer. According to the empirical formula, the number of neuron nodes m in the hidden layer is determined RBF , and the output of the neural network is the control quantity u. The Gaussian function is as follows:

[0031]

[0032] Where: represents the data center of the Gaussian function in the hidden layer, and each c ji represents the data center of the j-th hidden layer neuron for the input x i , ||·|| represents the Euclidean distance between vectors, and σ j represents the base width of the hidden layer neuron nodes. The network output is a linear combination of the hidden layer outputs , and the network output is calculated according to the weight vector :

[0033]

[0034] Step 2.2: Use the gradient descent method, combined with the learning rate η, the acceleration factor α, and the parameter values at the (k - 1)-th moment, to update the parameters of the radial basis neural network.

[0035]

[0036]

[0037] Among them, k represents the k-th moment when the system is running; E(k) represents the performance index function of the neural network output y RBF (k) approaching the actual output y(k) of the system; h j (k) represents the output of the j-th hidden layer node; Δω j (k) represents the change in the weight ω j (k) of the j-th hidden layer node, Δσ j (k) represents the change in the base width σ j (k) of the j-th hidden layer neuron node; Δc ji (k) represents the data center c i (k) of the j-th hidden layer node for the i-th input x ji (k); C j (k) represents the data center vector of the j-th hidden layer node for the input X(k).

[0038] Step 2.3: The parameters β1 and β2 of the control law are updated by using the gradient descent method.

[0039]

[0040] Among them: J represents the sensitivity of the output to the input; E1(k) represents the performance index function; v1(k) represents the transition signal given by the tracking differentiator; Δβ1(k) and Δβ2(k) represent the changes in the control law gains β1(k) and β2(k); u(k) represents the actual control quantity output by the controller.

[0041] Step 3: The implementation steps of the active disturbance rejection control method for the electric fuel pump based on the radial basis neural network proposed by the present invention are as follows: First, according to the content described in Step 1.1 and Step 1.2, establish the mathematical models of the permanent magnet synchronous motor and the gear pump, and establish the control system model of the electric fuel pump according to the traditional active disturbance rejection control method in Step 1.3; then design the radial basis neural network structure including the number of nodes and the activation function in the input layer, hidden layer and output layer according to Step 2.1, and use the parameter update method adopting the gradient descent method in Step 2.2 to update the data center C j of the radial basis neural network, the node base width σ j and the node weight ω j , and finally update the control law parameters β1 and β2 according to the formula in Step 2.3 to complete the design of the active disturbance rejection control system for the electric fuel pump based on the radial basis neural network.

[0042] Compared with the traditional control method, the beneficial effects of the present invention are as follows:

[0043] The present invention takes the active disturbance rejection control as the core control method, combines the radial basis neural network for tuning the controller parameters, and designs a brand-new control method for the electric fuel pump. The present invention realizes the active disturbance rejection control of the electric fuel pump based on the radial basis neural network, with significantly improved control effect, and is flexible and convenient to design and apply. It makes up for the deficiencies of the traditional control method, avoids the drawbacks of the traditional control method, is easy to implement, and has practical application value. Description of the Drawings

[0044] Figure 1 is the schematic diagram of the electric fuel pump control system;

[0045] Figure 2 is the structure diagram of the radial basis neural network adopted by the electric fuel pump control system;

[0046] Figure 3 is the flow chart of the improved active disturbance rejection control for the electric fuel pump;

[0047] Figure 4 is the speed curve diagram of the electric fuel pump under different input signals;

[0048] Figure 5 is the speed curve diagram of the electric fuel pump when the load suddenly increases;

[0049] Figure 6 is the speed curve diagram of the electric fuel pump when the load suddenly decreases;

[0050] Figure 7 is the comparison diagram of the speed curves between the improved active disturbance rejection control and the traditional method under the same input conditions. Detailed Embodiment

[0051] An active disturbance rejection control method for an electric fuel pump based on a radial basis neural network is realized based on an electric fuel pump control system; the electric fuel pump control system consists of four parts: a controller, a driver, a permanent magnet synchronous motor, and a gear pump, and is a speed-current double closed-loop control system; the permanent magnet synchronous motor is coaxially connected to the gear pump, and the gear pump load is driven by the permanent magnet synchronous motor, and there is a linear relationship between the flow output by the gear pump and the speed of the gear pump; the controller consists of a nonlinear state error feedback control law, a tracking differentiator, a linear extended state observer, and a radial basis neural network. The tracking differentiator gives the differential process of the expected value, the linear extended state observer gives the estimated value of the system state based on the actual output and control input of the system, the nonlinear state error feedback control law calculates the control quantity according to the error between the expected value and the actual state and the system disturbance value, and the radial basis neural network updates the controller parameters in real time based on the difference between the system expectation and the actual value based on the gradient descent method to achieve higher performance control of the system; the driver modulates the control quantity output by the control law into three-phase voltage to drive the electric fuel pump system to operate.

[0052] A self-disturbance rejection control method for an electric fuel pump based on a radial basis neural network, and the specific steps are as follows:

[0053] Step 1: Perform simulation modeling on the above electric fuel pump system.

[0054] Step 1.1: Model the permanent magnet synchronous motor. The mathematical modeling of the permanent magnet synchronous motor is usually based on several idealized assumptions, ignoring the core saturation effect, eddy current and hysteresis losses; not considering the influence of armature reaction generated during commutation; assuming that there is no mechanical damping inside the motor; and omitting the space harmonic components existing in the stator winding gap.

[0055] The voltage equation, flux linkage equation and electromagnetic torque equation of the permanent magnet synchronous motor are as follows:

[0056]

[0057] T e = p n Ψ f [i a sin(θ r ) + i b sin(θ r -120°) + i c sin(θ r +120°)]

[0058] Where: u a , u b , u c represent the stator voltages in the three-phase abc coordinate system, R s is the stator phase resistance, i a , i b , i c represent the three-phase stator currents, Ψ a , Ψ b , Ψ c represent the three-phase flux linkages; L aa is the self-inductance of phase A winding, M ab is the mutual inductance between phase A and B windings, θ r is the rotor angle, Ψ f is the main pole magnetic flux, and so on; p n is the number of pole pairs of the permanent magnet synchronous motor.

[0059] The equations of the permanent magnet synchronous motor are reduced in order and decoupled through coordinate transformation. The permanent magnet synchronous motor model after coordinate transformation is as follows:

[0060]

[0061]

[0062] Where: u d and u q and i d and i q and L d and L q and Ψ d and Ψ q respectively represent the equivalent voltage, equivalent current, equivalent inductance and equivalent magnetic flux in the two-phase rotating d-q coordinate system; T e and T L and J, ω r and ω e respectively represent the electromagnetic torque of the motor, the applied load torque, the moment of inertia of the system, the mechanical angular velocity and the electrical angular velocity; B is the friction coefficient.

[0063] Step 1.2: Gear pump modeling. The structure of the gear pump is an external gear pump with the same size specifications for the driving and driven gears, which is a typical positive displacement pump. When the displacement displ and speed n of the gear pump are known and the flow leakage is ignored, the output flow of the gear pump Q = displ·n, and the load torque T L = displ·Δp, where Δp is the pressure difference before and after the gear pump.

[0064] Step 1.3: Use the active disturbance rejection method to design the electric fuel pump controller. The active disturbance rejection controller consists of a tracking differentiator, a state error feedback control law and a state observer. The control law adopts a non-linear form, and the state observer adopts a linear form with reference to the linear active disturbance rejection theory. Taking the second derivative of ω r gives the second-order mathematical model of the speed loop:

[0065]

[0066] Where: is the second derivative of ω r , is the first derivative of ω r , b is the control gain, and w(t) is the total disturbance of the fuel pump system. Based on this, taking ω r as the state variable x1 and taking as the state variable x2, the state space expression of the system is established:

[0067]

[0068] Among them, f(·) represents a function containing the state variables x1 and x2, and y represents the system output.

[0069] Design the differential tracker of the system as:

[0070]

[0071] Among them, v1 is the transition process arranged by the tracking differentiator according to the expectation , v2 is the derivative of the signal v1, r0 is the speed factor, h is the system sampling step, and the superscript k represents the k-th moment of the system operation.

[0072] According to the system state space expression, design a third-order linear extended state observer for the system:

[0073]

[0074] Among them, e represents the estimation error of the state x1, and z1, z2, z3 represent the estimated values of the states x1, x2, x3; β 01 , β 02 , β 03 represent the observer gain coefficients.

[0075] Perform a non-linear combination on the error link:

[0076] u0 = β1fal(e1, a1, δ) + β2fal(e2, a2, δ)

[0077] Among them, u0 represents the output control quantity of the non-linear state error feedback control law, e1 represents the difference between the expectation v1 and the estimated value z1, and e2 represents the difference between the differential signal v2 and the estimated value z2; fal(·) represents a non-linear function, a1 and a2 are constants between 0 and 1, affecting the non-linearity degree of the fal(·) function, δ represents the width of the non-linear interval; β1 and β2 represent the control law gain coefficients.

[0078] Finally, compensate for the disturbance, and take the actual control quantity u as:

[0079]

[0080] Step 2: Improve the control law of the active disturbance rejection controller based on the radial basis neural network. Specifically: use the radial basis neural network to perform real-time optimal control on the parameters β1 and β2 of the non-linear state error feedback control law in Step 1.3 to improve the tracking performance and disturbance rejection ability of the controller.

[0081] Step 2.1: Neural network structure design. The radial basis neural network structure adopted in the present invention is as Figure 2 shown. The number of neuron nodes in the input layer is set to n RBF = 6, the input vector X = [u, y, v1, v2, z1, z2] T . The Gaussian function is used as the activation function of the hidden layer. According to the empirical formula, determine the number of neuron nodes m RBF = 6, the output of the neural network is the control quantity u, and the number of neuron nodes in the output layer is 1. The Gaussian function is as follows:

[0082]

[0083] Where: C j = [c j1 , c j2 ,..., c j6 represents the data center of the hidden layer Gaussian function, and each c ji represents the data center of the j-th hidden layer neuron for the input x i . ||·|| represents the Euclidean distance between vectors, and σ j represents the base width of the hidden layer neuron nodes. The network output is a linear combination of the hidden layer outputs H = [h1, h2,..., h6] T According to the weight vector W = [ω1, ω2,..., ω6] T , the network output is calculated as follows:

[0084] y RBF = W T H = ω1h1 + ω2h2 +... + ω6h6

[0085] Step 2.2: Update the parameters of the radial basis neural network. The learning and training process uses the gradient descent method to update the network parameters. The partial derivatives of the parameters to be updated are calculated respectively to obtain the change amount at the k-th moment. Combining the learning rate η, the acceleration factor α, and the parameter values at the (k - 1)-th moment, the basis function and weight values at the next moment are calculated. The performance index function is selected as the error between the network output and the actual system output:

[0086]

[0087] Among them, k represents the k-th moment of the system operation; E(k) represents the performance index function of the neural network output y RBF (k) approaching the actual system output y(k); h j (k) represents the output of the j-th hidden layer node; Δω j (k) represents the change amount of the weight ω j (k) of the j-th hidden layer node, and Δσ j (k) represents the change amount of the base width σ j (k) of the j-th hidden layer neuron node; Δc ji (k) represents the change amount of the data center c i (k) of the j-th hidden layer node for the i-th input x ji (k), and C j (k) represents the data center vector of the j-th hidden layer node for the input X(k).

[0088] Step 2.3: Update the parameters of the control law. The real-time optimization of the parameters β1 and β2 of the nonlinear state error feedback control law is also obtained by the gradient descent method. The differentials of β1 and β2 are calculated using the chain rule. The selection of the performance index function refers to the performance parameters of the radial basis neural network:

[0089]

[0090] where: J represents the sensitivity of the output to the input, E1(k) represents the performance index function; v1(k) represents the transition signal given by the tracking differentiator; Δβ1(β) and Δβ2(k) represent the changes in the control law gains β1(β) and β2(β); β(k) represents the actual control quantity.

[0091] Step 3: Specifically, the implementation steps of the active disturbance rejection control method for the electric fuel pump based on the radial basis neural network proposed by the present invention are as follows: First, according to the content described in Steps 1.1 and 1.2, establish the mathematical models of the permanent magnet synchronous motor and the gear pump, and establish the control system model of the electric fuel pump according to the traditional active disturbance rejection control method in Step 1.3; then, according to Step 2.1, design the radial basis neural network structure including the number of nodes and activation functions of the input layer, hidden layer and output layer, and use the parameter update method of the gradient descent method in Step 2.2 to update the data center C j of the radial basis neural network, the node base width σ j and the node weight ω j , and finally update the control law parameters β1 and β2 according to the formula in Step 2.3 to complete the design of the active disturbance rejection control system for the electric fuel pump based on the radial basis neural network.

[0092] Use the S-Function to implement the code of the active disturbance rejection controller based on the radial basis neural network. The specific implementation process is as Figure 3 shown. First, define the system size in the mdlInitializeSizes function, set the structure parameters of the network input layer, hidden layer and output layer, and initialize the values of the system state variables; in the mdlUpdate function, calculate the performance indexes E(k), E1(k) and the hidden layer output vector h(k), and use the gradient descent method to update the weight vector w(k), the data center matrix C(k), the base width vector σ(k) and the control law parameters β1(k), β2(k); finally, calculate the S-Function output value in the mdlOutputs function. The simulation model output of this controller S-Function is a 1×4 vector, including the control quantity u(k), the parameter β1(k), the parameter β2(k) and the neural network identification output y RBF (k) for system performance analysis.

[0093] Step 4: Verify the control effect of the electric fuel pump control system with the help of the MATLAB / Simulink simulation platform and examine the performance indicators.

[0094] The rotational speed transitions smoothly and rapidly, with good following characteristics: Figure 4 As shown, when changing from the current target rotational speed value to another target rotational speed value, the actual rotational speed can transition smoothly and rapidly to the given rotational speed. There is almost no overshoot phenomenon during the transition process, and the transition process is flexible and rapid.

[0095] The system has strong robustness and anti-interference ability: Figure 5 and Figure 6 are the rotational speed response curves during sudden load increase and sudden load decrease respectively. When an additional load disturbance is applied, the electric fuel pump control system can respond correctly in a timely manner and finally adjust to the current specified target rotational speed, remaining stable throughout the adjustment process.

[0096] The response speed is faster and the adjustment time is reduced: Figure 7 As shown, compared with the traditional active disturbance rejection control, the improved active disturbance rejection control combined with the radial basis neural network can reach the steady state value faster under the same input conditions, and the fluctuation amplitude is smaller, within the allowable error range.

Claims

1. A self-disturbance rejection control method for an electric fuel pump based on a radial basis neural network, characterized in that, Realized based on an electric fuel pump control system; the electric fuel pump control system is a speed-current double-closed-loop control system, which consists of a controller, a driver, a permanent magnet synchronous motor, and a gear pump; the permanent magnet synchronous motor is coaxially connected to the gear pump, and the gear pump load is driven by the permanent magnet synchronous motor. There is a linear relationship between the output flow of the gear pump and the rotational speed of the gear pump; the controller consists of a non-linear state error feedback control law, a tracking differentiator, a linear extended state observer, and a radial basis neural network. The tracking differentiator gives the differential process of the expected value. The linear extended state observer gives the estimated value of the system state based on the actual output and control input of the system. The non-linear state error feedback control law calculates the control quantity according to the error between the expected value and the actual state, as well as the system disturbance value. The radial basis neural network updates the controller parameters in real time based on the difference between the system expectation and the estimated value of the system state according to the gradient descent method to achieve higher performance control of the system; the driver then modulates the control quantity output by the controller into three-phase voltage to drive the operation of the electric fuel pump system.

2. The auto-disturbance rejection control method for an electric fuel pump based on a radial basis neural network according to claim 1, wherein The specific implementation steps of the neural network active disturbance rejection control of the electric fuel pump are as follows; Step 1: Perform simulation modeling on the above electric fuel pump system; Step 2: Improve the control law of the active disturbance rejection controller based on the radial basis neural network; Step 3: Complete the design of the active disturbance rejection control system of the electric fuel pump based on the radial basis neural network by updating the control law parameters.

3. A self-disturbance rejection control method for an electric fuel pump based on a radial basis neural network according to claim 2, characterized in that The specific content of Step 1 is as follows: Step 1.1: Model the permanent magnet synchronous motor; through coordinate transformation, the equations of each group of the permanent magnet synchronous motor are decoupled and reduced in order. The permanent magnet synchronous motor model after coordinate transformation is as follows: Among them: u d 、u q 、i d 、i q 、L d 、L q 、Ψ d 、Ψ q represent the equivalent voltage, equivalent current, equivalent inductance and equivalent magnetic flux in the two-phase rotating d-q coordinate system respectively; R s represents the stator phase resistance, Ψ f is the main pole magnetic flux, p n represents the number of pole pairs; T e 、T L 、J、ω r 、ω e represent the electromagnetic torque, external load torque, system moment of inertia, mechanical angular velocity and electrical angular velocity of the motor respectively; B is the friction coefficient; Step 1.2: Modeling of the gear pump; The structure of the gear pump is an external meshing gear pump with the same size specifications for the driving and driven wheels. It is a positive displacement pump. When the displacement sispl and rotational speed n of the gear pump are known and flow leakage is ignored, the output flow Q of the gear pump = displ·n, and the load torque T of the gear pump L = displ·Δp, where Δp is the pressure difference before and after the gear pump; Step 1.3: Use the active disturbance rejection method to design the electric fuel pump controller, and take the second derivative of ω r to obtain the second-order mathematical model of the speed loop: Wherein: is the second derivative of ω r , is the first derivative of ω r , b is the control gain, and w(t) is the total disturbance of the fuel pump system; Based on this, taking ω r as the state variable x1, and taking as the state variable x2, the state - space expression of the system is established: Among them, f(·) represents a function containing state variables x1 and x2, and y represents the system output; Design the differential tracker of the system as: Among them, v1 is the transition process arranged by the tracking differentiator according to the expectation , v2 is the derivative of the signal v1, r0 is the speed factor, h is the system sampling step, and the superscript k represents the k-th moment of the system operation; According to the system state space expression, design a third-order linear extended state observer for the system: where e represents the estimation error of state x1, and z1, z2, z3 represent the estimated values of states x1, x2, x0; β 01 , β 02 , β 03 represent the observer gain coefficients; Perform non-linear combination on the error link: u0 = β1fal(e1, a1, δ) + β2fal(e2, a2, δ) Among them, u0 represents the output control quantity of the non-linear state error feedback control law, e1 represents the difference between the expected value v1 and the estimated value z1, e2 represents the difference between the differential signal v2 and the estimated value z2; fal(·) represents a non-linear function, a1 and a2 are constants between 0 and 1, which affect the non-linearity of the fal(·) function, and δ represents the width of the non-linear interval; β1 and β2 represent the control law gain coefficients; Finally, compensate for the disturbance, and take the actual control quantity u as:

4. The auto-disturbance rejection control method for an electric fuel pump based on a radial basis neural network according to claim 3, characterized in that, The specific content of Step 2 is as follows: Use the radial basis neural network to perform real-time optimization control on the parameters β1 and β2 of the non-linear state error feedback control law in Step 1.3 to improve the tracking performance and disturbance rejection ability of the controller; Step 2.1: Neural network structure design; the number of neuron nodes in the input layer is set to n RBF , the input vector Adopt the Gaussian function as the activation function of the hidden layer, and determine the number of neuron nodes m in the hidden layer according to the empirical formula RBF , the output of the neural network is the control quantity u; the Gaussian function is as follows: Wherein: represents the data center of the Gaussian function of the hidden layer, and each c ji represents the data center of the j-th hidden layer neuron for the input x i ||·|| represents the Euclidean distance between vectors, and σ j represents the base width of the hidden layer neuron node; the network output is a linear combination of the hidden layer outputs According to the weight vector The network output is calculated as follows: Step 2.2: Use the gradient descent method to update the parameters of the radial basis neural network in combination with the learning rate η, the acceleration factor α, and the parameter values at the (k - 1)th moment; Among them, k represents the k-th moment when the system runs; E(k) represents the performance index function of the neural network output y RBF (k) approximating the actual output y(k) of the system; h j (k) represents the output of the j-th hidden layer node; Δω j (k) represents the change in the weight ω j (k) of the j-th hidden layer node, Δσ j (k) represents the change in the basis width σ j (k) of the j-th hidden layer neuron node; Δc ji (k) represents the data center c i (k) of the j-th hidden layer node for the i-th input x ji (k); C j (k) represents the data center vector of the j-th hidden layer node for the input X(k); Step 2.3: Also use the gradient descent method to update the parameters β1 and β2 of the control law; Where: J represents the sensitivity of the output to the input; E1(k) represents the performance index function; v1(k) represents the transition signal given by the tracking differentiator; Δβ1(k) and Δβ2(k) represent the variations of the control law gains β1(k) and β2(k); u(k) represents the actual control quantity output by the controller.

5. A self-disturbance rejection control method for an electric fuel pump based on a radial basis neural network according to claim 4, characterized in that, The specific content of step 3 is as follows: First, according to the content described in step 1.1 and step 1.2, establish the mathematical models of the permanent magnet synchronous motor and the gear pump, and establish the control system model of the electric fuel pump according to the traditional active disturbance rejection control method in step 1.3; then design the radial basis neural network structure including the number of nodes in the input layer, hidden layer and output layer and the activation function according to step 2.1, and use the parameter update method of the gradient descent method in step 2.2 to perform the data center C of the radial basis neural network j , the node base width σ j and the node weight ω j update, and finally update the control law parameters β1 and β2 according to the formula in step 2.3 to complete the design of the active disturbance rejection control system of the electric fuel pump based on the radial basis neural network.

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